ML20093E187
| ML20093E187 | |
| Person / Time | |
|---|---|
| Issue date: | 09/30/1984 |
| From: | Ginevan M NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| To: | |
| References | |
| NUREG-1029, NUDOCS 8410120006 | |
| Download: ML20093E187 (96) | |
Text
,
NUREG-1029 A. Computer Code for General Analysis of Radon Risks
- (GARR) f e
U.S. Nuclear Regulatory Commission 4
Office of Nuclear Regulatory Research 1
' M. Ginevan p" "%,
4 c
84101%[g6840930 N
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NUREG-1029 RH A Computer Code for General Analysis of Radon Risks l
(GARR) j M:nuscript Completed: September 1984 D:ta Published: September 1984 M. Ginevan i
Division of Radiation Programs and Earth Sciences l
Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission W:shington, D.C. 20666 l
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3 l
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l
ABSTRACT Evaluating the level of lung cancer risk associated with a given level of radon-daughter exposure is a complex matter.
There is the basic question as to whether one's risk assessment should apply absolute risk models (which principally consider the amount of radon-daughter exposure) or relative risk models (which consider both the amount of radon-daughter exposure and baseline
' ung cancer risk).
Even when a general model form has been selected, there are decisions as to' the exact form of risk projection and tbs appropriate method of accounting exposure over time. Apart from these uncertainties, there is a question as to how much a personal habit such as smoking can modify risk.
j This document presents a computer model for general analysis of radon risks that allows the user to specify a large number of possible models with a small number of simple commands. The model is written in a version of BASIC which conforms closely to the American National Standards Institute (ANSI) definition
-for minimal BASIC and thus is readily modified for use on a wide variety of computers and, in particular, microcomputers.
1.
Model capabilities include generation of single year life tables from 5-year abridged data, calculation of multiple-decrement life tablas for lung cancer for the general population, smokers, and nonsmokers, and a cohort lung cancer risk calculation that allows specification of level and duration of radon exposure, the form of the risk model, and the specific population assumed at risk.
Figure A, which shows the' process of specifying and executfr.g the cohort lung cancer risk calculation, illustrates some of these capabilities.
iii
FIGURE A REPRESENTATIVE GARR MODELING SESSION INPUT: KEYBD.(K) OR FILE FILE NAME FOR INPUT?) WM (F)?) K LCMD EE AT FIRST RISK?) 30 PURGE INPUT FILE?) N EE AT FIRST EXPOSURE?)
WORKING 29 POP. 1 =WMLCMD M E AT LAST EXPOSUPE?) 6 0
BASELINE RISK /WLM-R.R.?>.01 L.E.=50.167 R.R. OPTION (M,E,0R B)?)
DEATHS /10^5 -LC= 4835.7 B
RISK /WLM/PY-A.R.?> IE-5 LATENCY IN YEARS?) 9 RELRISK MODEL-M ANNUAL EXPOSURE IN WLM?)
L.E.=50.827 1
LOSSLE.(MONS)= 1.67 EXPONEHTIAL CORRECTIDH?)
D/10^5= 5906.0 Y
EXCESS D/10^5= 1199.2 EXPONENT =?).014 EE SPECIFIC SENSITIVIT!
ES?) N RELRISK MODEL-E L.E.=50.811 LOSS LE(MONS)= 1.87 D/10^5= 661a.4 EXCESS D/10^5= 1244.9 RADON RISK MODEL R.R. COEF=1. NE-902/WLM ABSRISK MODEL OPTION =8 L.E.=50.953 A.R.=1.00E-#5/PY/WLM LOSS LE(MONS)= 1.37 KE AT F.E.= 20 D/10^5= 5455.4 KE AT L.E.= 68 EXCESS D/10^5= 645.1 AGE AT FIRST RISK = 30 WLM PER YR.=le. NE-901 LATENCY = 9 RUN ANOTHER POPULATIOH?
EXPONENT COR=-1.40E-M2 N
SENSITIVITY =1 HEW INITIAL CONDITIONS?)
- "*"*"H**""
N EXECUTION ENDS iv
1 TABLEOFCONThNTS Bat 1.
INTRODUCTION............................
1 4
4 2.
ISSUES IN RADON RISK ASSESSMENT..................
2
+
3.
GARR ALG0RITHMS..........................
4
- 3.1 Brief Review of Cohort Risk Analysis.............
4 3.2 Specifying Population at Risk 9
3.3 Generating Single-Year Life Table:
The GRADUATE Program...
10 3.4 Considering Multiple Causes of Death:
The MULDEC Program...
17 3.5 Addressing Influence of Smoking:
The SM0KER Program.....
19 3.6 Calculating Lung Cancer Risk from Radon-Daughter Exposure:.The RADRISK Program...............
24 4.
RUNNING GARR ON THE HP-75.....................
27 4.1 HP-75 System.........................
27 4.2' Preparing Input File for GRADUATE and MULDEC.........
27 4.3 Running GRADUATE. Program...................
29 4.4 Running HULDEC Program....................
32 4.5 Running SM0KER Program....................
37 42
~4.6 : Running RADRISK Program 1
4.6.1 Input from Keyboard..................
43 4.6.2 Designation of Population at Risk and 47
. Interpretation of Output 50 4.6.3 Input Via File 4.6.4 Error Handling and Loading Input Files from Cassette..
51 51 4.6.5 Additional Output Features 53 4.6.6 Conclusion......................
l 4.7 ' LIST Utility.........................
53 57
- 4. 8 DUPER Utility 58 4.9 GARR Tape 4.10 Conclusion...........................
60 REFERENCES...............................
61 4
Appendix A:
PROGRAM LISTINGS AND VARIABLE LISTS............
65 L
}
1
.V i.
LIST OF TABLES 4
Tabir Title Page 1
Mortality Data from United States 1969 Population 11
^
^
2 Proportional Bias, (q q)/q, in q = 1 - [5 xP * ] f r Various Parametric Values of q and I................
13 3
ProportionalBias,(q-h)/qinkforVariousParametric Values of q and I......................
14 Absolute Bias ($
I) in $ for Various Values of q and I...
4 15 5
Comparison of Age-Specific Survival Probabilities Given in NCHS Life Table to Those Calculated from GRA0!! ATE Life Table Produced by GARE 18 6
Nonsmoker Lung Cancer Death Rates in Deaths /100,000 Person-Year........................
20 7
Sensitivity Analysis: Males.................
25 l
i l
l vi
LIST OF FIGURES Figure Title Page A
Representative GARR Modeling Session.............
iv i
1 Sample Input Data File for GRADUATE and MULDEC........
28 2
Sampie Output for GRADUATE..................
31 3
Sample Output from MULDEC, Including Partial Listing of Life Table (Ages 0 - 43) 35 4
Copy of NONSLC File Listing and Representative Output from SM0KER Program.................
38 5
Representative Output from RADRISK Progrem:
A.
Error Messages B.
Sensitivity File C.
Program Output, Including Model Paran,aterization D.
Input File for File Option................
45 6
Three Alternative Parameterizations of RADRISK Model 52 7A Representative Output from LIST Utility for a GR File (Ages 0 - 45).....................
55 78 Representative Outpuc from LIST Utility for a MULDEC File (Ages 0 - 45)..................
56 8
Output Listing Files on Standard GARR Tape 59 vil
-. a.
ACKNOWLEDGMENTS I would like to thank William A. Mills for making me aware of the problems that this program package addresses and for his support during its development.
My appreciation also goes to Jerome S. Puskin and Harold T. Peterson, Jr., for j
their review and discussions of this document throughout its development.
Finally, thanks to Alice S. Whittemore and Naomi H. Harley, whose careful critiques greatly improved the clarity of my presentation.
f 1
1 I
viii
1.
INTRODUCTION Radon gas presents a threat to public health because its short-lived " daughters" are potent lung carcinogens (Lundin,1971). Activities in which concern for radon-related lung cancer risk arises include uranium mining, uranium mill tailings disposal, and the " tightening" of homes as a part of energy conserva-tion efforts (USRPC; ICRP; Colls).
There is obvious diversity in both the conditions of exposure and the popula-tions at risk in different activities and, as noted below, an even broader diversity in expert opinion as to the type of risk model and modifying factors that are appropriate in a given radon risk assessment.
Because of this spectrum of exposure conditions and expert opinion, the computer code presented here was developed to provide the user with the means to con-struct General Analyses of Radon Risk (thus its name:
GARR), rather than to solve a particular risk model.
Its basic structure derives from the cohort life table that has been useful in more general considerations of radiation health effects (Cook; Bunger).
However, it differs from earlier approaches in several ways.
First, it provides great flexibility in specifying the population at risk and, in particular, the smoking status of that population.
Second, it allows one to specify such features of the model as age at first risk (most authors suggest that the risk of radon-induced lung cancer is effectively zero before a certain age), latency between exposure and response, the age-specific sensitivity to radon exposure, and the " discount rate" for past radon exposure (Harley,1981).
Third, it allows one to select either an absolute risk model (wherein lung cancer risk depends only on dose and is independent of the baseline lung cancer rate) or a relative risk model (wherein cancer risk is proportional to the baseline rate) and to specify the risk coefficient for the model selected.
Finally, it allows specification of the relevant exposure parameters, age at first exposure, age at last exposure, and exposure level.
This level of flexibility requires only a moderate amount of user input, but it is my belief that most models currently proposed for estimation of radon-related lung cancer risk can be implemented.
t 1
'P The GARR code differs from previous radiation risk assessment codes in another important way.
It was developed on and is designed for execution by a rela-tively small microcomputer.
Its present implementation is restricted to the Hewlett Packard model 75C portable computer.
However, the language is a fairly standard version of BASIC, and the program listings given in Appendix A should be readily translated for use on other small computers or, for that matter, any computer-that has a BASIC interpreter.
2.
ISSUES IN RADON RISK ASSESSMENT There is one point of unanimity in expert opinion regarding radon daughters:
Radon daughters under some conditions pose a significant hazard to human
}
health and the principal risk associated with this hazard-is the development of radiogenic lung cancer.
Beyond this, there is considerable divergence in opinion on almost every point of the particulars of calculating radon risk.
[ Note: The following discussion assumes a familiarity with basic units of i
radon-daughter measurement.
For amplification and clarification, see Evans.]
i One of the most basic dichotomies is the question of the form of the risk model. The first comprehensive study of lung cancer in American uranium miners (Lundin, 1971) suggests that there is greater than additive interaction between smoking and radon in inducing lung cancer.
However, the same authors l
(Lundin, 1979) later concluded that the principal differences between smokers and nonsmokers was in the time between exposure to radon and development of a lung tumor (latency) and that smoking and radon exposure were nearly additive j
in their effect on lung cancer risk.
This view is supported by Radford who based his conclusion on a study of Swedish miners. More recent evaluations I
using proportional hazards models (Hornung; Whittemore) return to the original view that smoking and radon act multiplicative1y, while Harley and Pasternack (1981) introduce a repair term in their model on the assumption that the effec-tiveness of a given exposure declines exponentially with time (i.e., there is repair of radiation damage).
2
. _ - - _ _ ~
Aside from these considerations, Cohen suggests that, since not all histologic types of lung cancer may be induced by exposure to radon daughters, one must be careful in specifying " baseline" lung-cancer rates for relative risk models.
(There is some evidence that this is true for adenocarcinomas (Kunz), but most histologic types seem to be elevated in radon-exposed populations (Archer; l
Kunz).)
Given that one can pick a risk model, the questior. arises as to which popula-
)
tion to use to determine the risk coefficient. Two populations, the United t.
States uranium miners (Lundin, 1971; 1979) and the Czech uranium miners (Kunz),
I form the principal basis for such exercises, but others such as the Swedish
[
iron miners (Radford; Axelson) or the Canadian fluorospar miners (Wright; i
Morrison) have also been used to generate risk estimates. The National Academy of Sciences has reviewed these and other studies and concluded that absolute i
risk coefficients in the range of 6 to 47 lung cancers per 1,000,000 person-years per working level month (WLM) express the range of risk estimates that i
can be developed from miner studies.
A similcr range for relative risk
~
coefficients is not given explicitly but values in the range of 0.3 to 4 percent per WLM increase in baseline lung cancer rate approximate the spread of i
estimates derivable from miner populations.
i l
The question of deriving estimates of risk for nonniner populations is compli-cated by the fact that miners represent an atypical-group and exposure situa-l tion. As noted earlier, most miner populations have a rather high percentage l
of smokers, and it is quite possible that smoking and radon daughters interact multiplicative1y in the induction of lung cancer.
Another problem concerns the high prevalence of other forms of respiratory disease in miner populations i
(the American Miners' nonmalignant respiratory' disease is the second largest j
excess cause of death after lung cancer (Waxweiler)). This is a problem because we do not know the extent to which exposure to the agents, other than radon, responsible for these diseases (primarily rock dust) modifies lung cancer risk.~ Miners are also performing heavy manual labor, which modifies their t
f breathing rate, and this may modify the actual dose to the lung for some given l
number of WLMs of exposure (Harley, 1982).
i i
I 3
i I
The.last issue has a parallel in considering extrapolation to the general public because children have higher breathing rates than adults as well as anatomical differences, and there may also be some differences between men and These factors may modify delivered dose for a given WLM exposure women.
(Harley, 1982; Hofmann).
(Children may also be more sensitive to a given delivered dose, but there is no empirical evidence for or against this idea.)
j Finally, there is an issue of conditions of exposure in that mine environments
{
are rather dusty. This means that a high percentage of radon daughters are
" attached" to particles (Evans).
It may be that this attached fraction is much lower in some nonmine environments, and at least one author (Wise) has suggested that a large unattached fraction can dramatically increase the delivered dose per WLM.
P This completes a synopsis of some of the major issues in radon risk assessment.
[
Its purpose is to inform the reader of potential pitfalls rather than to suggest a particular risk modeling approach. Those looking for a more compre-hensive review of issues, facts, and opinions should consult the following references:
NAS; UNSCEAR; Peterson; and Thomas.
i 3.
GARR ALGORITHMS 1-3.1 Brief Review of Cohort Risk Analysis l
A cohort analysis asks the question: What would be the mortality experience of a group of people of the same age who have the same baseline mortality experience if they are uniformly exposed to some toxic agent that adds a j
certain amount of excess mortality to their baseline mortality? In this sort 1
of analysis, two basic measures of effect can be calculated.
The first, pre-l mature deaths, is the number of persons (usually per 100,000) who die earlier than they would have because of the toxic agent. The second, loss of life expectancy, is a measure of how premature the premature deaths really are.
It i
is frequently expressed in one of two ways:
(1) loss of life expectancy par exposed individual and (2) loss of life expectancy per premature death.
i 4
I n x, the baseline The basic quantity of interest in any cohort analysis is 9
probability of dying in an interval of n years beginning at some exact age x.
For our calculations, n is always one. Thus we will refer simply to q which x
is the probability that a person exactly x years old will die in the next year.
Its converse, p = 1 q, is the probability of surviving from age x x
x to age x + 1.
A final quantity, S, given by x
x-1 p;
[x = 1, 2, 3,..., 100),
(1)
S
=
11 g
x i=0 (H is the notation for the product p, x pl... p _1.)
x I
i is the probability that a newborn is alive at age x.
S is taken as 1.
o Note also that the conditional probability of survival to age x + m, given that one is alive at age x, can be expressed as the ratio Sxm/S
- x Our models of radon risk are simplified because only one source of excess mortality, lung cancer, is of interest.
Here, in an absolute risk model, the excess probability of death in age interval x to x + 1, qex, is given by 9
= Cd (2) ex x,
where C is a constant with units of lung cancer cases per person per year per unit dose and d is the effective exposure acting at age x (the concept of x
effective exposure is discussed in detail below).
In a relative risk model, the risk coefficient, A, has units of proportional increase per unit exposure, and q is a function of qcx, the baseline risk.
ex This model can take one of two forms.
In the first 9
= Ad q (3) ex x cx.
5
f This is here termed our multiplicative relative risk model because excess risk is a simple product of risk coefficient, exposure, and baseline risk. A second possible formulation is 9
=_[(1 + A)
- 1]q (4) ex cx
- This is termed our exponential relative risk model because here risk increases exponentially with dose.
It is equivalent to the form of relative risk assumed in the class of statistical models termed proportional hazard models (Cox).
If A is small (less than 0.02) and exposure is fairly low (d is less than 20), Equa-tions 3 and 4 will give nearly equivalent results.
However, one should always be cautious in specifying exactly which model form one is talking about because the same inputs can give quite divergent results.
When an additional source of mortality q, is acting, we first calculate modified survival probabilities S' for ages beyond r, the age at first risk.
i Sj=S II (P ~9ex) -
(5) r x
x=r+1 In the calculation of the probability of premature lung cancer death, R,, one has 100 1
R, = y- [S i r er t9et].
(6)
I S
f t=r+1 r
i In this expression, f is the age at first exposure and r is the age at first l_
. risk.
(Note that, because we are working in discrete time, we adopt the conven-tion that dose received at age f cannot be expressed until age f + 1.
Thus it I
is always true that r > f.)
I i
l The reciprocal of S converts the other survival probabilities into survival f
probabilities conditional on being alive at age f.
Thus Equation 6 is simply I-the~ sum of the probabilities of surviving to all ages beyond exposure and dying of a premature lung cancer at those ages, which is the total probability of premature lung cancer death.
This is easily converted to expected deaths per, say, 100,000 exposed by multiplication (i.e., R x 100,000).
q 6
t Life expectancy, Ebf, for a person at age f (here equivalent to age at first exposure) is calculated as follows:
99 9
9f 1
x E
I 8 (1 + y )].
