Tobacco Documents Online

Evaluation of Suitability of Using Fontham et. al. (1994) Study to Derive a Dose Response Model for Environmental Tobacco Smoke Background In order to estimate the potential lung cancer risk associated with a specified exposure to environmental smoke ( ETS) a mathematical model must be derived. Such a model which relates the increase in the absolute lung cancer risk to an assumed time dependent ETS exposure is referred to as a dose response model. In order to derive such a model information demonstrating that lung cancer rates increase as ETS exposure increases must be available. For such information to be useful the observed trend must also be statistically significant (i.e. the probability is small that the observed positive trend was as large as it was without a real ETS effect being present. ) Dr. Steven Bavard Office of Health and Environmental Assessment EPA. who is the federal governments primary scientist working on ETS cancer effects analysis. expressed the strong opinion that the best evidence for an lung cancer risk trend is supplied by the Fontham et. al. (1994) study. The single most meaningful part of this study was believed to be the subset who were exposed to ETS as a child. were self- responders (i.e. were the source of their own exposure estimates to ETS rather than spouse or relative), and the cases were defined as having any type of lung cancer. The specific analysis on this subpopulation regarded as most relevant had the odds ratio adjusted for age, race, study area, fruit consumption. vegetable consumption. supplementary vitamin index, dietary cholesterol. family history of lung cancer. The independent variable was a composite measure of ETS exposure obtained on the job, in the home, and in social settings. The adjusted odds ratio with 95% confidence limits for each of five exposure range categories is displayed below in Table 1. This information is taken from Fontham et. al. (1994)-Table 8. Table 1- Evidence Considered by EPA to be the Strongest Indication of a ETS Related Trend Smoke-Years of Exposure During Adulthood 97.5% Upper Bound Adjusted Odds Ratio 2.5% Lower Bound None (0) --- 1.0 --- 1-11 (6) ~.21 1.85 0.66 12-28 (20) 8.05 2.99 1.11 29-47 (38) 9.00 3.33 1.23 >47 (58) 10.42 3.83 1.41 The purpose of the following analysis is to explore the reasonableness of using the above data set or similar data sets in the Fontham et. al. (1994) study to derive a dose I

response model for ETS. The tirst step will be to explore the validitv of the claimed positive trends. Evaluation of Observed Positive Trends Several factors make it difficult to directiv evaluate the validity of the trend test for this data set. First. the complete data set for each individual (except identification information) is required to run an exact statistical test for a trend. Second a reference to the exact statistical test that was used in obtaining the noted "Trend P=0.001" values was not specified. However with the given data in the published paper and several reasonable approximations-assumptions it is possible to evaluate the observed trend in a preliminary manner. Non Parametric Trend Test Without making additional assumptions about the information in Table I the only test of the null hypothesis that smoke-years of ETS exposure has no effect on the odds ratio that is possible to make is nonparametric in form. We ask the question if there was no effect of ETS what is the probability that the five odds ratios were in ascending order of ETS exposure. In total there are 5! = 120 possible orderings of the five odds ratios. Out of these 120 orderings the single ordering that was most consistent with a monotonically increasing trend was observed. Thus under the null hypothesis the probability of this occurring by pure chance is p=1i 120=0.00833<0.01. This suggests that unless a classification bias or a monotonic association with a lung cancer confounder exists, the null hypothesis should be rejected. In other words the data is consistent with a positive trend due to ETS that can not be explained by random variabilitv. Statistical Significance of Adjacent Log Odds A very stringent criteria for assessing whether a trend exists is that each log odds in ascending order of ETS exposure is statistically significantly greater than the previous log odds. If this was found to be the case. there would be very little question that a real ETS effect existed. To Perform such a test with the published data it is necessarv to assume that the log of the odds ratio is normally distributed with variance that can be estimated from the length of the given confidence intervals. It follows directly from the definition of a confidence interval for a normal random variable that the standard error can be expressed as 6= in[Odds Ratio 97.5% Upper Bound/Odds Ratio 2.5% Lower Bound]/(2* 1.96) and by definition the variance of the log odds ratio is V=a, . Based on this approach the variance for each of the odds ratios is calculated. Using the additional assumptions discussed in Table 2 the log odds and their variances are also obtained by approximate methods. 2