(7)
J, -
bf
- T + ET x
f x=f+1 Equation 7 assumes that survival to a particular age contributes 1 year to life expectancy, S /8, while death during a particular year of life contributes x f 1 half-year to life expectancy ([S /S ][q /2]).
(The observant reader may have x f x
noticed that our calculations to this point are truncated at age 100.
Correc-tions for this are introduced below.)
l The new life expectancy, E,f, is then I
r q'"
h[x=I S(1+[q E,f=[q
)+S (8)
+
x r2 f
f+1 t+9 S{(1+
et)3,
+
t=r+1 Equation 8, which takes into account the new source of mortality, is a simple modification of Equation 7.
(Note Equation 5.)
l Loss in life expectancy, E, is simply:
Et=Ebf - E,f.
L One peculiarity of human mortality. is that, during the first year of life (starting at age 0), most of the deaths take place early on.
Therefore, the contribution of deaths in this interval to total life expectancy is less than the 0.5 year assumed elsewhere. We use 0.1 year (i.e., q,/10) for calculations starting at age 0.
It is also true that persons dying in an age interval may
(
live, on average, more or less than 0.5 year in the interval depending on the I
age interval and population considered, but for our purposes 0.5 is a more j
than adequate approximation.
I i
l 7
f Finally, a correction is made to both life axpectancy and risk of death calcu-lations because it is assumed that no one lives beyond age 100.
The expected number of years, G, to be lived by a person reaching age 100 is taken as G = 0.8/qgg,
where q99 is the probability of dying during the 99th year.
This is used to modify life expectancy as follows:
E, = E + (5100 )
(')
0 where E is the life expectancy before modification, E,is modified life expec-tancy, and S is the probability of surviving to age 100 in our model popula-100 tion (i.e., conditional on being alive at age of first exposure and with excess lung cancer mortality in effect).
The quantity G is also used to find g 100 e
for use in the excess risk calculation.
In the absolute risk model g 100 = Cdggg (10)
G e
where d is the effective exposure acting at age 99 + G vears and g 100 is gg e
the excess lung cancer death probability experienced by those over 100 years old.
The relative risk form of this correction is given by either 9e100 = Ad q
gg,g c100'
( )
or g 100 = [(1 + A'dggg - 1]q 100' e
c where q 100 is the baseline probability of dying of lung cancer beyond one's c
100th birthday.
8
A The probability of premature lung cancer death is modified as follows:
9 (12)
R,, = R, + S100 e100 The not effect of each of these corrections is quite small, so much so that good results can be obtained by truncating at age 99. The reason for their inclusion here is that they, at least in theory, improve our approximation to a cohort followed to extinction and do not greatly increase computational complexity.
This completes the calculations for the basic cohort risk calculation as used in GARR. Those wishing additional reading on cohort life tables can consult Elandt-Johnson; Keyfitz; or Bunger.
I 3.2 Specifying Population at Risk In our model, the actuarial characteristics of the population at risk are specified by the age-specific probabilities of dying of lung cancer and the
-age-specific probabilities of dying of all other causes for the ages 0 to 100+.
These quantities can be obtained directly from sources such as the United States Decennial Life Tables (NCHS,1975).
If this option is selected, one simply looks up the q values for x = 0 - 99 and sets q100 equal to one. Age-x specific probabilities of lung cancer death can be obtained by the formula (13) q
- 9 ("cx!"tx) cx x
where s and a are the number of deaths from lung cancer and all causes cx tx occurring in persons of age x.
The background mortality probability qbx is i
obtained by subtraction.
That is 9bx *9
~9 (14) x cx This calculation is very simple but, for 1 year intervals, requires rather detailed input data that are of somewhat limited availability (e.g., the last U.S. decennial life table available is for the years 1969-1971) and that are 9
,. _.. _ ~ _
. ~.. _ _, -. - - -,., - -, - _ _.. -. - - - -.
m--_,_-..,
rather laborious to input.
The GARR code simplifies matters by providing two programs, GRADUATE and MULDEC, which generate q and q for single years using c
b input data from NCHS 5 year abridged mortality data (e.g., NCHS, 1974).
3.3 Generatina Single-Year Life Table: The GRADUATE Program An excerpt from an NCHS abridged life table is shown in Table 1.
It provides 9 values for intervals 0-1,1-5, and 5 year intervals 5-10,..., 80-85.
The nx problem is to use these data to find q values for x = 0 - 99.
For age 0 this x
is given.
For ages 1 to 4 one can simply take q
- 1 ~ 4p (15) x where 4py = 1 4q1 Similarly for ages 5 to 9 and 10 to 14 q +m
- 1 ~ S xP*
(16) x where m = 0 - 4, x = 5 or 10.
Beyond age 15 the annual probability of death changes with age.
Thus to esti-mate q, for higher ages, one must make some assumptions about how mortality behaves in the population under consideration.
A variety of approaches are l
discussed by Keyfitz in Chapter 10; the one used in our program contains elements of several of these together with some unique aspects dictated by the l
necessity of being able to solve the problem fairly quickly on a small micro-computer.
The assumption made in our approach is that the annual q values tend to x
increase by a constant percentage from year to year, which is a good approxi-j mation to reality for many populations.
That is 9 +1
- 9 l (17) x x
i 10
TABLE 1 MORTALITY DATA FROM UNITED STATES 1969 POPULATION (NCHS, 1974)
-AGE PROBABILITY TOTAL LUNG CANCER INTERVAL OF DEATH (n x)
DEATHS DEATHS 9
WHITE MALES 0-1 0.0213 32158 0
1-5 0.0033 5033 0
5-10 0.0024 4273 3
10-15 0.0024 4299 5
15-20 0.0077 12552 5
20-25 0.0101 13497 13 25-30 0.0086 9914 19 30-35 1.0092 8993 92 35-40 0.0132 12782 359 40-45 0.0210 22373 1133 45-50 0.0337 36257 2224 50-55 0.0540 53156 3938 55-60 0.0851 76206 6185 60-65 0.1294 97922 8045 65-70 0.1828 112983 8301 70-75 0.2655 124755 7147 75-80 0.3524 125861 4818 80-85 0.4630 102653 2156 85-90
- 1 60602 696 90-95 23182 147 95-100 5197 18
-100+
633 2
WHITE FEMALES 0-1 0.0161 22950 0
1-5 0.0028 4078 4
5-10 0.0016 2829 1
j' 10-15 0.0015 2519 2
15-20 0.0029 4615 4
i 20-25 0.0033 4690 13 i
25-30 0.0035 4177 16 L
30-35 0.0049 4932 49 35-40 0.0076 7591 162 4
40-45 0.0120 12189 426 45-50 0.0181 20543 819 50-55 0.0272 28210 1165 55-60 0.0402 38264 1511 60-65 0.0598 49602 1447 65-70 0.0940 66888 1393 70-75 0.1522 90550 1263 75-80 0.2352 113486 969 00-85 0.3671 116612 644 t
85-90
- 1 87714 303 90-95 41662 94 95-100 11393 14
- ~
100+
1569 2
- 85+
11
where I is a constant greater than 1 and generally in the range of 1.04 to 1.09.
This is approximately equivalent to assuming a Gomportz survival function (Elandt-Johnson).
From this point, numerical arguments are used to derive estimates frq and I, assuming this process fits the data.
x A preliminary estimator for q +2 (the annual death probability at the midpoint x
of the interval defined by 5 x) is taken as 9
e +2 " 1 ~ S xP*
(18) x i
where S x
- 1 ~ 5 x' P
9
^
A computer program was devised to examine the behavior of q +2 for various x
parametric values of q +2 and I.
The results of this computation are presented x
in Table 2.
^
Clearly, q +2 is consistently biased (that is, it overestimates q +2), and the x
x the magnitude of the bias depends almost entirely on I.
This observation sug-gests that the estimate of q +2 might be substantially improved by adding a x
correction based on I.
The term chosen, B, which is derived from fitting a quadratic in I to the data in the second row of Table 2, is given by B = -0.778 + 1.5711 - 0.793I2 (19)
ThisBisthenusedtoconstructanewestimatorofq,hwhichisgivenby h+2*A+2(1+B).
(20) x x
The result of applying this correction to Table 2 is shown in Table 3.
The cor-rection is very successful in that 4 +2 and our parametric q +2 agree almost x
x exactly.
The foregoing assumes that I is known, but in practica it does not matter that it is not.
An excellent estimate is given by l
i=[4/4_5]O.2 (21) x x 12
TABLE 2 PROP 0RTIONAL BIAS, (q - 4)/q, in 4 = 1 - [5 xP'3 FOR VARIOUS PARANETRIC VALUES OF q AND I PARAMETRIC I 1.03 1.06 1.09 1.12 PARAMETRIC q 0.10
-0.00097
-0.00376
-0.00821
-0.01415 0.01
-0.00088
-0.00342
-0.00746
-0.01286 0.001
-0.00087
-0.00339
-0.00739
-0.01274 13
i l
TA8tE 3 PROP 0RTIONAL BIAS, (q q)/q, in q FOR VARIOUS PARAMETRIC VALUES OF q AND I i
PARAMETRIC I 1.03 1.06 1.09 1.12 PARAMETRIC q 0.10
-0.00010
-0.00032
-0.00078
-0.0013 0.01
-0.00001
-0.00002
-0.00003
-0.0000 0.001
-0.00000
-0.00005
-0.00004
-0.00012
^
4=5p.2 and 4 = 4(1 + c) where c is a quadratic correction of the 0
Note:
2 form c = -0.778 + 1.5711 - 0.7931,
14
Table 4 gives absolute bias in 5, (5 - I) for various paranietric values of q and I.
This bias is negligible.
Application of these formulae to generating a single year life table for ages above 15 is as follows:
For each 9
5x (22) q +2 = 1 S x P
x 5 is then calculated (for the interval x - 3 to x + 2) as in Equation 20.
x Thenh+2 is calculated using x
A A
I = (I + I +5) 2 (23) x x
and Equations 18 and 19.
Intermediate values of k are calculated using x
^
^
iI 9 +2+1
- 9 +2 x+5 (24) x x
for i = 1 - 4.
The final problem is extrapolating from h to h g (q(100) = 1).
82 g
Here I is taken as A
A A
I = (I80 + I75 + I70)/3 (25) and k +i
- 82*I 82 15
TABLE 4 ABSOLUTE BIAS (I - I) IN I FOR VARIOUS VALUES OF q ANO I (All Entries Should Be Multiplied by 10~4 )
PARAMETRIC I 1.03 1.06 1.09 1.12 PARAMETRIC q 0.10 0.0403 0.3932 1.6371 4.8684 0.06 0.0218 0.2078 0.8404 2.4040 0.03 0.0101 0.0950 0.3768 1.0524 0.01 0.0032 0.0299 0.1172 0.3228 i
i I
l l
l 16 l
Table 5 presents life expectancies calculated from Equation 7 with the modifications given in the text, and the survival function calculated as in Equation 1, both using q values derived from our procedure.
Comparing these x
(labeled GARR) with the values taken directly from the relevant NCHS life tables suggests that the GRADUATE program does a good job of producing single-year life tables that accurately represent the mortality experience of the population at risk.
3.4 Considering Multiple Causes of Death:
The MULDEC Program Table 1 also contains sex-and age-specific values for total mortality and for mortality from cancers of the trachea, bronchus, and lung.
These, together with the g values from GRADUATE, allow calculation of qcx, the annual proba-x bility of lung cancer death, for ages 0 through 100.
Because there are so few lung cancer deaths prior to age 20, we will begin our consideration at age 20 and assume earlier q values are zero. However, cx it should be noted that the MULDEC program is capable of generating q and bx q
values starting at age 0 and for an arbitrary number of excess causes cx of death (see page 70, Appendix A). One can obtain the probability of dying of lung cancer in the 5 year period beginning at age x, given that one has C
died' S x, as C
(27)
S x " 5"cx# "tx 5
where a and a are defined as in Equation 13. One could simply apply this c
t values.
to all q, values in the interval (as in Equation 13) to obtain gcx However, this has the rather unrealistic feature of applying a step function with 5 year intervals to our laboriously calculated single year q schedule.
x Therefore we consider C to represent the value of C at the middle year of Sx the interval (i.e., Ce2) and obtain intermediate values by linear interpola-tion. That is, i-
{
17
TABLE 5 COMPARIS0N OF AGE-SPECIFIC SURVIVAL PROBABILITIES GIVEN IN NCHS LIFE TABLE TO THOSE CALCULATED FROM GRADUATE LIFE TABLE PRODUCED BY GARR POPULATIONS WF WM NM (75.1T[75.23)
(67.75T6'7.82)
(60.47/60.52)
AGE NCHS GARR NCHS GARR NCHS GARR 15 0.9781 0.9781 0.9708 0.9708 0.9527 0.9527 20 0.9753 0.9754 0.9634 0.9641 0.9415 0.9423 25 0.9721 0.9723 0.9537 0.9549 0.9231 0.9250 30 0.9686 0.9687 0.9455 0.9465 0.9023 0.9039 35 0.9638 0.9639 0.9368 0.9375 0.8761 0.8775 40 0.9565 0.9566 0.9245 0.9249 0.8421 0.8434 45 0.9451 0.9452 0.9050 0.9054 0.7977 0.7992 50 0.9279 0.9281 0.8745 0.8749 0.7429 0.7438 55 0.9027 0.9029 0.8273 0.8277 0.6718 0.6728 60 0.8664 0.8665 0.7569 0.7575 0.5840 0.5850 65 0.8146 0.8143 0.6589 0.6604 0.4813 0.4816 70 0.7381 0.7373 0.5385 0.5391 0.3631 0.3627 75 0.6257 0.6255 0.3956 0.3972 0.2362 0.2420 80 0.4786 0.4777 0.2562 0.2572 0.1575 0.1600 85 0.3029 0.3024 0.1375 0.1378 0.0997 0.1010 Note: White Females (WF), White Males (WM), and Nonwhite Males (NM) are shown.
Numbers in parentheses are life expectancy at age 0.
18
C +2+1 = M S - 1)C +2 + iC,7V5 (28) x x
x The values for q and qbx are thus cx A
=qC (29) cx xx 1
and abx " 4 (1 - C ).
(30) x x
This process of separating the q values into their cause-specific components x
is called constructing a multiple-decrement life table (Chiang).
The reader should note that all these calculations make the assumption that causes of death are mutually exclusive (i.e., one can die of one and'on'ly one cause) and independent (i.e., deaths from one cause at one age do not modify the expected number of deaths from another cause at a later age).
l 3.5 Addressing Influence of Smoking: The SMOKER Program The procedures described to this point will create values for background proba-bilities of death (qbx) and probability of lung cancer death (qcx) f r ages 0 through 100+, given abridged mortality data of tt}e form shown in Table 1.
Should one have such data for a pure population of smokers or nonsmokers one could generate a population at risk in a straightforward manner using GRADUATE and MULDEC.
In practice, such data are unavailable and one must resort to a modeling approach.
l Certain information about the mortality experience of smokers versus nonsmokers l
is readily obtainable.
From the 1979 Surgeon General's Report on smoking (U.S.
I Public Health Service), we can obtain information as to the proportion of the population who are smokers and the general mortality experience of smokers versus nonsmokers.
Likewise, information about the lung cancer rates experienced l
by nonsmokers is available.
Table 6 presents nonsmoker lung cancer rates for males and females derived from the American Cancer Society study of cancer in i
19 l
TABLE 6 NONSMOKER LUNG CANCER DEATH RATES IN DEATHS /100,000 PERSON-YEAR (Garfinkel)
AGE MALE FEMALE 45-49 4.55 3.60 50-54 7.63 5.30 55-59 10.13 7.07 60-64 17.26 13.60 65-69 27.43 16.17 70-74 25.97 20.83 75-79 44.27 34.70 80-84 68.87 45.80 85-89 94.80 52.47 20
nonsmokers (Garfinkel).
This kind of information is used by a GARR program called SM0KER to create hypothetical populations of smokers and nonsmokers.
The first problem is to separate the general population q values into age-x specific total mortality probabilities for smokers, qsx, and nonsmokers, gnx' To do this, SM0KER requires a general population life table like that generated by MULDEC, an estimate of the proportion of smokers in the population at age 35, 035, and a value for the all-cause standardized mortality ratio, M, (Fleiss) in smokers as compared to nonsmokers. We assume that the age-specific mortality ratio, M, which equals qsx/9nx, starts at 1 at age 34 and increases linearly to x
M at ages 45 and beyond.
By our definition, 9
- 9 N
(31) sx nx x Then at age x 4 = (1 - O )4
+0N9 (32) x x nx x x nx and rearranging q
- 4 /[(1 - O ) + (0 N )]
(33) nx x
x xx and 4
- N9 (34) sx x nx This approach can be applied iteratively for subsequent ages because we have assumed M known for all x (for x less than 35 M = 1 and q
- 9
- 9 ) and, x
x sx nx x
assuming differential mortality is the only thing affecting the age-specific proportion of smokers in the population, (35)
O,7=0px sx!E0 9
+ (1 - 0)pnx]
x4 x sx 21
s (Here the p's are defined as in Equation 1.)
1 Age-specific lung cancer death probabilities for nonsmokers, qncx, are derived from the nonsmoker lung cancer death rates, S x, shown in Table 6.
We take r
1 qnex+2
- 5"x/100000.
(36)
These midpoint values are then used to generate I values as in Equation 21.
x And interpolation is performed as in Equations 24 through 26.
Ages 45 and 46 are handled as follows:
Snc47-1
- Snc47 SO (37)
/I where i = 1; 2.
The reader may note that rates are not precisely equivalent to probabilities, but in this case the difference is very small (less than 4
2 percent).
For ages less than 45, q
- 4 unless q is greater than q If this ncx cx cx nc45 holds, q is set equal to g At older ages (90+), a check is also made nex nc45 to determine whether q is greater than q If this is true, q is set ncx gx.
nex equal.to q (This makes the assumption that nonsmokers cannot have higher cx.
lung cancer probabilities than the general population.)
The nonsmoker lung cancer death probabilities can also be modified by a user-supplied multiplier U that reflects the extent to which the calculated lung cancer death probabilities overestimate or underestimate risk in the nonsmoker population of interest. The new values are given by qkx
- 9 U.
(38) ncx Age-specific nonsmoker probabilities, g bx, for background mortality are then n
determined by subtraction. That-is
~9 I )
g bx
- 9nx nex n
for all x.
22
At this point the only remaining quantities of interest are the age-specific probabilities of lung cancer death for smokers, q These are developed as sex.
follows.
From values already calculated we can determine asx, the age-specific proportion of deaths who were smokers, (40)
= 0 (q,x/q )
a sx x
x We can also find ancx, the proportion of deaths who were nonsmoking lung cancer:
(41)
- nex = (1 - asx)(9ncx!9nx)
Now we find ascx, the proportion of. deaths who were smoking lung cancer:
i a
- (9 9)-a (42) scx cx x ncx Finally q is calculated as:
sex 9
- 9sx(ascx/asx) sex At the option of the user, an arbitrary minimum risk of lung cancer, R, in smokers relative to nonsmokers for ages 45 and above may be declared.
In this j
case if q
< Rq then q
= Rq scx ncx scx nex l
The last, trivial calculation is determining q bx by subtraction in the same s
way as Equation 39, which completes both life tables.
At this point the reader may be concerned by some of the assumptions made in our development'of smoker and nonsmoker populations.
For example, the relative proportion of smokers versus nonsmokers at various ages is determined by much more than differential mortality (i.e., historical smoking " cohort" effects),
(
'and the all-cause standard mortality ratio for smokers is not constant across 23
ages.
Nonetheless, any model is, to some extent, arbitrary (else it would be unwieldy), and the procedures outlined here generate reasonable actuarial prpulations for smokers and nonsmokers in that differences in life expectancy and lung cancer risk between smokers and nonsmokers agree with those reported in the Surgeon General's Report (U.S. Public Health Service) (see Table 7).
Further, if one is dissatisfied with these assumptiors, they are easily modified by using the same approach but providing parametric 6 and M values explicitly x
x for each x, or by performing a sensitivity analysis using the options for specify-ing 8 (Equation 32), M (Equation 34), and U (Equation 38).
An example of such an exercise is shown in Table 7.
This illustrates the relative insensitivity of tha actuarial characteristics of the smoker population generated to the choice of U and 035' Likewise, it is true that our procedure could yield q values greater than 1.
sx However, in practice this does not happen, and the program provides adequate diagnostic information to assure the user that it has generated reasonable results.
3.6 Calculating Lung Cancer Risk from Radon-Daughter Exposure: The RADRISK Program The calculation of radon-daughter-induced lung cancer risk is performed by the RADRISK progra.n.
The basic functioning of this program is as described in the review of cohort risk analysis presented earlier.
Required inputs include sets of qbx and q values defining the population at risk; C and A coefficients cx fcr the absolute and relative risk models, respectively; f, the age at first cxposure; g, the age at last exposure; L, the latency or time between exposure cnd onset of risk; h, the age at first risk (a number of models assume risk is z2ro before some age regardless of age at exposure or latency); and w, the continuous exposure to radon daughters in working levels. One may also elect to assume that sensitivity, Z, varies across ages and that the effect of dose delivered decays exponentially with time by specifying a decay rate constant, r.
At first glance, this large number of possible inputs would seem to make for a very complicated model; but, in fact, all these complications can be incorporated 24
TABLE 7 SENSITIVITY ANALYSIS:
MALES M = 1.75 N0hSM0KER LUNG CANCER DEATH PROBABILITIES OBSERVED 2X OBSERVED NS S
NS S
Proportion Smokers at Age 35 0.40 LE 70.0 64.6 70.0 64.6 LC 668 10656 1280 9764
'0.50 LE 70.5 65.1 70.6 65.1 LC 698 8633 1334 803E 0.60 LE 71.1 65.6 71.1 65.6 LC 731 7306 1392 6904 l
Note:
LE = Life Expectancy; LC = Expected Lifetime Lung Cancer Deaths Per i
100,000; S = Smokers; NS = Nonsmokers.
25
into one term, d, the effective exposure acting at age x.
Otherwise, our calcu-x lation is a straightforward application of Equations 1 through 12.
RADRISK assumes a constant annual exposure, d, given in working level months, y
.for the period of exposure.
-The' exposure acting at age t, d, is for the simplest case (continuous exposure) t df = (t - f)dy, (43) i.e., the difference between the age at present and the age at first exposure times the annual exposure.
More generally, y i-L-1,-r(t-i+L); t > m d =IdZ (44) t i=m
)
i d = 0; t <-m t
Here m = f + L + 1 and k = t if t < g; otherwise k = g.
Verbally, this says that the exposure active at. time t is a function of the age-specific sensitiv-ity at the age it was received and that risk from exposure received in the past decays exponentially from the time it was received.
Further, only exposure received at least L + 1 years in the past is effective in determining risk (if exposure begins at age f, risk cannot-commence until age f + 1).
Finally, a restriction'not reflected by Equation 45 is that if t < h, the age at first risk, then d 0.
=
t i
This completes the description of the new algorithms used in RADRISK (remember, the rest of RADRISK follows Equations 1 through 8) and thus the algorithmic description of GARR as a whole.
26
, - - ~,.
.~ ----- m.
.---m
,---_,---...e.
~.. ~. -,
4.
RUNNING GARR ON THE HP-75 4.1 HP-75 System The following discussion assumes a minimal configuration of an HP-75C portable computer with an 8k memory expansion module (24k RAM total), an HP 82161A digital cassette drive, and an HP 821622A thermal printer. When the HP-IL interface loop is configured (refer to Section 9 of your HP-75 Cwner's Manual (Hewlett Packard)), the cassette drive should be named ":CA" and the printer should be named ":PR."
Note also that the printer must be declared as the system print device. The command PRINTER IS ":PR" must be executed.
The following discussion assumes that the reader is somewhat familiar with the HP-75 and its Owner's Manual.
For example, we always assume that adequate memory is available for program execution.
However, if one copies a large number of files to memory, at some point an error #16, "not enough memory,"
will be generated. These errors can be avoided by judicious use of the PURGE and COPY commands, but we do not treat such problems explicitly here.
For questions of this sort, the reader is referred to the HP-75 Owner's Manual.
- 4. 2 Preparing Input File for GRADUATE and MULDEC Figure 1 reproduces a representative input file for use in both GRADUATE and MULDEC.
Line 10 is an optional comment line.
Line 15 is a mandatory title (this is included to force the user to add a title), which can be up to 32 characters in length.
Lines 20 and 30 are the DATA statements containing the 9 values from the abridged life table arranged from x = 0 to x = 85.
19 5x Line 32 is an optional comment line.
Line 35 is a DATA statement giving the number of disease-specific causes of death (for our purposes it is always 1).
Line 40 is an optional comment line.
Lines 50 and 60 contain the 22 5"tx values from the mortality compilation (x = 0, 1, 5, 10,.. 90, 95, 100) arranged 27
FIGURE 1 SAMPLE INPUT DATA FILE FOR GRADUATE AND MULDEC 10 i MORTALITY SClO ULE FOR F,1%9 15 M TA MORTRLITY F 19 69-20 MTA.0161, M28,.001 6,. N15,.0029. 0033. # 3 5,.0049,.N76,.012 30 MTA.0181 0272,'.040 2,.0598,.094,.1522,.2352
,.3671,1 32 ! NUM0ER OF SPECIFIC CAUSES OF BEATH 35 MTA 1 40 ! TOTAL MATHS # 69 N MTA 22950,4070,2029, 2519,4615,4690,4177,4932
,7519,13109,20543 60 MTA 20210,30264,4960 2,66000,90550,113406,116 612,07714,41662,t1393,15 69 70 ! LWG CANCER BERTHS W 69 80 MTA 0,0,0,0,0,13.16, 49,162,426,019,1165 90 MTA 1511 1477,1393,1 263,969,644,303,94,14,2 l-l 28
from x = 0 to x = 85.
Line 70 is an optional comment line.
Lines 80 and 90 contain the 22 5"cx values arranged in the same fashion as the 5"tx values.
The reader who is fluent in BASIC can refer to the program listings for GRADUATE and MULDEC (Appendix A, pp. 67-70) to determine the necessary features of the input file.
Others are urged to follow exactly the format of the sample file shown in Figure 1 since this will always work.
Details of creating data files can be found in the HP-75 Owner's Manual.
4.3 Running GRADUATE Program To run the GRADUATE program, first determine that the program is in memory.
Also make sure a file of input data like that discussed in the previous section is in memory.
(Execute the CAT ALL command to scan the file directory.) If GRADUATE is not in memory, it must be loaded from cassette.
The relevant command is COPY " GRADUATE:CA" T0 " GRADUATE" Similar comments apply to the data file.
To run the GRADUATE program, enter EDIT " GRADUATE" and then RUN or simply enter RUN " GRADUATE" (These comments apply to the other programs in GARR as well.) The computer will display the prompt l
FILE FOR ABRIDGED?>
l l
29
Enter the name of a file configured as in Figure 1.
If the file is not configured properly or does not exist, the error message BAD OR NONEXISTENT FILE l
will be generated on the printer, and you will receive the prompt for a file.
l At this point two possibilities are raised.
First, you may have mistyped the file name.
In this case simply reenter the correct nasce.
Second, there may be something wrong with the file.
In this case enter EDIT " FILE" where " FILE" is the desired file name.
The computer should reply FILE B
564 tt:tt 00/00/00 Desired Basic Length time date file in bytes created created where the fields have the meanings indicated by the labels.
The two most important fields are the length in bytes, which should be about 564, and the file type, which should always be B for BASIC.
If the length is zero, this means the file is not in memory.
Consult the HP-75 Owner's Manual (Hewlett Packard),pp. 135-136, for the procedures involved in copying it to memory.
A file type other than B probably means you have referenced the wrong file.
Consult the HP-75 Owner's Manual, Appendix B, for information on file types.
If an appropriate file has been specified, an output like that in Figure 2 is generated. The first line is the name of the file referenced, in this case "WFLC."
The second line gives the title read from the input file.
This serves as a check that the appropriate file has been referenced.
Following this are q values for x = (17; 22; 27 77; 82), the B values used to correct x
the q values (Equation 19), and the I values used to perform geometric inter-x polation (Equation 23). The last four items output are the I value used to 30
FIGURE 2 SAMPLE OUTPUT FOR GRADUATE a n nen u u n****
<x(52)=.0109 GRADUATE LIFE TABLE b.00899 emen n u n u me**
!= 1.099 ex(57)=.0175 B=.00822 INPUT FILE =W LC I= 1.095 TITLE: MORTALITY M 1%9 ex(62)=.6272 ex(l?)=.0015 p.M656 b.02219 I= 1.084 I= 1.160 ex(67)=.6393 u(22)=.0020 b.W616
>0.000M I= 1.082 I= 1.012 ex(72)=.0595 u(27)=.0017 p.W556
>0.00000
[= 1.077
!=.991 ex(77)=.0829 ex(32)=. M18 0=,00452 k.N193
!= 1.069
!=1.H4 ex(82)=.1164 ex(37)=. W26 p.N495 b.00691 t= 1.073
!= 1.087 u(42)=.0842
!(85+)= 1.075 k.00895
!= 1.099 P 0F BEATH IM =.398 u(47)=.0068 b.00918 I= 1.101 PRO 8 0F SURVIVAL TO IN=.N164 LE=67.8241 31
extrapolate q from x = 82 to x = 99, the probability of death during the x
100th year of life (age S9), the probability of surviving to one's 100th birthday, and the calculated life expectancy at birth (Equation 5). These quantities are provided to allow the user to check the validity of the generated single year life table.
In general, I values should be in the range of 1.06 to 1.12 for ages 32 and above, and the q values should agree closely x
with those obtained by manual application of Equation 17.
Finally, the life 1
expectancy should be within 0.5 year of the life expectancy given for the abridged life table. A single year life table produced by a GRADUATE run that satisfies these criteria can be assumed to be reasonably accurate.
At the end of a GRADUATE run, consult the file directory (enter CAT ALL) and you will find a new file with the name FILEGR l
1.e., the name of the input file plus the letters GR.
For the case of our example (Figure 2), this will be named WFLCGR. This file contains the single-year life table that will be used by MULDEC.
Attempting to list this file will generate the message WARNING:
line too long This does not mean there is any problem with the file.
Rather, the file has been generated to occupy the minimum amount of memory and is not fully listable en the display.
For a discussion of this point, see the HP-75 Owner's Manual,
- p. 228. These files can be listed using the GARR LIST utility described below.
This completes our discussion of the GRADUATE program.
A program listing for GRADUATE is given in Appendix A.
l
'4. 4 Running MULDEC Program l
l To run the MULDEC program, follow the same initial steps outlined for GRADUATE.
l A minimum of two additional files, one like that used for input to GRADUATE and l
32 l..
MULDEC (Figure 1) and a "GR" file containing q values for ages 0 to 100+, must x
be in memory. After you enter RUN "MULDEC"
.you will get the prompt SINGLE YR LIFE TABLE FILE?>
This asks for the name of a "GR" file of the form generated by GRADUATE.
For our example we would reply WFLCGR.
If there were a problem with this name, a BAD OR NONEXISTENT FILE message would be generated and should be handled as in the GRADUATE program.
(MULDEC will continue prompting for a file until execution is halted or a valid file name is entered.)
Following entry of a valid "GR" file, you will get the prompt FILE FOR DEATH DATA?>
This asks for an input file of the format described under Section 4.2, " Preparing i
Inrut File for GRADUATE and MULDEC." Invalid file names will be handled in I
the manner described above.
l l
For our example, the input file name would usually be WFLC l
l That is the same file used to generate the GR file.
(However, here we are interested in the death data that are used as in Equation 26.) The option i
33 a
m
+.-
of entering a different file name is provided because it might be of interest to generate multiple-decrement life tables with the basic mortality experience of one population but with the proportional mortality experience of another.
An example might be "what would a population with the life expectancy of women and the proportional lung cancer experience of men look like in our risk model?".
If a valid file name is entered (or else " BAD OR NONEXISTENT FILE" will be i
generated), the prompt HEADING FOR OUTPUT?>
will appear.
This asks for a string of up to 32 characters, which will be written on the first.line of the output file.
This is used to label the file and may contain whatever information the user chooses.
Following this, you will get the prompt OUTPUT FILE NAME?
which asks for the name under which you wish to store the multiple-decrement life table that will b'e generated.
For our example (Figure 3), the name chosen is i
WFLCMD After this information has been generated, the computer will display the word WORKING for about 30 seconds.
During this period, the qbx and q values are calculated cx and the output file is created.
34
FIGURE 3 SAMPLE OUTPUT FROM MULDEC, INCLUDING; PARTIAL LISTING OF LIFE TABLE (AGES 0 - 43) essesessesses***
19 6.07E-004 6.74E-00 CONSTRUCT MULDEC se**se**********
20 6.22E-404 1.04E-M6 l
MORTALITY FILE =WFLCCR 21 6.38E-004 1.42E-M6 DEATH DATR=WFLC 22 6.55E-004 1.82E-906 0UTFILE: HFLCMD 23 6.67E-904 2.00E-006 RGE tby acx 24 6.74E-004 2.16E-M6 0 1.61E-002 0.00E+M0 25 6.82E-004 2.33E-M6 1 7.01E-004 0.00E+000 26 6.90E-904 2.51E-M6 2 7.01F-M4 0.00E+M0 27 6.90E-004 2.69E-906 3 7.01E-004 0.00E+006 28 7.45E-404 3.78E-406 4 7.01E-004 0. NE+000 29 7.96E-904 5.02E-906 5 3.20E-404 0.00E+990 30 8.50E-404 6.42E-006 6 3.20E-M4 0.00E+M0 31 9.00E-404 7.99E-906 7 3.20E-404 0.00E+000 32 9.70E-004 9.74E-406 0 3.20E-004 0.00E+000 33 1.05E-903 1.31E-405 9 3.20E-404 0.00E+000 34 1.15E-403 1.70E-405 10 3.00E-404 0.00E+000 35 1.25E-003 2.15E-405 11 3.00E-404 0.00E+000 36 1.36E-403 2.67E-M5 12 3.00E-404 0.00E+000 37 1.40E-403 3.26E-405 13 3.00E-404 0.00E+000 38 1.62E-403 3.93E-405 14 3.00E-494 0.00E+400 39 1.77E-403 4.70E-405 15 4.43E-404 0.00E+000 40 1.94E-M 3 5.57E-405 16 5.06E-904 0.00E+400 41 2.12E-M 3 6.58E-405 17 5.77E-404 0.00E+000 42 2.31E-903 7.73E-M5 le 5.92E-904 3.28E-907 43 2.51E-M 3 8.79E-M 5 35
The proept LIST MULDEC?>
will now appear.
If you answer N, no listing will be produced and the message EXECUTION ENDS will appear. - If your answer is Y, the message HIT ANY KEY TO STOP will appear, and a listing of qbx and q values will commence (see Figure 3).
cx As the message implies, hitting any key will cause listing to stop and the message EXECUTION ENDS will appear.
Note that if you do not list the file at this point and wish to list it later, you must use the GARR~ LIST utility. Otherwise, the message WARNING:
line too long will be generated as it was for the "GR" file produced by GRADUATE.
One additional comment regarding MULDEC should be made.