Table 2- Reconstructed Data to ne in the Form of Latural LoQ Odds Ratio for Adjusted Case- Data Used ~s for Self Responaers %~no were Exposed as Children Taken from Fontham et. at. ( 1994) Table 8 Ratio of V Sli'latlCe (lt t-[ttt!latCft f:Np,-titere t:,tintatctt L.w„; Odds to Var1:213C1• of F.stlm.ttc<t (;ru--t) \-Jolt Xtfju%ted Lua Lo~~tktd+. Lou, t)d-!% Variaaer 1'4-r % t:t~-t.c-1 c:tr+ Odds Ratio for Ratio for the .~dietstcd i.t>•~ Uttaet;asted ltljtiNted [ a,e Mld. Case control 1~ l'1'~ttt Kcrit-r,-r:ti o! k ariat-r. 1••r 1~I#tt~cr~1 t_u; t hldh (0) .;-47 5 0~~~~~ .___ ; ~ 4.49 1-ll (6) 956 0.15796 0.2''"80 9.04388 22.79 _- ~ _0) - ! 07948 0.08038 0.25 5 47 0.02053 48.71 ,9-47 ~8) -9.97178 0.08174 0.25777 0.02107 17.96 ?48 58) -0.83189 0.08156 0.26034 0.02123 47.10 Assumptions Used to Generate Information in Table 2 • For control group log odds and its variance are approximately equal for the adjusted and the unadjusted case. •Adjusted log odds is approximately equal to adjusted log odds ratio minus control log odds. • Variance unadjusted log odds is equal to the sum of the reciprocals of the number of cases and the number of controls at a given exposure level. • For each exposure group the ratio of the variance of log odds to variance of log odds ratio is the same for the adjusted and unadjusted case. • Log odds ratio variance is obtain from 95% confidence bound under the assumption CJt of normalitv. - -.~ Cn • Weight for adjusted log odds is the reciprocal of its variance. 00 Cz Based on the information in Table 2 the standard normal deviate for the difference between each of the adjacent log odds values is also computed. This is achieved by subtracting adjacent values in the second column and dividing by the square root of the 3

sum of adjacent values in column tive These results and the individual p values for each test are displayed in Table 3. Table 3- Test for Statistical Sicnificant Differences Between .kdjacent Log Odds Smoke- Years None Variance 1-sided Z Log Odds Difference Log Statistic Odds 1-11 0.615 19 0.26661 1.19 12-28 0.48008 0.06441 1.89 29-47 i).10770 0.04160 0.~3 >47 ).1=989 ().04230 0.68 This Table indicates that the only adjacent log odds that are statistically significantly different from each other are 1-1 1 vs. 12-28 which is significant at a p=.05 level due to the use of a one sided test. This general lack in statistical significance difference in adjacent values is also apparent by viewing Figure 1 which shows the large overlap in confidence bounds between adjacent log odds values. Approximate Linear Trend Test It appears that the trend tests employed in the Fontham et. al. (1994) analysis assumed that the bias was zero. In other words the "regression" line went through the origin on the log odds ratio scale. If their was a bias this could mean that the observed trend was really an artifact of some extraneous factor not adjusted for in the analysis. This possibility could be tested formally if the data for individuals was available for analysis. Lacking such information it is necessary to make some additional assumptions about the data in Table 1. The first assumption to be made is that the average value in a ETS exposure interval is equal to the midpoint of the closed interval. The second assumption is that the average exposure level in the open interval is ten greater than its lower bound. These are simply reasonable first approximations that are required if ftirther non-parametric approaches to testing trends are to be employed. It would of course be far more desirable to have the actual mean values of smoke-vears of ETS exposure for each of the exposure groups. In lieu of such information we shall use as average values the quantities shown in parenthesis ( in the first column of Table 1. With this assumed and real information it is possible to conduct approximate trend tests and investigate the effects of the intercept (i.e. estimated bias) on the significance of the slope (i.e. positive trend). 4