If lung cancer mortality is input before total mortality, the message l
FAILED CONSISTENCY CHECK l
ORCER OF CAUSES WRONG?
l l
l will be generated on the printer and execution will terminate.
If this happens, 1
make sure that total deaths precede lung cancer deaths in the input file f
(Figure 1) and try again.
36 l
i This completes our discussion of the MULDEC program.
A program listing is given in Appendix A.
4.5 Running SMOKER Program To run the SM0KER program, follow the same initial steps outlined for GRADUATE.
A minimum of two additional files must be in memory.
The first of these is a file containing qbx and q values for ages 0 to 100+ in the format generated cx by MULDEC. The second file must be named "NONSLC" and contains the nonsmoker death rates for the ages shown in Table 6 arranged in the format shown in Figure 4 (if one wishes to use Table 6, Figure 4 may simply be copied).
The first prompt is FILE FOR MULDEC?
which asl5 for the name of the file containing the qbx and q values.
An cx invalid file name will generate the now familiar BAD OR NONEXISTENT FILE Following this, the program looks for the NONSLC file.
If this is not found, the message NONSLC INVALID OR MISSING l
l l
is generated on the printer and the prompt l
LOAD FROM CA?>
will appear in the display. To continue execution, place a cassette containing a copy of NONSLC in the tape drive and answer Y.
The file will then be loaded into memory.
l 37
FIGURE 4 COPY OF NONSLC FILE LISTING AND REPRESENTATIVE OUTPUT FROM SM0KER PROGRAM le ! N0HSM0KER DEATH RAT AGE: 49 ES IN MATNS.
SM0K/N0HS:LUNGC-MULIEC P. OF 3.-N.S.=6.16E-M 3 20 l PER 100000 PEOPLE.
P. OF 3.-S.=1.08E-002
$00RCE:GARFINKEL(1981)
R,R.-l,C.=2.07E+001 30 ! MALES FIRST SMR(TOTAL)=1.75E+000 40 MTA 4.55,7.63,10.13, 17.26,27.43,25.97,44.27, INFILE=2LC 68.87,94.8 AGE 59 50 ! THEN FEMALES P. OF B.-N.S.=1.58E-002 60 MTA 3.6,5.3,7.07,13.
BAB OR NONEXISTANT FILE P. OF B.-S.=2.77E-402 6,16.17,20.83,34.7,45.8, R.R.-L.C.=3.06E+001 52.47 SMR(TOTAL)=1.75E+000 70 ! END INFILE=NMLCMD SEX = MALE AGE = 69
- ERROR ***
P. OF B.-N.S.=3.6tE-402 U= 8.000 P. OF D.-S.=6.32E-402 OUT OF RANGE.5(Uf3 R.R.-L.C.=2.88E+001 SMR(TOTAL)=1.75E+000 U= 1
- ERROR ***
AGE = 79 P= 45.000 P. OF I.-N.S.=7.82E-002 OUT OF RANGE.!(P(.9 P. OF 3.-S.=1.37E-401 R.R.-L.C.=1.72E+M1
% SM0KERS=.45 Sm(TOTAL)=1.75E+000
- ERROR ***
SMR= 10.000 AGE = 89 OUT OF RANGE 1(SMR(5 P. OF 3.-M.S.=1.77E-M 1 P. OF l.-S.=3.09E-M L SMR= 1.75 R.R.-L.C.=6.56E+000 SMR(TOTAL)=1.75E+000 swERRORu*
i RELRISK= 40.000 OUT OF RANGE 1(RR(20 AGE = 99 P. OF B.-M.S.=3.96E-031 MIN RELRISK-L.C.= 5 P. OF 3.-S.=6.93E-M 1 R.R.-L.C.=5.00E+000
% SM0KERS VS. AGE SMR(TOTAL)=1.75E+000 AGE =40 P=4.49E-001 ACE =50 P=4.41E-401 NONS. FILE =NONS AGE =60 P=4.19E-401 SM0K. FILE =SM0K AGE =70 P=3.67E-M 1 i
AGE =80.P=2.58E-401 LIFE EXPECTANCIES AGE =90 P=8.89E-402 NONSM0KERS FIRST AGE = 39 LE= 70.29 P. OF 3.-N.S.=2.72E-003 PR08. OF SURVIVAL P. OF l.-S.=3.74E-M3 TO IM =2.97E-003 R.R.-L.C.=5.86E+000 SMR(TOTAL)=1.38E+000 LE= 64.81 PROB. OF SURVIVAL 38 TO 100=9.6SE-0%
l
The prompt MULTIPLIER FOR NONS. L.C.?>
is now given. This asks for a multiplier in the range of.5 to 3 that is l
used, as in-Equation 37, to modify nonsmoker lung cancer death probabilities.
An answer of 1 leaves these quantities unmodified.
An answer outside the range of 0.5 to 3 generates an error message (Figure 4) and causes the prompt to repeat.
The next prompt is MALE OR FEMALE?>
One may answer M or F to select male or female lung cancer rates from NONSLC.
An answer other than M or F causes females to be selected by default.
The next prompt STARTING P OF SM0KERS?>
asks for the proportion of 35 year-old smokers in the population.
Your reply must be a number in the range of 0.2 to 0.9.
If this range is exceeded, an error message of the form shown in Figure 4 is generated and the prompt is repeated.
The next prompt is SM0KER VS NS. TOTAL SMR?>
This asks for the all-cause smoking mortality ratio for smokers versus nonsmokers at ages 45 and above.
A number in the range of 1 to 5 is expected.
Exceeding this range will generate an error message (Figure 4) and cause the prompt to repeat.
39
The next prompt is MIN RELRISK L.C.?>
This asks for a minimum value of the relative risk of lung cancer in smokers versus nonsmokers at ages 45 and above.
Your answer must be in the range of 1 to 20 (see Figure 4).
Two final sets of prompts are HEADING FOR NONS.?>
and FILE NAME FOR NONS.?>
These ask for the heading (up to 32 characters) that will be written at the top of the nonsmoker file and the name of the file into which the nonsmoker file should be written.
Similar prompts appear for the smoker file.
After this information is provided, the life expectancies for smokers and nonsmokers as well as their probabilities of surviving to 100 (S100) are printed and the message EXECUTION ENDS appears on the display.
Program execution is now complete.
Returning to the output of SM0KER reproduced in Figure 4, we start with the title SM0K/NONS: LUNGC-MULDEC This is followed by the phrase INPUT FILE = WMLC 40
and the error message BAD OR NONEXISTENT FILE Taken together, these tell us that we attempted to access an inappropriate file named WMLC.
l Then we see INPUT FILE = WMLCMD l
followed by SEX = MLE l
The first phrase says that our input file is named WMLCMD; the second says that we selected the male portion of NONSLC.
Following these is an error message that says
- ERROR ***
P = 45.00 OUT OF RANGE.1 < P <.9 and the phrase
% SM0KERS =.45 These tell us that we attempted to declare 45 as the proportion of smokers at age 35 and that we corrected this to 0.45.
Similar error messages appear for the all-cause standard mortality ratio (SMR) and for the minimum relative risk of lung cancer.
The next section of output is labeled
% SMOKERS VS. AGE 41
This gives the calculated age-specific proportion of smokers in the population (Equation 34) at 10 year intervals starting with age 40.
Here.the proportion of smokers falls from 0.449 at age 40 to 0.089 at age 90.
I Most of the remaining output is devoted to displaying the age-specific probabil-ity of death, q, in nonsmokers (P. OF D. - N.S.), age-specific probability of x
death in smokers (P. OF D. - S), age-specific relative risk of lung cancer in smokers versus nonsmokers (R.R. - L.C.), and the age-specific all-cause SMR of smokers versus nonsmokers (SMR(TOTAL)) for 10 year intervals starting at age 39.
This information is provided to give the user some insight as to the char-acteristics of the populations generated. Note that, for ages 49 and above, the all-cause SMR equals the SMR specified in setting up the prograra (1.75 in this case).
The final pieces of information provided are the names of the nonsmoker and smoker files generated (for our example, NONS and SM0K, respectively) and life expectancies and probabilities of survival to 100 for nonsmokers.and smokers.
Note that both output files from SM0KER are the same format as that produced by MULDEC. Therefore, they too must be listed using the GARR LIST utility.
This completes our discussion of the SM0KER program. A program listing is given in Appendix A.
4.6 Running RADRISK Program To run the RADRISK program, verify that it is in memory and enter RUN "RADRISK" After a few seconds (which are required for initialization), you will receive the prompt INPUT: KEYBO.(K) or FILE (F)?>
42
This prompt asks whether you wish to parameterize the model by inputting values from the keyboard or by providing a data file containing the necessary inputs.
~
We will-consider input from the keyboard first, i.e., we assume that the option K is selected.
4.6.1 Input from Keyboard
~
The first prompt is AGE AT FIRST RISK?>
which asks for the first age at which excess lung cancer risk can be greater than zero. Thereplyexpectedisanumberinthefangeof5to50.
Ages outside this range cause the message s
AGE'AT FIRST RISK (nnn)
OUT OF BOUNDS; 4 < A0 < 51, where nnn is the faulty input, to appear on the prin,ter and the prompt for age, at first risk to be repeated.
~'
4
'.i i
The next prompt S
s l~
AGE AT FIRST EXPOSURE?>
i 3
i is self-explanatory.
If a riumber less thanl0 is entered, the age at first s
exposure is set equal to 0; if a number greater than 99 is entered, age at first exposure is set equal to 99.
J i
The prompt 3
\\
r I
AGE AT LAST EXPOSURE?>
/
i follows logically.
Ifthereplyislesstha71,ageatlastexposureisset l
equal to 0.
If the reply is greater than 100, it is set equal to 100.
i x
I l
$3 L
s s
~
t
Following entry of age at first exposure and age at last exposure, RADRISK checks to make sure that the former is less than or equal to the latter.
If this is not the case, an error message of the form AGE F.E. (nnn) > AGE L.E. (mmm),
where nnn and mmm are the ages at first and last exposure that cause the problem, appears.on the printer and the prompts for ages at first and last exposure are repeated.
Following this, the prompt RISK /WLM - R.R.?>
tsks for the value for the relative risk coefficient.
Your response must be in the range of 0 to 0.2.
A reply outside this range causes an error message similar to that generated for an "out of bounds" age at first risk (see Figure SA) to appear on the printer. When a relative risk coefficient greater than zero is entered, the prompt R. R.
OPTION (M, E, OR 8)?>
appears.
Entering M in reply causes the multiplicative form of the relative risk model (Equation 3) to be executed.
Similarly, if E is entered, the exponential form of the model (Equation 4) is executed.
A reply of B calls up both models as will replies other than M, P, or B.
(That is, B is the default option.)
l The next prompt RISK /WLM - A.R.?>
l Esks for a value for the absolute risk coefficient. This must be in the range of 0 to 0.0002 or an "out of bounds" error message (Figure SA) will appear on the printer.
44 e
FIGURE 5 REPRESENTATIVE OUTPUT FROM RADRISK PROGRAM:
A. ERROR MESSAGES, B. SENSITIVITY FILE, C. PROGRAM OUTPUT, INCLUDING MODEL PARAMETERIZATION, D. INPUT FILE FOR FILE OPTION A.
C.
AGE AT FIRST RISK ( 2)
RADON RISK MODEL POP. 2 =WMNSMD OUT OF BOUNDS; 4(A0(51 R.R. COEF=1.00E-002/WLM BASELINE ACE F.E.( 99)> AGE L.E.(
OPTION =B L.E.=70.567 1)
A.R.=1.00E-005/PY/WLM DEATHS /10^5 -LC= 698.5 ACE AT F.E.: 0 RELATIVE RISY(1.00E+000)
ACE AT L.E.=lef OUT OF BOUNDS; 0(Rl(.2 AGE AT FIRST RISK = 30 RELRISK MODEL-M WLM PER YR.=10.00E-001 L.E.=70.523 ABSOLUTE RISK (2.00E-004)
LATENCY =le LOSS LE(MONS)=
.53 OUT OF BHDS; 0(R2(2E-4 EXP0HEHT COR=-1.00E-002 B/10^5= 1964.1 AGE SP.SEN=SENS EXCESS D/10^5= 367.8 LATENCY ( 50.000) ne******nnene OUT OF BOUNDS; 0(=T7(46 ununnuneuen POP. 1 =WMSMMD RELRISK MODEL-E EXPOSURE LEVEL (50.00E+0 L.E.=70.510 01)
BASEllHE LOSS LE(MONS):
.68 OUT OF BOUNDS; 0(W1(100 L.E.=65.081 D/10^5= !!79.0 DEATHS /10^5 -LC= 6632.8 EXCESS B/10^5= 483.5 RELRISK MODEL-M RBSRISK MODEL L.E.=64.607 L.E.=70.136 LOSS LE(M0HSi= 5.69 LOSS LE(MONS)= 5.17 D/10^5=12591.2 D/10^5= 2598.4 B*
EXCESS D/10^5= 4255.4 EXCESS D/10^5= 1913.0 5 ! ACE SPECIFIC SENSITI RELRISK MODEL-E VITIES FOR RADRISK L.E.=64.475 le DATA 3,3,3,3,3,3,3,3, LOSS LE(MONS): 7.27 3,3,2.5,2,1.5,1,1,1,1,1, D/10^5=13721.5 1,1,1,1,1,1,1,'
EXCESS D/10^5= 5469.3 20 DATA 1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1 ABSRISK MODEL 30 DATA 1,1,1,1,1,1,1,1, L.E.=64.760 1,1,1,1,1,1,1,1,1,1,1,1, LOSS LE(MONS)= 3.86 D.
1,1,1,1,1,1,1,1 D/10^5=10118.4 40 M TA 1,1,1,1,1,1,1,1, EXCESS D/10^5= 1621.0
-1,1,1,1,1,1,1,1,1,1,1,1, la ! STANDARD IMPUT PARC METERS FOR RADRISK 1,1,1,1,1,1,1,1 20 M TR 30,0,100,.01,B,.
50 MTA 1.1,1,1,1,1,1,1, 00001,10,1,Y,.01,Y,SENS 1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1 45
l It should be noted that if either the relative or absolute risk coefficient is specified as zero, RADRISK skips execution of that model because no effect is assumed a priori.
The program next asks for LATENCY IN YEARS?>
The reply must be in the range of 0 to 45 or an "out of bounds" error will appear on the printer (see Figure 5A).
The next quantity requested is ANNUAL EXPOSURE IN WLM?>
This asks for the constant working level month per year exposure that is assumed.
Replies in the range of 0 to 100 are accepted.
Otherwise, an "out of bounds" error is generated (Figure SA).
The next query is EXPONENTIAL CORRECTION?>
If your reply is Y, the prompt EXPONENT =?>
. appears.
This asks for a constant in the range of -0.2 to 0, which is used to decrease effective exposure (the r of Equation 45) over time.
Replying N to the query " EXPONENTIAL CORRECTION" results in no correction (i.e., r = 0).
46 m
4 LThe next prompt in the sequence is
- AGE SPECIFIC SENSITIVITIES?>
This asks'whether a data file containing 101 numbers specifying age-specific sensitivities for the ages 0 to 100+ is to be read in.
If the answer is Y, the' query i
. FILE FOR AGE SENS?>
- asks for the name of the file. At this point, one can either provide a valid file'name or reply
~
-NONE which aborts the request for a sensitivity' file and assumes all age-specific sensitivities are unity.
A' sample input file for this' option is shown in
- Figure 58.
This file assumes that children under 10 are 3 times as sensitive to radon damage as those who are older and that sensitivity declines to 1 at ages 13 and beyond.
4 4.6.2 Designation of Population at Risk and Interpretation of Output At this point the model parameterization (Figure SC) is listed, and the prompt f.
FILE NAME FOR INPUT?>
1 l
asks.for the ' file containing the multiple-decrement life table that describes
(
the mortality. experience of the population assumed at risk (e.g., an output
[
' file of MULDEC or SM0KER).
If the name NONE is entered, the "NEW INITIAL
' CONDITIONS?>" prompt described below is displayed because RADRISK assumes.that
-you do not want to run any populations at the exposure regime specified.
- Obviously, you'cannot name a valid input file NONE.
l 47
m Following the entry of.a valid file,-the prompt PURGE INPUT FILE?>
appears.: If your answer is Y, the input file will be erased from memory;
.otherwise, it will:be retained in memory.
This feature is included to prevent-
-memory overflow when a number of input files are loaded from tape (described below under Section 4.6.4).
After this, the output shown in Figure-5C is generated.
r In the model parameterization shown in-Figure SC, the relative risk coefficient is 0.01;.both forms of the relative risk model have been selected; the absolute risk coefficient is 0.00001; age at first exposure is 0; age at last exposure is:100 (lifetime exposure is assumed); age at first risk is 30; the exposure is' 1 WLM per year; latency is 10 years; an exponential correction (r) of -0.01 z is assumed; and age-specific sensitivities of the form shown in Figure 5B are e
input from a file called SENS.
The first population entered is WMSMD, a population of male smokers.
The
. part ofL the output labeled BASELINE-shows that with no radon exposure the life i~
expectancy of this population is about 64.8 years, and 9,529 lung cancer deaths per: 100,000 are expected. The section labeled RELRISK MODEL-M shows that, under cur multiplicative relative risk model, life. expectancy is reduced 6.41 months,
[.
End 4,855.'7 premature lung cancer deaths (EXCESS DEATHS /10^5) per-100,000
~
j persons at risk are expected.
The next section, labeled RELRISK MODEL-P, shows:
l that-the proportional form of the relative risk model predicts somewhat greater effects.
Here the loss in life expectancy is 8.26 months, and the premature deaths'are 6,294.8. The section labeled ABS RISK MODEL shows that for the absolute risk model loss in life expectancy is 3.95 months, and the premature i
?
der.th's are 1,670.7.
. Close inspection of the output shown in Figure 5.also makes the point that i_
premature lung' cancer deaths'are not precisely the same thing as excess lung.
- cancer deaths. As noted above, the premature deaths under the multiplicative relative risk model equal 4,855.7.
If we instead tried subtracting total lung 4
6 48 i
. - -.. ~. - - -. - -. _. - - - - -.... -. -,.. -... - - -, - - - - -. -. ~ -.... -. -
i cancer deaths expected in the absence of exposure from total lung cancer deaths expected in the presence of exposure (D/10^4), we get 14005.6 - 9529.9 = 4475.7 or a difference of 380 deaths from our " premature" figure.
Similar differences are apparent in our other models. This illustrates the fact that, because an excess source of cancer mortality " competes" with the baseline level of the cancer, the total cancer observed in the exposed population is always less than would be expected from summing bc;eline and premature cancer deaths.
After the output for population 1 (WMSMMD) is generated, we receive the prompt RUN ANOTHER POPULATION?>
In our example we answered Y, which generated FILE NAME FOR INPUT?>
Our reply was WMNSMD, which specified a file for male nonsmokers and generated the final section of the output using the new population and the previously entered model specification.
RADRISK will process populations for a given set of input parameters until one answers N to "RUN ANOTHER POPULATION?>." At this point, the prompt NEW INITIAL CONDITIONS?>
l appears.
An answer of N stops execution and causes the message l
EXECUTION ENDS to appear on the display. An answer of Y returns us to the prompt " INPUT:
KEYBO.(K) OR FILE (F)?>."
l l
49
4.6.3 Input Via File If we answer F to the prompt just mentioned, we are asked FILE NAME?>
i which requests the name of a file configured as in Figure 50.
If the answer to this prompt is "NONE," you will be returned to keyboard input.
The only necessary part of such a file is the data statement which contains, in this order, age at first risk, age at first exposure, age at last exposure, the relative risk coefficient, the choice of relative risk models (a reply must be included; if the relative risk coefficient is zero, use B), the absolute risk
- coefficient, latency, exposure level-in WL, the answer to whether or not an exponential reduction factor is desired, a value for the exponential factor (this must be included; if a reduction is not specified, use zero), the answer to whether or not a file of age-specific ser.sitivities is to be used, and the name of such a file (here, too, a name must be given; if the preceding answer is N, use the name "N0NE").
For the example file, the reader can verify that we have specified the same model parameterization used in our example output for RADRISK.
If this format is not followed, error messages will be generated as described in the following section.
A useful feature of output from a file is that all the error checks provided for keyboard input are in effect for file input.
Thus one will be asked for substitute values for any bad arguments (but only for bad arguments). A specific example might be reversing age at first and last exposure.
This generates the message AGE F.E. (nnn) > AGE L.E. (mmm) on the printer and prompts for revised ages of first and last exposure.
Such an " error" could be of practical use.
Say that we want to consider the same risk models for individuals exposed at different age ranges (as in an occupa-tional setting). We can construct an input file with the age of first exposure greater than the age of.last exposure.
Each time we run the model we specify this file and are prompted only for ages of first and last exposure.
In practice this saves a bit of time and typing.
50
4.6.4 Error Handling and Loading Input Files from Cassette
-Thus far in our discussion of input files, we have assumed that valid files were resident in memory.
If this is not the case, the message FILE XXXX???
will appear on the printer, where XXXX is the problem file name, and the prompt-ON CASSETTE?>
appears.
This sequence means either that there is something wrong with the
-file format of XXXX or that it is not in memory.
If your response is Y, RADRISK attempts to load the file named XXXX from cassette.
The user should be cautious in answering Y to the last prompt.
That is, make sure a cassette containing the
' file of interest is in the drive.
If this is not the case, a further error occurs'and RADRISK, having determined thc the necessary file is not in memory i'
or on cassette, halts execution and displays the messge EXECUTION ENDS To prevent such a termination, reply N and you will be returned to the prompt asking for the relevant information (e.g.,
either " INPUT: KEYBD (K) OR
[
FILE (F)?>," " FILE FOR AGE SENS?>," OR " FILE NAME FOR INPUT?>"). The first I
two of these may be aborted by answering "NONE."
The last must be answered with a valid file name.
If no valid input file for the population exists, one must be created using GRADUATE, MULDEC, and SM0KER.
4.6.5 Additional Output Features r
Figure 6 displays 3 additional outputs from RADRISK.
These are intended to illustrate how changes in model specification affect the output.
In the first, the model specification is the same as shown in Figure 5 except that age at first exposure is changed to 10, the exponential form of the relative risk i
model is specified, and the absolute risk coefficient is given as zero.
Note l
that, as stated earlier, specifying the coefficient as zero prevents execution 51 l
FIGURE 6 THREE ALTERNATIVE PARAMETERIZATIONS OF RADRISK MODEL seseeeeeeeeeeeeeeese seesesseessessessess sesseeeeeeeeeeeeeeee
- eeeeeeeeeeeeeeeees eseeeeeeeeeeeeeeeeee seeeeeeeeeesseeeese*
RADON RISK MODEL RADON RISK MODEL RADON RISK MODEL R.R. COEF=1. NE-002/WLM R.R. COEF=0.00E+000/WLM R.R. COEF=0.00E+000/WLM OPT 10H=E OPT 10H=
OPTION =
A.R.=6.00E+000/PY/WLM A.R.=1.00E-005/PY/WLM R.R.=0.00E+000/PY/WLM AGE AT F.E.= le AGE AT F.E = 30 RCE AT F.E.=
0 AGE AT L.E.=100 AGE AT L.E.=100 AGE AT L.E.=100 AGE AT FIRST RISK = 30 AGE AT FIRST RISK = 30 AGE AT FIRST RISK = 30 WLM PER YR.=le.00E-001 WLM PER YR.=le.00E-001 WLM PER YR.=00.00E-001 LATENCY =le LATENCY =le LATENCY =10 EXPONENT COR=-1.00E-002 EXPONENT COR=00.00E-001 EXPONENT COR=00.00E-001 SENSITIVITY =1 SENSITIVITY =1 SENSITIVITY =1 eeeeeeeeeeeeeeeeeees seeeeeeeeeeeeeeessee eseesseeeeeeeeeeeese seeeeeeeeeeesesseees eseeeeeeeeeeeeeeeees eseeeeeeeeeeeeeeeees POP. 1 =WMSMMD POP. 1 = MSMMD POP. ! = MSMMD BASEllHE BASELINE BASELINE i.E.=56.848 L.E.=38.109 L.E.=65.081 N ATHS/le'5 -LC= 8871.1 EATHS/10^5 -LC= 9117.1 DEATHS /te^5 -LC= 8632.8 RELRISK MODEL-E ABSRISK MODEL
- nmneseenes L.E.=56.500 L.E.=38.052 LOSS LE(MONS)= 4.18 LOSS LE(MONS):
.68 I/10^5=11990.1 B/10^5= 9553.4 i
EXCESS 3/10^5= 3344.0 EXCESS D/10^5= 470.3 f
eeeeeeeeeeeeeeeeeee.
seseeeeeeeeeeeeeeees i
I i
l l
52
-of the absolute risk model and that specifying the age at first exposure as 10 changas life expectancy to 56.57 years.
The latter change is because we are_now' calculating life expectancy at age 10 rather than at age 0.
l The next two outputs drop the exponential correction and age-specific sensi-tivities, change age at-first exposure to 30 and 50, respectively, and suppress execution of first the relative risk and then both models.
4.6.6 Conclusion This completes what is designed to be a tutorial on running the RADRISK model.
Review of this material should enable even persons with little prior knowledge 1-of computers or computer programming to run RADRISK and thus produce a wide variety of radon risk models. A program listing is given in Appendix A.
4.7 LIST Utility 4
We noted earlier that GRADUATE, MULDEC, and SM0KER all generate output files that cannot be listed using the system LIST command.
This section describes the LIST utility that allows review of both file types (remember, MULDEC and SM0KER generate the same file format).
To use LIST, simply enter RUN " LIST" You will (assuming the file is in memory) receive the prompt PRINTER (P) OR DISPLAY (D)?>
v if you answer D, the file will be listed on the display; if you answer P, the j
file will be listed on the printer (other replies cause the printer to be selected by default).
Following this, you will receive the prompt FILE NAME?>
1-f 53 f
,,--.~------,n.
..,. _,,.,,, +..... -.,..... - -. -
,..,-,,..-...m,
-,,.. - - _ _. -. _. -, _,, - - ~ -
If the answer is the name of a GRADUATE output file, you will get the output shown in Figure 7A; if the answer is the name of a MULDEC or SM0KER output file, you will get the output shown in Figure 78.
In either case, as soon as output begins, you will receive the messags HIT ANY KEY TO STOP As the message implies, hitting any alphanumeric key will stop the file from listing and will generate the prompt LIST ANOTHER FILE?>
If this is answered Y, you return to the PRINTER (P) OR DISPLAY (D)?> prompt; otherwise EXECUTION ENDS appears on the display.
In the event that you enter a name that is invalid, you will receive the message BAD OR NONEXISTENT FILE on the printer and will be prompted for a revised file name.
LIST cannot load I
files from tape, so any files you wish to list must be in memory.
A final problem that may arise is that, if the ATTN key is hit during toe listing of a file on the display, subsequent print operations will be directed to the display. To remedy this, enter PRINTER IS ":PR" or RUN " LIST" 54
r FIGURE 7A REPRESENTATIVE OUTPUT FROM LIST UTILITY FOR A GR FILE (AGES 0 - 45)
N4ME=MLCGP 22 1.98~-003 P(PE=GR 23 1.96E-M3 AGE o 24 1.90E-003 0 2.13E-002 25 1.84E-403 1 8.26E-404 26 1.78E-M3 2 8.26E-404 27 1.73E-003 3 8.26E-404 28 1.75E-003 4 8.26E-G04 29 1.77E-M3 5 4.80E-004 30 1.8E-M3 6 4.80E-404 31 1.82E-003 7 4.80E-404 32 1.85E-M3 8 4.80E-404 33 1.98E-003 9 4.80E-404 34 2.13E-403 10 4.80E-004 35 2.29E-003 11 4.80E-004 36 2.46E-M3 12 4.80E-404 37 2.65E-M3 13 4.80E-M4 38 2.89E-403 14 4.80E-004 39 3.!E-003 15 9.47E-004 40 3.49E-403 16 1.20E-003 41 3.83E-M 3 17 1.51E-003 42 4.21E-403 18 1.68E-403 43 4.62E-M 3 19 1.69E-403 44 5.00E-003 20 1.70E-M3 45 5.59E-M 3 21 1.88E-003 55
FIGURE 78 REPRESENTATIVE OUTPUT FROM LIST UTILITY l
FOR A MUl.0EC Fli.E (AGES 0 - 45)
HAME=MLEMD 21 1.88E-903 1.45E-006 j
TYPE =MULEC 22 1.98E-903 1.9tE-Mi HERDINC=
l M 69 LC 23 1.96E-M3 2.27E-906 l
AGE ebx ter 24 1.99E-903 2.56E-904 0 2.13E-M 2 0 ME+ Me 25 1.84E-903 2.83E-996 1 8.26E-H4 0.00E+ M0 26 1.78E-903 3.0SE-M6 2 8.26E-M4 0.99E+990 27 1.72E-M 3 3.31E-M4 3 8.26E-M4 0.00E+990 28 1.74E-M 3 6.26E-906 4 8.26E-M4 0.09E+ M0 29 1.76E-M3 9.39E-906 5 4.80E-004 0.00E+M0 30 1.79E-H 3 1.24E-985 6 4.00E-M 4 9.NE+M 0 31 1.81E-M 3 1.56E-905 7 4.0E-004 0.NE+990 32 1.83E-M31.89E-M5 8 4.00E-M 4 8. NE+000 33 1.95E-M3 2.73E-M5 9 4.00E-M 4 0. NE+000 34 2.99E-403 3.79E-M 5 le 4.00E- # 4 0. NE+M 0 35 2.24E-M 3 4.80E-905 11 4.00E-464 0.00E+M 0 36 2.40E- # 3 6.94E-M 5 12 4.0E-404 0.00E+000 37 2.57E-M 3 7.44E-M 5 13 4.0 E -464 0.0M +0 M
'38 2.80E-M 3 9.43E-M 5 14 4.00E-404 0. NE+M 0 39 3. N E-M 3 1.18E-M4 15 9.47E-404 0.00E+400 40 3.34E-M 3 1.45E-004 16 1.2E-403 0.00E+M9 41 3.65E-M 3 1.77E-M 4 17 1.5tE-403 0.00E+400 42 3.99E-M 3 2.13E-M 4 le 1.60E-M 3 3.07E-M 7 43 4.37E-M 3 2.44E-004 19 1.6E-M3 6.49E-M7 44 4.8E -903 2.79E-M 4 4s 5 m -pal 1.ter-ma4 56
4 followed by the ATTN key in answer to the first prompt.
Either sequence will reactivate the printer.
This completes the discussion of the LIST utility.
A program listing is given in Appendix A.
4.8 DUPER Utility The last program to be included in the GARR package provides the means for making a backup copy of all the files included in the GARR standard tape (see listing in Figure 8). To run this program, enter copy " DUPER:CA" TO " DUPER" (make sure the GARR tape is in the drive; also make sure at least 16,000 bytes of memory are free before DUPER is copied).
Then enter RUN " DUPER" Several minutes will elapse while the tape drive loads files from tape to memory. The HP-75 will beep when this operation is completed and the message CHANGE CASSETTE (GARR>BACK) AND ENTER Y WHEN READY i
will appear on the printer along with the prompt l
READY?
on the display. When this occurs, remove the GARR tape from the drive, replace it with the tape that will contain the backup copy, and enter Y
to the prompt.
l I
57
Several more minutes will elapse while files are written to the backup tape.
When writing is completed, the HP-75 will beep again and print the message CHANGE CASSETTE (BACK>GARR) ENTER Y WHEN READY and the display will prompt READY?
When this occurs, change cassettes and enter Y
Several more minutes will elapse while the remaining programs are copied to memory. The message to change from the GARR tape to the backup tape is then printed, and the READY prompt appears.
Remove the GARR tape, insert the backup, and enter a final Y.
The tape drive will be busy for a few more minutes. When it stops, the backup tape contains a copy of the GARR tape.
This can be verified by entering CAT ":CA" which allows you to scan the file directory of the cassette.
This completes our discussion of DUPER.
A program listing is given in Appendix A.
4.9 GARR Tape The final section describes the files resident on the GARR tape as created by DUPER.
The listing of files shown in Figure 8 gives the contents of the GARR tape.
The first two files, GRADUATE and MULDEC, contain the GARR programs of the same name. The next, NONSLC, contains a copy of the nonsmoker lung cancer rate file shown in Figure 4.
Following this is SM0KER, which contains the 58
FIGURE 8 OUTPUT LISTING FILES ON STANDARD GARR TAPE
> CAT ":CA-Nane Tn e Len Tine Date
.CRADVATE B 2568 09:18 10/18/83 MULDEC B 2560 16:33 11/01/83 NONSLC B 512 16:44 06/21/83 SM0KER B 5376 16:29 11/01/83 STANDARD B 256 19:22 99/14/83 RABRISK B 6144 11:25 11/07/83 SENS B 768 16:45 11/02/83 NHLC B 768 11:26 11/H/83 NFLC 8 768 13:14 M/19/83 LIST 8 1280 11:46 11/H/83 BUPER B 768 15:34 11/H/83 59
i GARR program of the same name.
The STANDARD file contains a copy of the input file for RADRISK parameters shown in Figure SA.
The RADRISK file contains our risk assessment model. The SENS file contains the age-specific sensitivity file whose listing appears in Figure 58.
The files WMLC and WFLC contain the type of mortality input files required by GRADUATE and MULDEC (WFLC is listed in Figure 1).
Finally, LIST and DUPER contain the GARR utilities of the same names.
Taken together, these files contain all the information needed to work through the examples given in the preceding sections and should enable new users to rapidly verify that they understand how to run the various GARR programs.
4.10 Conclusion This concludes our discussion of GARR on the HP-75.
At this point, the reader has a firm grasp of how to go about constructing radon risk models.
I would I
greatly appreciate user feedback as to the truth of the last statement.
Can you construct input files that work? Is the syntax confusing? Does the SM0KER program provide sufficient flexibility in specifying smoker versus non-smoker populations? Has your favorite radon health risk model been omitted from RADF.ISK? Answers to these questions and any other comments the user may have would be greatly appreciated.
In the meantime, I hope that the present form of GARR is a useful tool for radon risk assessment.
60
m._ _
l i
REFERENCES Archer, V.E., G. Saccomanno, and J.H. Jones, " Frequency of Different Histologic l
Types of Bronchogenic Carcinoma As Related to Radiation Exposure,"
Cancer 34:2056-2060, 1974.
- Axelson, 0., and L. Sundell, " Mining Lung Cancer and Smoking," Scandinavian Journal of Work and Environment 4:46-52, 1973.
I i-Bunger, B.M., J.R. Cook, and M.K. Barrick, " Life Table Methodology for Evaluat-ing Radiation Risk: An' Application Based on Occupational Exposures,"
i Health Physics 40:439-455, 1981.
Chiang, C.L., Introduction to Stochastic Processes in Biostatistics, John Wiley and Sons, NY, 1968.'
Cohen, B.L., " Failures and Critique of the BEIR III Lung Cancer Risk Estimates,"
i Health Physics 42:267-283, 1982.
j Colld, R., and P.E. McNall, Jr. (eds.), " Radon.in Buildings," National Bureau of Standards Special Publication 581, 1980.