The fotm of the relationship that is probably the closest to what is being assumed by the Fontham group is that the increase in the log of the odds ratio is linearly related to average ETS exposure. Stated in another way the assumption is that the line passes through the origin or equivalently the control value of the log odds ratio is known to be equal to zero with certaintv. This model assumes that the entire increase in the log odds is due to ETS. To test this hypothesis the best fitting straight line through the origin is obtained using weighted linear regression where the weights are the inverse of the estimate log odds variance. The regression line obtained by this technique has the numerical form . ln(odds) _-2.17475+0.028267*(adult smoke-vears ). where the intercept is fixed at the assumed control log odds. A simple alternative model is that all of the increase in the log odds is due to a ETS independent bias. This alternative results in horizontal line that is equal to the weighted mean of the log odds of the four exposure groups. These two possibilities are depicted in Figure 1 and the resulting residual sum of squares of observed compared to predicted are given in Table 4. Table 4 - Goodness of Fit of Various Models to Natural Log Odds Approximate Adjusted Values Self Responders Fontham et. al. (1994) Table 8 1'tt%.i.at littt}t>cr of l)rf!rce) af I+fIr s,E N IFOel Il1lerpretatiun #if !'arstttetcr• I rrrtiF,n) llodet 1:5litnaird antl "h.. \ altiv Control and all Weighted Mean exposure groups 1 4 ~~ ri-Ohtr•ct ~ttut cIt tCiti-m{}l:}rriI 14.072 equivalent (.0071) All observed effect Linear with is due to ETS intercept fixed at ( log odds ratio 3 23.136 control level linear throush (.0001) oriein ) Control fixed all All observed effect exposure groups is due to a constant ~ ~ 8.486 equal to their exposure group (.0370) weiehted mean bias Control fixed Observed effect is linear relationship ' due to both bias _ ~ 1•831 for exposure and ETS exposure (.4003) groups Mechalis-Menton I Observed ETS ~ saturation with effect is sub-linear _ ~ 0.135 possible bias (.9347) a -Q ;

It is informative to note that the model which assumes that all the effect is due to bias is more precise ( as measured by residual sum of squares ) than the model which assumes all of the effect is due to ETS. It is possible that the observed trend may in fact be due to a combination of bias and ETS. To test this hypothesis the log odds is regressed against the ETS exposure measure with the control data omitted. Again the parameters are obtained by minimizing the weighted least squares. The interpretation of this model is that the difference between control and the intercept is bias and the slope is ETS effect. As shown in Figure 1 and Table 4 this model fits considerably better than assuming all effect is due to either bias or ETS. The model in this case may be expressed as -?.17-175 smoke-years = 0. ln(odds) = -1.-12"201 - 0.01 108*(smoke-years) smoke-years > 0. When the bias is adjusted for in this manner the effect of ETS is only about 39.2 °'o of what it was when the total effect was assumed to be due to ETS. Saturation Model for the Effect of ETS on the Odds Ratio It is of some interest to explore other parametric forms of how smoke-years effects the ln(odds) rather than log-linear to see if the observed bias remains under alternative formulations. In particular it is informative to look at the increase in the log odds as a saturation type of phoneme. To explore this type of relationship a Mechalais- Menton (MM) model is fitted to the data again by minimizing the weight least squares. The resulting model has the numerical form 0. 1 7174*(smoke-years) ln(odds) = -2.16056 - l+ 0.11339*(smoke-years) A summary of the results obtained from this analyses is also shown in Figure 1 and Table 4. As can be seen in Figure 1 the fit seems almost to good when the scatter around the regression line is compared to the confidence intervals of the individual points. In fact even if the true relationship was MM in form we would only expect a fit as good as was observed about 7% of the time based on a Chi-square goodness of fit test. This suggest some sort of bias may be in operation that results a stronger trend than is in reality underlying the true unknown relationship. Of course it also demonstrates that an alternative explanation to what can be interpreted as bias exists that explains the observed data. However it is difficult to interpret the observed MM relationship within a plausible biological context. 6