Cook, J.R., B.M. Bunger, and M.K..Barrick, "A Computer Code for Cohort Analysis of Increased Risks of Death," United States Enviror. mental Protection Agency; Office of Radiation Programs Technical Report 520/4-78-012, 1978.
i Cox, D.R., " Regression Models and Life Tables (with discussion)," Journal I
of the Royal Statistical Society, Series B, 34:187-220, 1972.
L l-Elandt-Johnson, R.C., and N.L. Johnson, Survival Models and Data Analysis, i
. John Wiley and Sons, NY, 1980, 1
Evans, R.C., " Engineers' Guide to the Elementary Behavior of Radon Daughters,"
- ~
Health Physics 38:1173-1197, 1980.
61
_=.
l Fleiss, J.L., Statistical Methods for Rates and Proportions, John Wiley and Sons,'NY, 1981.
Garfinkel, L., " Time Trends in Lung Cancer Mortality Among Nonsmokers and a Note on Passive Smoking," JNCI 66:1061-1066, 1981.
Harley, N.H., and B.S. Pasternack, "A Model for Predicting Lung Cancer Risks Induced by Environmental Levels of Radon Daughters," Health Physics 40:301-316, 1981.
Harley, N.H., and B.S. Pasternack, " Environmental Radon Daughter Dose Factors in a Five-Lobed Human Lung," Health Physics 42:789-799, 1982.
Hewlett Packard, HP-75 Owner's Manual, Hewlett Packard Company,1982.
1 Hofmann, W., " Dose Calculations for the Respiratory Tract from Inhaled Natural Radioactive Nuclides As a Function of Age II: Basal Cell Dose Distributions and Associated Lung Cancer Risk," Health Physics 43:31-44, 1982.
Hornung, R.W., and S.S. Samuels, " Survivorship Models for Lung Cancer Mortality in Uranium Miners - Is Cumulative Dose an Appropriate Measure of Exposure?"
in Radiation Hazards in Mining:
Control, Measurement, and Medical Aspects, M. Gomez (ed.), Society of Mining Engineers of American Institute of Min-l ing, Metallurgical, and Petroleum Engineers, Inc., NY, pp. 363-368, 1981.
ICRP, " Limits for Inhalation of Radon Daughters by Workers," Annals of the ICRP i,
(Publication 32), Pergamon Press, NY, 1981.
Keyfitz, N., Introduction to the Mathematics of Population, Addison-Wesley, Reading, MA, 1977.
Kunz, E., J. Sevc, V. Placek, and J. Horacek, " Lung Cancer in Man in Relation to Different Time Distribution of Radiation Exposure," Health Physics 36:699-706, 1979.
9 J
i 62
u ---
~ --
Lundin, F.E... J.K. Wagoner, and V.E. Archer, " Radon Daughter Exposure and Respiratory Cancer Quantitative and Temporal Aspects," United States Public Health Service, NIOSH-NIEHS Joint Monograph No. 1, 1971.
Lundin, F.E., V.E. Archer, and J.K. Wagoner, "An Exposure-Time-Response Model for Lung Cancer Mortality in Uranium Miners:
Effects of Radiation Expo-sure, Age, and Cigarette Smoking," in Energy and Health, N.E. Breslow and A.S. Whittemore (eds.), Society for Industrial and Applied Mathematics, Philadelphia, PA, pp. 243-264, 1979.
Morrison, H.I., D.T. Wigle, H. Stocker, and A.J. de Villiers, " Lung Cancer Mortality and Radiation Exposure Among the Newfoundland Fluorspar Miners,"
in Radiation Hazards in Mining:
Control, Measurement, and Medical Aspects, M. Gomez (ed.), Society of Mining Engineers of American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., NY, pp. 372-376, 1981.
NAS, The Effects on Populations of Exposure to Low Levels of Ionizing Radiation:
1980, National Academy Press, Washington, DC, 1980.
NCHS, " Vital Statistics of the United States 1969," Volume II, Mortality, Part A, United States Department of Health, Education, and Welfare Publica-tion No. (HRA) 74-1101, National Center for Health Statistics, Rockville, MD, 1974.
NCHS, United States Decennial Life Tables for 1969-1971," Volume 1, No. 1, l
United States Department of Health, Education, and Welfare Publication No. (HRA) 75-1150, National Center for Health Statistics, Rockville, MD, I
1975.
l l
Peterson, G.R., and L.E. Sever, "An Appraisal of Selected Epidemiologic Issues from Studies of Lung Cancer Among Uranium and Hard Rock Miners," Hanford Environmental Health Foundation Report USUR-02, Hanford, WA, 1982.
i
.I 63
_ =
Radford, E.P., and K.G. St. Clair Renard, " Lung Cancer in Swedish Iron Miners Exposed to Low Doses of Radon Daughters," New England Journal of Medicine 310:1485-1494, 1984.
Thomas, D.C., and K.G. McNeill, " Risk Estimates for the Health Effects of Alpha Radiation," Research Report INFO-0081, Atomic Energy Control Board, I
Ottawa, Canada,.1982.
UNSCEAR, " Sources and Effects of Ionizing Radiation," United Nations Scientific Committee on the Effects of Atomic Radiation 1977 Report to the General Assembly, United Nations, NY, 1977.
USRPC, " Report of the Task Force on Radon in Structures," United States Radia-tion Policy Council Publication RPC-80-002, 1980.
U.S. Public Health Service, " Smoking and Health, A Report of the Surgeon General," United States Department of Health, Education, and Welfare Publication PHS-79-50066, 1202 pp., 1979.
Waxweiler, R.J., R.J. Roscoe, V.E. Archer, M.J. Thun, J.K. Wagoner, and F.E.
i
]
Lundin, Jr., " Mortality Follow-up Through 1977 of the White Underground Uranium Miners Cohort Examined by the United States Public Health Service,"
in Radiation Hazards in Mining:
Control. Measurement, and Medical Aspects, I
M. Gomez (ed.), Society of Mining Engineers of American Institute of Min-ing, Metallurgical, and Petroleum Engineers, Inc., NY, pp. 823-830, 1981.
i Whittemore, A.S., and A. McMillan, " Lung Cancer Among U.S. Uranium Miners:
A Reappraisal," JNCI 71:489-499, 1983.
i Wise, K.N., " Dose Conversion Factors for Radon Daughters in Underground and Open Cut Mine Atmospheres," Health Physics 43:53-64, 1982.
Wright, E.S., and C.M. Couves, " Radiation-Induced Carcinoma of the Lung - The St. Lawrence Tragedy," Journal of Thoracic and Cardiovascular Surgery i
74:495-498, 1977.
64
4 APPENDIX A PROGRAM LISTINGS AND VARIABLE LISTS 65
GRADUATE VARIABLE LIST VARIABLE DES,CRIPTION C1 Step increment C7 Quadratic correction term
- Fl$
Abridged input file name F2$
Output file name I
Loop counter 19 Flag variable J
Loop counter; delimiter K,:K1, X2 Working variables, age-specific probability of death L
Loop counter L1, L2 Loop delimiters
.L9 Life expectancy Q1(18)
Abridged life table Q2(100)
Graduated life table S
Step incrementer (line 510);
years lived beyond 100th birthday (line 830)
S1(18)
Age-specific step increments S9 Survival T7$
Abridged filt title V1 Age variable 4
i
'I f
l 67 4
GRADUATE PROGRAM LISTING 10 ! GRADUATE STANDAPI A 280 Sl(!)=(01(!!/01(I-1) 660 PRINT USING 670 s S 8RIGED LIFE TABLE TO 9 T
)^.2 670 IMGE /*!(85+)= *,dd 0 IM+
290 NEXT I
.ddd/
15 ! FINAL REVISION 10/1 300 S1(18)=(Sl(17)+St(16 680 K1=02(82) 8/83
)+S!(15))/3 690 19=0 20 PRINT USING 30 310 I CORRECT 01 FOR S 7M FOR !=83 TO 99 30 IMGE //**mem*"*
320 FOR !=4 TO 17 710 Kl=Kt*S
- n o m */* GRADUATE LIFE 330 Cl=($1(1)+S1(I+1))/2 720 02(!)=K1 TABLE */******* m m m 340 IF Cl(1.04 THEN C7:0 730 IF 02(!)(1 THEN 780
- ///
9 COTO 370 740 IF 19=0 THEN PRINT U 40 I!M 01(18),02(100),$1 350 C7=.77816+1.57115*C SlHG 750 ; !
(18) 1.79272*Cl^2 750 IMGE /*FIRST I AT r 50 INPUT
- FILE FOR A8 RIG 360 01(I)=C7*01(I)+01(D GE *,ddd./
EB?)*;Flt 370 Vl=(!-1)*5+2 760 19=1 60 PRINT
- INPUT FILE =*3F 3M PRINT USING 390 ; V1 770 02(1)=1 18
.01(D.C7,Cl 780 NEXT I 70 F28=F18&*GR*
390 IMAGE 'u (*,dd,*)=*,
790 PRINT USlHG SM i 02 80 ON ERROR GOSU8 IO N 8 d.dddd/*8=*,d.ddddd/*1=*
(99)
GOTO 50
,dd.ddd/
800 IMGE /*P OF DEATH 1 90 AS$1GN 8 1 TO F18 404 NEXT I M3
- d.ddd/
1M READ 8 1 ; T78 410 ! B0 INTERVALS 2-3 0 810 02(tH)=1 110 READ 0 1 ; 01() 4 AS GES 5-14 820 ! **FINISHEDu..NOW SIGN 4 1 TO
- 420 FOR !=1 TO 2 CHECK LE 120 0FF ERROR 430 L1=5*1 830 $=.8/02(99) 125 BISP
- WORKING
- 440 L2=Ll+4 840 $921-02(0) e L9=S9+0 130 PRINT
- TITLE: *;T78 450 FOR J=Lt TO L2 2(0)*.1 0 PRINT "
460 02(J)=01(I+1) 850 FOR !=1 TO 99 140 l DO INTERVAL 0 AGE 470 NEXT J 864 L9=.5+S9*02(!)+L9 0-1 480 NEXT I 870 S9:S9*(1-02(D) 150 02(0)=01'0) 490 I 90 INTERVALS 4-17 880 L9:L9+S9 160 l DO INTERVAL i AGE AGES 15-82 890 NEXT I 1-4 500 K1=01(3) 9 K2:01(4) 900 IMAGE *LE=*,dd.dddd 170 K (1-01(1))^.25 0 K=
510 S=Sl(4) 910 L9=L9+S9*S 1-K 520 02(15)=K2/S^2 920 PRINT USING 930 ; $9 180 FOR !=1 TO 4 530 02(16)=r2/S 930 IMGE /* PROB 0F SURY 190 02(D=K 540 02(17)42 IVAL*/*TO I M =*,d.ddddd/
2M HEXT I 550 Jul3 940 PRINT USING 9M s L9 210 ! RESCALE INTERVALS 560 FOR !=5 T0 17 954 ASSIGN I 1 TO F28 2-18 570 K!*2 9 K2:01(D
%8 PRINT 0 I s 020 220 I TO ANNUAL A'!ERAGE 584 S=Sl(D 970 ASSIGN 0 1 TO *
(GE0 METRIC) RISK OF 590 J=J+5 0 K=J+4 980 BISP
- EXECUTION ENDS 230 I DEATH AND GET GE9 600 FOR L=J TO E HETRIC INCREMENTS (SI) F 610 K1=K!*S 9 02(L)=K1 990 EMI OR INTERPOLATION 620 NEXT L 1000 PRINT USING 1910 240 01(2)=1-(1-01(2))".2 630 NEXT I 1810 I MGE //*8AD OR NON 250 01(3)=l-(1-01(3))^.2 640 i PREPARE EXTRAP. 83 EXISTENT */* FILE *//
264 FOR !=4 TO 17
-100+
1920 ASSIGN I 1 TO
- 270 Gl(D=1-(1-01(D)".2 650 S=Sl(18) 1934 RETURN l
68
r:
MULDEC VARIABLE LIST VARIABLE ~
DESCRIPTION A$
Answer to prompt line 930 D1(2,21):
Deaths array - converted to probabilities (line 330)
Fl$
General input-file name F2$
Output file name H1$
Heading for output I
Loop counter
~J Loop counter K
Number of specific causes of death (always 1)-
K$
Keyboard variable L1, L2 Loop delimiters M
Loop counter N
Indexvariable(line530), loop counter (line 640)
Q2 Single-year life table; working
. array (line 870)
Q3(2,100)
Multiple-decrement life table
.S.
Additive. step increment S$
Format variable T1(21)
Working array--reads in death data Z
Working variable 69
MJLDEC PROGRAM LISTING 10 S8='/*
334 Il(I.J)=ll(1,J)/Bl(6 6M FOR J=Li TO L2 20 l MULEC CALCULATES P
,J) 690 T3=T3+S 0 03(I,J)=T3 ULTIPLE 344 2 Z-Il(1,J) 700 NEXT J 30 ! ECPEMENT LIFETABLE 350 NEXT I 714 EXT N FROM INPUTS FROM 364 IF Z(4 THEN COTO 114 720 03(1,90)=43(1,97)+$
44 ! E ATH FILE AND OUTF 0
734 GI(I,99)=43(f.98)+S ILE OF GRADUATE 370 ll(0.J)=Z 744 03(I,lM)=l!(!,21) 45 i FINAL REVISION 11/1 3M HEXT J 754 NEXT I
/83 390 INPUT *NEADING FOR 0 764 i CREATE N ATH PR06' 54 PRINT USING 60 UTPUT?P; Hit S BY CAUSE 64 IMAGE //,'***********
440 INPUT '0UTPUT FILE N TM FOR !=4 T0 K
- / CONSTRUCT MUllEC AME?'aF28 700 FOR J=4 TO IM
- /***********e*e****/
410 PRINT "
?M 93(1,J)=03(i.J)*02(J 70 I!M Bl(2,21),02(IM).
420 PRINT '0VTFILE:
- F2
)
fl(21),03(2,lM) 8 900 NEXT J 80 INPUT ' SINGLE YR LIFE 430 PRINT "
010 NEXT I TABLE FILE?)*iF18 444 IISP 'NORK!hC'
$20 f COPY TO OUTFILE AS r
98 PRINT 'MORTAllTY FILE 454 l SCALE E ATH P'S 6 INSTRUCTED
=*>F18 TO IM 930 AS$1GN 8 i TO F28 IM ON ERROR GOSUB 1990 464 FOR !=4 TO K 044 PRIN1 8 i s Hit,K 0 GOTO 80 470 03(1,0):31(1,0) 854 FOR !=4 70 K 110 IMAGE ddd,2X,d.ddde 400 FOR J 1 TO 4 864 FOR Jet TO I M 120 ASSIGN I I TO F18 490 03(1,J)=Di(1,1) 870 02(J) 03(i.J) 130 READ I 1 i 02 0 500 EXT J GM NEXT J 140 AS$1GH I 1 TO
- 514 1 30 INTERVALS 2-3 0 890 PRINT S I ; 020 154 INPUT ' FILE FOR M AT GES 5-14 900 NEXT I N MTA? PJFl8 520 FOR Mal TO 2 918 IISP '90NE*
164 ON ERROR COSUB !!!$
530 L1=5*M 0 L2*Ll+4 0 N 920 INPUT ' LIST MUllEC1) 4 0 GOTO 154
=M+1
- 198
!?$ PRINT "
544 FOR J Lt TO L2 930 IF As=*Y' THEN 950 I M PRINT ' K ATH DATA ';
$$$ 03(I.J)=81(1,H) 944 COTO 1964 Fl8 564 NEXT J 954 IISP ' HIT ANY FEY TO 190 AS$1GN I I TO F18 570 NEXT N STOP' 2M REAR 8 1,35 i K 590 l 30 INTERVALS 4-26; 960 PRINT ' AGE ebs 210 0FF ERROR AGES 15-97 ecx' O PRINT "
220 FOR !=0 TO F 590 S=(Ild,4)-II(1,3))/
970 FOR J=4 TO I M 230 REAR 8 1 ; il O 5
980 K8 KEY 8 0 IF kfO" 244 FOR Jat TO 21 600 03(!,15)=310,4)-263 THEN 1964 250 ll(1,J)=Ti(J) 614 03(1,16)stl(1,4)-S 999 PRINT J 264 NEhi J 620 03(!,17) 31 0,4) 1000 FOR !=0 TO K 270 NEXT I 634 Listi 1910 PRINT USING 1924 ;
280 f SCALE SERTHS TO PR 644 FOR N=5 TO 20 03(I,J):
0 PORTIONS 654 ZrN-1 1929 IMAGE IX,d.dde 290 AS$lGN 8 i TO
- 660 S=(I!(1,H)-II(1,2))/
1934 NEXT I 300 FOR Jet 70 21 5
1944 PRINT USING $$
310 Zal 670 Ll*Ll+5 0 L2*Ll+4 0 1954 NEXT J 315 ON ERROR COTO !!40 T3 ll(1,2) 320 FOR !st TO K 70
MULDECPROGRAMLISTING(continued)
ING I!SP
- EXECUTION EN3 S*
10,'8 CLEAR VARS 1000 END 1999 PRINT USING !!N llN MTURN lite PflNT USING !! N ll N IMAGE /*000 Of NONE XISTANT FILE */
llM RETURN 1140 PRINT USING 1150 llM IMAGE //*FAILES CON SISTANCY CHECK */*0tBER 0 F CAUSES tlRONG9'//
1864 END i
71
t i
i SM0KER VARIABLE LIST s
VARIABLE DESCRIPTION A2, A3 Working variables
.A$.
Answer to prompt line 160 A7$
Answer to prompt line 2080 D(1,8)
Nonsmoker lung cancer death :ates Fl$
General input / output file name-H1$
Headings for output files I
Loop counter J
Loop counter K1, K2 Working constants K
Loop delimiter L
Loop counter L1, L2 Loop delimiters L9 Life expectancy (19 Minimum relative risk of lung cancer, smoker versus nonsmoker N
Flag variable (male, female) 01 Relative risk of l'ung cancer, smoker versus nonsmoker 02 Age-specific SMR P
Proportion of smokers in the population P2 Proportion of deaths which are due to lung cancer.
)
, ?3 Prop _ortion of deaths who were smokers F4 Proportion of deaths who were nonsmokers who died of lung cancer PS?
Proportion of deaths who are smokers who s'
died of lung cancer Q(100)
Working array Q0, Q1 Working mortality variables Q2(1,100)
Nonsmoker multiple decrement lifetable, working _ array (line 1860)
Input and smoker (line 1660) multiple Q3 s
decrement lifetable
-S Multiplicative increment-graduation of 1
.T rionsmoking lung cancer (line 240),
smoker versus nonsmoker SMR j~
(line 660), expected number of. years lived beyond 100th birthday (line 1930)
S9 Smoker versus nonsmoker SMR, survival
>3
>(line 1920) s 1
TJ Additive increment, all-cause SMR o.
U Multiplier for nonsmoker lung cancer Z
Constant equal to 1 29 Counter for age-specific output
.72
SM0KER PROGRAM LISTING 10 ! MKE LUNG CAN.' MULT 260 02(1,45)=K1/S^2 650 PRINT *% SM0KER$=*;P
. DECREMENT LIFE TABLES 270 02(1,46)=K1/S 660 INPUT 'SM0KER VS. NS 20 l NONS.AND SM0K.
2M G2(1,47)=K1
. TOTAL SMR7)*sS 30 PRINT USING 40 290 K2=Bl(N,0) 670 IF S)1 AND S(5 THEN 40 IMAGE //* * * ** * *
- 300 J:43 710 w o n u n*/*SM0K/NONS:L 310 FOR !=1 TO 8 680 PRINT USING 690 ; S UNGC-flVLKC"/*M"HM**
320 K1=K2 0 K2=B1(N,1) 690 IMGE /***ERRORn**
- n w o n***///
330 $=(K2/Kl)^.2
/*SMR=,ddd.ddd/*0UT OF 50 IIM 31(1,8),02(1,100) 340 J=J+5 0 K:J+4 RANGE 1(SMR(5 /
,03(1,100),0(100) 350 FOR L=J TO K 700 COTO 660 64 INPUT
- FILE FOR MUllE 360 K1=K1*S 0 02(1,L)=K1 710 PRINT SMR= *;S C?) *;F1s 370 NEXT L 720 INPUT MIN RELRISK L 70 PRINT *INFILE=*; Fit 380 NEXT I
.C.?)*;M9 80 ON ERROR COSUB 1810 0 390 ! PREPARE EXTRAP. 88 730 IF M9)1 ANI M9(20 TN GOTO 60
-100+
EN 770 90 ASSIGN 0 1 TO Fit 400 K1=DI(N,8) 744 PRINT USING 750 ; M9 -
I M REAR 8 1 : T78,1,03(
410 FOR !=88 TO 99 750 IMAGE /*** ERROR ****
,)
420 K1=Kl*S
/*RELRISK= *,ddd.ddd/*00 lie ASSIGN 4 1 TO
- 430 02(1,1)=K1 T OF RANCE 1(RR(20*/
120 ON ERROR GOTO 2060 444 NEXT I 760 GOTO 720 130 ASSIGN I 1 TO NONSL 454 FOR I=0 TO 44 770 PRINT
- MIN RELRISK-L C-460 FOR J:0 TO 1
.C.=
- M9 Ile READ 6 1 ; 31(,)
470 02(J,1)=03(J,I) 7M IISP *NORKING*
150 ASSIGN 0 1 TO
- 4M NEXT J 790 ! ADJUST INTERYALS 3 155 0FF ERROR 0 N=1 490 NEXT I 5-43 160 IIPUT *MLE OR FEML 500 FOR !=35 TO 44 800 0FF ERROR E?(M/F))*;As 514 IF 03(1,1))02(1,45) 810 T=(S-1)/10 0 S9:1+T 170 IF As= M* THEN H=0 TEN 02(1,1)=92(1,45) 820 L1=35 0 L2=43 180 IF At=*M* THEN PRINT
$20 NEXT I 830 29=40
- SEX = MALE
- ELSE PRINT
- 530 FOR I=86 TO 99 840 ! CALL NESSM SEX =FEMLE*
540 IF 03(1,1)(02(1,1) T 850 GOSUB 1450 182 INPUT MULTIPLIER F0 NEN 02(1,1)=03(1,1) 860 ! NOW 30 44-99 R NONS. LC.7)*;U 550 NEXT I 870 T=0 0 S9:S 104 IF U(.5 OR U)3 THEN 560 02(1,1M )=03(1,100) 880 L1=44 0 L2=99 186 ELSE 190 570 ! GRABUATION OF NONS 890 1 CALL NESSM 186 PRINT USING 188 ; U
. L.C. COMPLETE 900 GOSU8 1450 0 COTO 182 500 !
910 1 30 INTERVAL 1M N0 180 IMGE /*** ERROR ***
590 ! BEGIN SM0KE-N.S. C NSM0KERS IST
/*U= *,dd.ddd/*0UT OF RA ALC.
920 00:02(0,99)+02(0,98)
NCE.5(U(3*/
600 INPUT
- STARTING P OF 930 0t=92(1,99)+02(1,98) 190 PRINT *U=
- U SM0KER$?)*;P 944 02(0,100)=00/(00+01) 195 i SCALE RATE TO PR08 610 IF P).1 A M P(.9 THE 950 02(1,100)=1-02(0,100 200 FOR I=0 TO 8 N 650
)
210 31(N,1)=31(N,1)/1000 620 PRINT USING 630 ; P 968 00:03(0,99)+03(0,98) et e ll(N,1)=ll(K,I)*U 630 IMGE /*** ERROR ****
970 01-03(1,99)+03(1,98) 220 EXT I
/* P=,ddd.ddd/*0UT OF 980 03(0,100)=00/(00+01) 230 ! 30. AGES45-100 RANGE.1(P(.9 /
998 03(1,l M )=1-03(0,100 240 K1=ll(N,0) e K2=Bl(N 640 GOTO 600
)
,1) 0 $=(K2/K1)".2 73
SM0KERPROGRAMLISTING(continued) 1000 FOR !=39 TO 99 STEF 1330 PRINT I 1 ; H!s,Z 1680 IF O!(M9 AND I)45 T 10 1340 FOR !=0 TO 1 NEN 03(1,1)=M9*02(1,1) left A2:02(0,I)+02(1,1) 1350 FOR Js0 TO 100 1690 ! GET SM0KER BACKGP 1920 IF A2>1 TEN PRINT 1360 0(J)=03(I,J)
OUND
- N.S. P)1 AT AGE *;I 1370 NEXT J 17M 03(0.I)=00-03(1,1) 1830 93=03(0,1)+03(1.D 1386 PRINT 01 ; 00 1710 $9=S9+T.
1944 IF A3)! TEN PRINT 1390 NEXT I 1720 Mal-M 0 01:1-01
- SMIKER P)! AT AGE *;I 14M ASSIGN 0 1 TO
- 1730 P=P*00/(P*00+(1-P)*
1950 01:03(l,I)/02(1,D 1418 GOSUB 1840 01) 1968 02=A3/A2 1420 IISP *EECUTION END 1740 0(I)=P 1970 PRINT USING 1980 ;
S*
1750 IF 29)! THEN GOTO 1 I,92,A3,01 1430 CLEAR VARS 790 1000 IMAGE /* AGE =*,ddd/*
1440 END 1760 PRINT USING 1770 ;
P. 0F I.-N.S.=*,d.dde/*P 1450 IF LD35 THEN 1480
-I.P
. OF 3.-S.=*,d.dde/*R.R.
1460 PRINT "
1770 IMAGE
- AGE =,dd,2X,
-L.C.=*,d.dde 1470 PRINT *t SM0KERS VS P=*d.dde 1990 PRINT USING !! N 3
. AGE-1780 29:29+10 02 1488 FOR !=L! 10 L2 1790 NEXT I
!!00 IMAGE 'SMR(TOTAL)**
1490 ! FIN 3 TOTAL DEATN 1800 RETURN
,d.dde/
P-GEN POP 1810 PRINT.USING 1820 lite NEXT I 1500 00:03(0,I)+03(1.D 1820 IMAGE //* BAD OR NON 1120 Z=1 1514 I FIND TOTAL K ATH EXISTENT FILE *//
!!30 1 PREPARE TO OUTPUT P-NONS.
1830 RETURN 1140 INPUT
- E A3!NG FOR 1520 01:08/(1-P+S9*P) 1840 ! FINB LIFE EXPECTA NONS.?)*;Mit 1530 ! GET SACKGROUHF N0 NCY NONS.;SM0K.
!!50 INPUT
- FILE NAME F0 NS.
1858 FOR J=0 TO 100 R NONS.?)*;Fl*
1540 02(0,I)=01-02(1,0 1860 02(0.J)=02(1,J)+02(
1160 ASSIGN 0 1 TO F18 1550 l FIND % KATHS BUE 0,J) 1170 IISP
- WORKING
- TO L.C.
1870 02(1 J)=03(0,J)+03(
1100 PRINT *NONS. FILE =*
1560 P2:030,D/06 1,J)
- Fl$
1570 ! FIND % IEATNS WHO 1880 NEXT J 1190 PRINT I 1 ; NI$,2 SM0KE 1890 PRINT USING 1900 1200 FOR !=0 TO 1 1500 P3=P*01*S9/00 1900 IMAGE /* LIFE EXPECT 1210 FOR Jat TO 100 1590 i FIND % KATHS N.S ANCIES*/*NONSM0KERS FIRS 1220 0(J)=92(I,J)
. -L. C.
T*/
1230 NEXT J 1600 P4=(1-P3)*02(1,D/(
1910 FOR !=0 TO 1 l
_1240 PRINT I 1_; 00 02(0,D+020,D) 1920 L9=0 0 S9=1 1250 EXT I 1610 ! FIND % DEATH SM.-
1930 S=1/02(1,99) 1260 ASSIGN 0 1 TO
- L.C.
1940 FOR J=0 TO 99 1270 INPUT *NEASING FOR 1620 P5=P2-P4 1950 L9=L9+.5eS9*02(1,J)
SMOK.?)*;M18 1630 I FINI P. OF BEATM-1960 S9=S9*(1-02(I,J))
1200 INPUT
- FILE NAME F0 TOTAL FOR SM0K.
1970 L9=L9+S9 R SM0K.7)*;Fi$
1640 00=S9801 1980 NEXT J 1290 ! SU0 ROUTINE NESSM 1650 i FIN 3 P. OF 3. SMO 1999 L9=L9+S9'S.4*02(1, 1300 ASSIGN 0 1 TO F18 KER-L.C.
8) 1310 IISP
- WORKING" 1666 03(1,D=00*P5/P3 2000 IMAGE *LE: *,dd.dd 1320 PRINT *SM0K. FILE *'
1670 01=43(1,D/02(1,D
=;Fl$
74 a
.-m i-
w
=
w
- - -----+i -
m.,r um-vi
-- - -.--r
-n---
SM0KERPROGRAMLISTING(continued) 2010 PRINT USING 2000 ;
L9 2020 IMAGE
- PROB. OF SUR VIVAL */,*TO 100=,d.dde
/
2030 PRINT USING 2020 i S9 2640 NEXT I 2050 RETURN 2060 PRINT "
2070 PRINT *NONSLC INYAL ll OR MISSINC*
2075 PRINT "
2000 INPUT *LOAB FRON 09
?)*;A78 2998 IF A78="Y* THEN 210 0 ELSE 2130 2100 PURCE *NONSLC' 2110 COPY *NONSLC:CA* TO
- NONSLC' 2120 COTO 130 2130 IISP
- EXECUTION END S*
2140 EMB l
l 1
1 75
RADRISK VARIABLE LIST VARIABLE DESCRIPTION A
Loop counter A0 Age at first risk A3 A0-1 A5 Age at last exposure A9 Age at first exposure A3$
Answer to prompt line 110 C0 Lung cancer death probability C2 Baseline lung cancer deaths C8 Excess lung cancer probability C9 Lung cancer death probability D0 Dose variable D1 Baseline lung cancer deaths RR and AR Models D2 Excess lung cancer deaths RR and AR Models D9(100)
Dose array E8 Excess lung cancer mortality E9 Total lung cancer mortality F$
General input file name F4$
File name - error handling subroutine F7$
File name - sensitivities file.
G9 Coefficient for exponential correction H5 Dose range delimiter H6 Dose range delimiter I
Loop counter J
Loop range delimiter-dose subroutine K0 Age at first exposure plus latency K1 Loop range delimiter
-K2 Loop range delimiter K6 Working variable MS Model specifier flag M$
Model indicator for output LO Life expectancy L1 Life expectancy L2 Loss in life expectancy Q(1,100).
Life expectancy L9 Multiple-decrement life table QS-Probability of death at age 100 Q9 Total age-specific probability of death 76
VARIABLE DESCRIPTION R1 Relative risk coefficient R2 Absolute risk coefficient R9 Local risk coefficient R5$
Answer to prompt line 710 SO Survival S7(100)-
Sensitivity array S9 Survival S$
Answer to prompt line 2170 S7$
Answer to prompt line 790 T7 Latency W1 Exposure in WLM/ year Y1 Approximate number of years lived beyond the 100th birthday Z
Number of excess causes of death.
(Always 1) 27 Flag variable Z$
Answer to prompt line 1110 l
77
RADRISK PROGRAM LISTING le i FINAL VERSION 11/1/
258 IF A3* O*K THEN 270 564 GOTO 520 83 268 IMPUT
- AGE AT FIRST 570 i GET LATENCY 20 ! RAly)N RISK CALCULAT EXPOSURE?) *;A9 5M IF A380 K" THEN 600 ION FOR RBSOLUTE AIG REL 270 IF A9(9 THEN A9=0 590 INPUT LATENCY IN YE ATIVE RISK 280 IF A9)99 THEN A9=99 ARS?> ;T7 30 ! SM0KERS,NONSM0KERS, 290 IF 27:1 THEN 310 600 IF T7)=0 AND T7(46 T ANI GENERAL POP.-MALES 300 IF A3$ 0 K THEN 330 HEN 640 ANI FEMALES 310 INPUT
- AGE AT LAST E 610 PRINT USING 620 ; T7 40 IMAGE //* RADON RISK M XPOSU2E?) *;AS 0 GOTO 570 03EL*//?R.R. 00EF=*,d.dd 320 27=0 620 IMAGE / LATENCY (,dd e,*/WLM*/*0PTION=*,h/*A 330 IF A5(1 THEN A5=0 d.ddd,*)*/*00T OF BOUNDS
.R.=*,d.dde,*/PY/WUl*
340 IF A5>100 THEN A5:10
- 0(=T7(46-50 IMAGE
- AGE AT F.E.=*,
0 630 ! GET CONTINUGUS EXP ddd/* AGE AT L.E.=,ddd/*
350 IF A9(=R5 THEN 410 OSURE M CONVERT TO WLM AGE AT FIRST RISK =*,ddd 360 PRINT USING 376 ; A9 640 IF A380*K" THEN 660 60 IMAGE *NLM PER YR.=*,
,A5 654 INPUT *RNNUAL EXPOSU dd.dde/* LATENCY =*,dd/ EX 370 IMAGE /* AGE F.E.(*,d RE IN WLM?) *iW1 PONENT COR=*,dd.dde dd,*D AGE L.E.(*,ddd,*)
660 IF Wl(0 GR WD99 THE 70 SHORT 99(100),S7(100)
N 670 ELSE 700 N IIM 0(1,108) 380 27=1 670 PRINT USING 680 ; Wt 90 C9=0 398 GOTO 260 600 IMAGE /* EXPOSURE LE let 27=0 400 ! CET RISK COEFFICIE VEL (*,dd.dde,*)*/*0UT OF lit INPUT
- INPUT: KEYBL.
HTS 80VHBS; 0(W1(100-(K) OR FILE (F)?) *;A38 410 IF A380*K* THEN 430 690 COTO 650 i
120 IF A38=*K" THEN tie 420 INPUT
- RISK /WLM-R.R.
700 IF A380*K* THEN 720 i
130 ON ERROR G0SUB 2130
?> *;RI 710 IF UT
- EXPONENTIAL C 0 COTO !!0 430 IF RI)=0 ANI Rl(.2 T ORRECTION?) *;R5$
140 I WUT
- FILE NAME?) -
HEN 470 720 IF R5$ 0*Y THEN 780
- F$
440 PRINT USING 450 ; R1 730 IF R3$ 0*K* THEN 750 150 IF F$=*NONE" THEN A3 450 IMAGE /* RELATIVE RIS 740 INPUT EXPONENT =?) -
$="K" K(,d.dde,*)*/*00T OF B0
- G9 l
160 IF A3*=*K* THEN 210 UNIS; 0(#1(.2*
750 IF C9(0 AND C9).2 T 170 ASSIGN 0 1 TO F$
464 COTO 420 HEN 780 100 REA8 0 1 ; A0,A9,A5, 470 IF Rl:0 THEN M8=*
- 760 PRINT USING 770 ; C9 R1,Rs,R2,T7,W1,R58,G9,S7 0 GOTO 510 0 GOTO 740 8,F7$
475 IF A380*K THEN 490 770 IMAGE /* EXPONENTIAL (
190 ASSIGN 0 1 T0
- 6 Or 480 INPUT R.R. OPTION (P
- dd.ddE,*)*/*0UT OF BOU F ERROR
,E,0R B)?) *;MS NBS;.2(G9(0*
l 200 IF A380*K* THEN 220 490 IF R$=*M* OR Ms=*E-780 TF A380*K THEN 800 l
210 IW UT
- AGE AT FIRST THEN 510 790 INPUT *RGE SPECIFIC l
RISK?) *;AS 500 M*= B' SENSITIVITIES?) *;S78 j
i 220 IF A6(5 OR AG)50 THE 510 IF A380*K" THEN 530 000 IF S7$ 0*Y THEN 894 l
N 230 ELSE 250 520 INPUT
- RISK /WLM/PY-9 010 ON ERROR GOSUB 2130 230 PRINT USING 240 ; AS
.R.?) *;R2 0 GOTO B30 e GOTO 210 530 IF R2)=0 ANI R2(.000 820 IF Alf0*K" THEN 840 i
l 240 IMAGE /* AGE AT FIRST 2 THEN 570 830 INPUT
- FILE FOR AGE l
RISK (*,ddd,*)*/*0UT OF 540 PRINT USING 550 ; R2 SENS.?> ";F78 l
GOUN3S; 4(96(51' 550 IMAGE /* ABSOLUTE RIS 840 IF F?$=*NONE THEN 8 l
K(*,d.dde,-)*/*0UT OF BH 90 ELSE F$=F78 IS; 0(R2(2E-4*
78
RADRISK PROGRAM LISTING (continued) 850 ASSIGN 0 1 TO F$
1150 PRINT "
1460 PRINT USING 1470 ;
860 READ 8 i ; $7()
1160 ! DO SURVIVAL TO AG N$,L9,L2,D2 870 ASSICH I 1 TO
- 6 0F E AT FIRST RISK 1470 IMAGE *RELRISK MODE F ERROR 1170 K0=R9+T7 L,n/*L.E.=*,dd.ddd/*L 880 COTO 920
!!80 IF K0(100 THEN 1210 OSS LE(MONS)=*,ddd.dd/*D 898 FOR !=0 TO 100 1190 PRINT USING 1200 9
/10^5=*,ddddd.d 900 S7(I)=1 COTO 1690 1480 PRINT USING 1490 ;
918 NEXT I 1200 IMAGE //*NO RISK */
D1 920 PRINT **n H
- u** n e
- ACE AT FIRST*/* RISK C.E 1490 IMAGE
- EXCESS B/10^
nu n * *
. 100*/
5=*,ddddd.d//
936 PRINT ***n n u e n**
1210 Kl A9 1500 ! THEN DO EXPONENTI
- nn u
- 1220 R3=A0-1 AL YERSION-R.R.
940 PRINT USING 40 ; R1, 1230 IF K0)A3 THEN K2=K0 1510 IF M8=*M* THEN 1560 Ms,R2 ELSE K2=R3 ELSE 1520 958 PRINT USING 50 ; A9, 12 4 S9=1 9 L9=0 9 C9:0 1520 L9:Le 8 S9:S6 0 C9:
A5,AS 1250 GOSUB 1740 C6 9 C8=0 0 R9:R1+1 0 M5 960 PRINT USING 60 ; WI, 1260 ! DO BASELINE K2+1
=3 9 M8=*E' T7,C9 TO 99 1530 COSUB 1900 970 IF S7$=*Y* THEN 990 1270 K1=K2+1 1540 PRINT USING 1470 ;
980 PRINT
- SENSITIVITY =1 1280 Se=S9 9 L9=L9 6 C0=
H$,L9,L2,D2 0 COTO 1000 C9 0 K2=99 1550 PRINT USING 1490 ;
1290 GOSUB 1740 D1 F7$
1300 ! FINISH BASELINE 1560 ! B0 A.R. M0 EEL 1000 PRINT *****n u n**
1310 Yl=.8/09 1570 IF R2=0 THEN 1640 up ***
- 1320 L9:L9+S98Y1 1580 L9:Le 9 S9=SO 9 C9=
1920 FOR A=1 TO 66 1330 C9=C9+S9*0(1,100)
C0 0 C8=0 9 R9=R2 9 M5=1 1930 ! CET POPULATION 1340 L1=L9 9 C2=C9*10000 1590 COSU8 1900 1940 DN ERROR GOSUB 2130 0
1600 PRINT USING 1610 ;
e GOTO 1968 1350 PRINT USING 1360 ;
L9,L2,92 1950 PRINT *** * * *****
L1,02 1610 IMAGE *ABSRISK MODE enen **
- 1360 IMAGE
- BASELINE */*L L*/*L.E.=,dd.ddd/* LOSS 1960 INPUT
- FILE NAME F0
.E.=*,dd.ddd/*BEATHS/le^
LE(MONS)=*,ddd.dd/*D/10^
R IMPUT?\\ *;F$
5 -LC=*,ddddd.d//
5=*,ddddd.d 1965 IF F$=* NOME
- THEN 1 1370 ! CET DOSE DISTRIBU 1620 PRINT USING 1630 ;
690 TION BY AGE 31 1978 RSSIGN I 1 TO FS 1380 IF A)1 THEN 1400 1630 IMAGE
- EXCESS D/10^
1000 REAI 8 1 ; H$,Z 0(,
1390 GOSUB 2250 5=*,ddddd.d//
)
1400 ! NOW 90 R.R. MODEL 1640 INPUT *RUN ANOTHER 1999 RSSIGN 8 1 TO
- 1410 ! MULTIPLICAT!YE YE POPULATION? *;A$
1100 0FF ERROR RSION FIRST 1650 IF R$=*Y THEN 1660 1110 IMPUT
- PURGE INPUT 1420 IF Rl=0 THEN 1560 ELSE 1670 FILE?) *;Z$
1430 IF M8=*E' THEN 1510 1660 NEXT A 1120 IF Z$=*Y THEN PURG ELSE 1440 1670 PRINT *** n u*en**
E F$
1440 L9:Le 8 S9=SO 4 C9=
nonen*
1130 IISP *NORYING*
C0 0 C8=0 0 R9=RI O M5=2 1680 F=3 1140 PRINT
- POP.*;A;*=*;
e Nt=*M-F8 1450 COSUB 1990 79
RADRISKPROGRAMLISTING(continued) 1690 INPUT *NEW INITIAL 2060 C9=C9+S9*E9 2400 G9=EXP(G9)
CONIITIONS?) *iAt 2070 L9=L9+S9*Y1 2410 N =W1*S7(A9)*C9'T7 1700 IF A$=*Y' THEN 90 E 2000 L2=(L1-L9)*12 2420 FOR !=HS TO K2 LSE 1710 2090 31=C8*1M MS 2430 39(D=M 1710 IISP *EXECl! TION END 21 M 32=C98100000 2440 M= N*G9 S*
2110 RETURN 2454 IF DH6 THEN 2470 1728 EHI 2120 ! ^"^^^^^""^
2460 N= M+W1*S7(I-T7)*G 1730 1 ^"""""^^""
2130 ! ERROR HANILING F0 9^T7 1740 l SU8 ROUTINE LC BAS R MTA INPUT 2470 NEXT I E
2140 PRINT ".
2400 IF P5=1H AND H5(18 1750 IF KD0 THEN 1800 2150 PRINT
- FILE ;F$i*
O THEN 2500 ELSE 2490 1760 09=0(0,0)+0(1,0)
???*
2490 N= N*G9^(95-1) G G 1770 S9=S9*(1-09) 2160 PRINT "
0TO 2580 1780 L9=L9+09*.1+S9 2178 INPUT *0N CASSETTE?
2500 J=IP(95+.5)-l 1790 K!=Kl+1
) *;S$
2510 IF J<1 THEN 2580 1000 FOR I K1 TO K2 2128 IF StD*Y' THEN 223 2520 FOR !=1 TO J 1810 09=0(0,D+0(1,D 0
2530 K6=I-T7+99 1820 L9=L9+09eS9*.5 2190 F4$=F$t*:CA*
2540 IF K6)lM THEN K6=1 1930 C9=C9+S9*0(1,D 2200 PURGE F8 09 1848 S9=S9*(1-09) 2210 ON ERROR COTO.1710 2550 M=30*G9 1950 L9=L9+S9 2220 COPY F48 TO F8 2560 N= M+W1*S7(K6)*G9^
1968 NEXT I 2230 RETURN T7 1870 RETURN 2240 ! ""^^^^^""^^^
2570 NEXT I 1000 ! "^"^^"^^^^"*
2250 ! DOSE SU8 ROUTINE 2500 39(I M )= M 1890 ! RISK SUBROUTINE 2260 05:0(0.99)+0(1,99) 2590 RETURN j
1900 FOR !=K1 TO K2 2270 05=.8/05 l
1918 IF M5(2 THEN K9=1 E 2280 M =W1*S7(A9) 0 H5=A l
LSE K9=0(1,D 9+T7+1 0 H6=A5+T7 1920 IF M5(3 THEH E8=B9(
2290 IF R58=*Y' THEN 240 D*R98K9 ELSE E8=(R9^t9(
0 D-1)*K9 2300 FOR !=H5 TO K2 l
1938 E9=E8+0(1.D 231019(D=M 1940 09=0(0,D+E9 2320 IF DH6 THEN 2340 1950 L9=L9+09eS9*.5 2330 M= M+Wi*S7(I-T7) 1960 C8=C8+S9*E8 2340 NEXT I l
1970 C9=C9+S9*E9 2350 IF A5=l M AND H5(18 1900 S9:S9*(1-09) 0 THEN 2370 ELSE 2360 1990 L9:L9+S9 2364 39(100)=39(99) O CO 2000 NEXT I TO 2590 2010 Yl=.8/99 2370 19(100)= M+05*W1*S7 2020 IF M5(2 THEN K9:1 E (100)
LSE K9=0(1,1# )
2380 GOTO 2590 2030 IF M5(3 THEN E8=39(
2390 1 EXPONENTIAL CORRE 100)*R9*K9 ELSE E8=(R9^D CTION i
9(!M)-1)*K9 2400 G9=EXP(G9) 2040 E9=E8+0(1,100) l 2050 C8=C8+S9*E8 t
80
l LIST VARIABLE LIST VARIABLE DESCRIPTION Al$
Reply to prompt line 120 D$
Reply to prompt line 30 F$-
Input file name H$
MULDEC heading I
Loop counter J
Loop counter
_.K.
Loop delimiter--read from MULDEC file
. K$
Keyboard variable Q(100)
Array for GR file S$(1,100)
Array for MULDEC file Q3 Format string 81
LIST PROGRAM LISTING 10 ! LIST UTILITY FOR G4 320 IMAGE IX,d.dde/
RR 330 HEXT J.
20 DIM Q(100),03(1,100) 340 RETURH 25 PRINTER IS :PR-350 ! "^"^"^"^""^ ^
30 INPUT PRINTER (P) OR 360 !
BISPLAY(D)?) ;B$
370 ON ERROR COSUB 580 0 40 IF D$= B* THEN PRINTE GOTO 60 R IS
- 375 RESTORE I 1 60 INPUT
- FILE NAME?)*;F 400 READ I 1 ; H$,K,03(,
)
70 GOSUB 200 410 ASSIGN I 1 TO
- 120 INPUT LIST ANOTHER 429 0FF ERROR FILE? ;Al$
425 PRINT
- TYPE =MULBEC-130 IF A180 Y" THEH 170 430 PRINT ** 9 PRINT HE 140 PRIHT USING 150
' ABING=* O PRINT H$ 6 PRI 150 IMAGE ///
NT "
160 GOTO 25 440 S$= /-
170 BISP
- EXECUTION ENDS 450 BISP HIT ANY KEY TO STOP-175 PRINTER IS :PR-460 PRINT AGE tbx 18e END tcx 0 PRINT -
190 t ""^""^""^"^
470 FOR J=0 TO 100 200 OH ERROR GOSUB 370 9 475 NAIT.2 GOTO 340 480 K$= KEY $ 9 IF K$()"
210 PRIHT " 9 PRINT HA THEN 560 ME=*;F$
490 PRINT J; 220 ASSIGH I 1 TO F8 500 FOR I=0 TO K 230 READ I 1 ; Q()
510 PRINT USING 520 ; 03 24011SSIGN I 1 TO * -
(I,J);
245 IRINT -TYPE =GR O PR 520 IMAGE 1X,d.dde INT "
530 NEXT I 250 0FF ERROR 540 PRINT USING S$
260 BISP HIT ANY KEY TO 550 NEXT J STOP-560 RETURN 270 PRINT ACE ex 4 P 570 ! """^^^"^"""
RINT "
580 ! ERROR HAMBLING SUB 280 FOR J=0 TO 100 590 PRINT USING 600 285 NAIT.2 600 IMAGE / BAB OR N0 HEX 290 K$= KEY $ 0 IF K$()"
ISTENT FILE */
THEN 340 610 RETURN 300 PRINT J;
)
310 PRINT USING 320 ; Q(
J) i 82
DUPER VARIABLE LIST VARIABLE ~
DESCRIPTION D$
Reply to prompts lines 130, 230 F$
Internal file name G$
Cassette file name I
Loop counter K
Loop counter e
I i-t 83
DUPER PROGRAM LISTING 10 ! IUPER COPIES GARR T 0 BACKUP TP'E 20 FOR K=1 TO 2 30IFK=1THENRESTORE2 90 ELSE RESTORE 300 40 FOR I=0 TO 4' 50 READ F8 60 G$=F86 :CA*
70 ON ERROR GOSUB 270 0 GOTO 80 et COPY G$ TO F$
90 NEXT I 100 IF K=1 THEN RESTORE 290 ELSE RESTORE 300 110 BEEP 0 BEEP O BEEP 120 PRINT
- CHANGE CRSSET TE (GARR)6ACK) AND ENTER Y NMEN READY" 130 IMPUT *REABY?*iB$
140 FOR I:0 TO 4 150 READ F$
160 COPY F$ TO :CA-170 PURGE F$
180 NEXT I 190 IF K=2 THEN 240 200 BEEP O BEEP O BEEP 210 PRINT USING 220 220 IMAGE *CNQNCE CASSET TE (BACK)GARR)*/* ENTER Y NMEN REABY' 230 INPUT *REABY?*;D$
240 NEXT K 250 COPY *)UPER TO *:CA 260 END 270 PURGE F$
200 RETURN 290 MTA GRABUATE, NUL K C', NONSLC*,*SM0KER,-
STAMBARD*
300 MTA "RABRISK*, SENS
- *NMLC*,*NFLC,* LIST-i
- U.S. GOVEB10ENT FRINTING OFFICE: 19A4-421-299 3 338 84
NRC PonM 335 (7773 U.S. NUCLEAR REGULATORY COMMl8840N
- 1. REPORT NUM8E R (Ass,pved by DDC)
BIBLIOGRAPHIC DATA SHEET NUREG-1029 7
- 4. TITLE AND SUBTITLE (Add vobme Na,if appicierrear)
- 2. (Leeve elet*J A Computer Code for General Analysis of Radon Risks (GARR) r
- 3. RECIPIENT'S A ESSION NO.
- 7. AUTHOH(Si
- 5. DATE REPO[T COMPLETED M. Ginevan
/
l vEma Monm September 1984 I
- 9. PERFORMING ORGA ZATION NAME AND MAILING ADDRESS (include I,a Code /
DATE IdPORT ISSUED MONT l YEAR Division of Radi ion Programs and Earth Sciences sap *amha" ion Office of Nuclear egulatory Research 8I,*"'*"*'
O.S. Nuclear Regul tory Commission wachinntnn. nc 9rm45 8 A "' *'" * >
- 12. SPONSO' RING ORGANIZATION MAME AND MAILING ADDRESS (include I,a codel p
Same as 9.
$. 11. CONTRACT NO.
/
- 13. TYPE OF REPORT PE RICO COhE RED (/nclusere asses /
Technical Report
[
- 15. SUPPLEMENTARY NOTES
/
- 14. (Leave DIst&J
- 16. ABSTR ACT 000 words or less) t{l
.9 Evaluating the level of lung cancer risk associated with a given level of radon-daughter exposure is a complex mitte'r. There is the question of whether one's risk assessment should apply absolute risk models or relative risk models and, even when a general model fornit as been selected, there are decisians as to the exact form of risk proj tion, the appropriate method of accounting exposure ove. time, and how snuch a rsonal habit such as smoking can modify risk. This document presents a comp er model for general analysis of radon risks that allows the user to"specify a rge number of possible models with a small number of simplejommands. Thegmodel is written in a version of BASIC which conforms closely to the Ameri n National Standards Institute (ANSI) definition for minisnal BASIC and thu is readily modified for use on a wide variety of computers and, in particular, ' crocomputers.
ilila il
- 17. KEY WORDS AND DOCUMENT ANALYSIS 17a. DESCRif' TORS Radon, Cigarette Smoking, Q
Lifetables, Risk Assessment, 4
Microcomputer, Lung Cancer.
/I Computer Flodel ly El 17b. IDENTIFIERS /OPEN END63 TERMS f
18 AVAILABILITY STATEMEN) f
- 19. SECURITY CLASS (T* s reporrt 21 NO OF PAGES Unclassified Unlimited 2o SECURITY CLASS (Th,s py/
22 PRICE NEC F ORM 33$ (7 77)
r I',
UNITED STATES rouarw< tass rait mstact a rets raio NUCLEAR REGULATORY COMMISSION w$$".. [ c.
WASHINGTON, D.C. 20555 et nuir m. in OFFICIAL SUSINESS PENALTY FOR PRNATE USE. s300 120555078877 1 1ANIRH US NRC h0[fy Y DF Ttoc g
W S01 PU8 NGT BR-PDR N WA sh INGTON DC 20555
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