Alternative Explanation for Observed Trends If the adjusted relative risk is plotted against smoke-years in both the exposed and not exposed as a child groups a clear picture at tirst appears to emerge. As can be seen in Figure 2 a simple empirical multiple regression model seems to describe the data relatively well. The interpretation of the model is that both childhood and adult smoke- years have some effect but there also exists a pronounced effect for adult smoke-years childhood exposure interaction. This interpretation is appealing because it is just the type of response that would be anticipated if the Moolgavkar et. al. (1993) model for smoked cigarettes was extrapolateable to ETS exposure levels. This is because the model predicts a strong promotional effect that is highly dependent upon the total duration of exposure. The data as noted strongly suggests that childhood exposure has a pronounced synergistic effect with subsequent adult duration of exposure. which would be anticipated if a promotional effect was present. However, a simple alternative explanation for the observed trends exists that can be evaluated for the unadiusted odds ratios. The cases and controls given in Table 8 of Fontham et. al. ( 1994) are displayed in Table ~ along with the resulting odd ratio estimates and 9t',°% confidence bounds for both the effect of childhood exposure and the joint effects childhood and adult exposure for each adult exposure interval. The results shown in Table 5 are quite surprising. When the data is analyzed in this manner there is no suggestion of a childhood or a joint childhood and adult effect. This is in direct contrast to the Fontham et. al. (1994) interpretation of a strong effect of adult smoke vears when the individuals were exposed as a child. There is no plausible biological explanation for the inconsistency of the two analyses. A simple empirical fact is that for some unknown reason ( e.(Y . random error. bias. et.) either there are to manv lung cancer cases in the no childhood exposure-adult exposed control group or to few lung cancer cases in the childhood exposed-no adult exposure control group. Either way the interpretation of the data in Table 8 as establishing a positive trend is not logically justified. Of course the analysis was conducted using only the crude unadjusted rates. However the high correlation between the crude and adjusted analysis given in Fontham et. al. (1994)- Table 8 strongly suggests that if access to the complete data set was available comparable results for an adjusted analysis would also be obtained. 7

Table 5- Alternative Method of Evaluating Effects of ETS Exposure on Odds Ratio for Different Duration and Life Periods of Exposure no childhood exp. c hildhood exp. smoke- years cases con trols i c ases i co ntrols ~ odds ratio od childhood ds ratio joint adult and adult exposure . childhood exposure I + exposure control 5 : 44 ; 0.351 1.000 ~~ (0.098-1.26) , 1-11 90 _2 9 137 !, 0.828 ~ 0.653 (0.409-1.68) (0.319-1.34) 12-28 28 i 97 69 201 ~ 1.189 ~ 1.060 ~ i (0.67-1-2.10) I (0.615-1.83) 29-47 36 97 i 67 204 ~ 0.885 1 1.014 i i (0.521-1.50) (0.588-1.75) ~ _ 48 31 80 70 182 0.993 i 1.187 (0.566-1.74) ~ (0.668-2.05) Since the evidence that childhood exposure has an effect on the odds ratio is non- existent for the unadjusted data it is informative to combine the exposed and not exposed as a child categories to test for a trend. Such an analysis is depicted in Table 6. 8

Table 6- Effect of Adult Smoke Years Independent of Childhood Exposure on Crude L nadjusted Odds Ratio with 95°% Confidence Bounds When the artificial effect of dividing the data into exposed and unexposed as a child are removed the apparent trend is not nearly as pronounced as the previous case. It is noted that none of the individual lower confidence bounds for an exposure group are greater than one. An approximate trend test is significant but in this case the strength of the ETS effect is estimated to be only about 29.6% as much as in the situation where the questionable adjustment for childhood ETS exposure is made. Conclusions In the July 14, 1995 issue of Science in a"Special News Report" entitled Epidemiology Faces Its Limits, a number of the worlds leading scientists in the field of quantitative epidemiology, caution about the use of positive results unless the strength of the association is very strong. They have particular concerns about case control studies which are particularly prone to positive biases. Dr. Norman Breslow who is very prominent in establishing the mathematical rational upon which case control studies are based cautions *'People (may) think they have been able to control for things that are inherently not controllable.'' In this light it is very important not to use a epidemiology study to derive a dose response relationship that does not have unequivocal evidence of a positive trend. At first it appears that the Fontham et. al. (1994) study may contain very strong evidence of a trend with relative risks in the highest exposure group approaching 9

four. However two lines of evidence based on summary information contained in the paper suggest that much or all of the observed effect could be due to some unknown systematic bias. First the shape of the observed dose response appears to be more consistent with all effect due to a bias model than a total effect due to a linear ETS model. Also an alternative saturation model which fits the data surprisingly well suggests that a relationship which is contrary to what would be expected from how cigarettes quantitatively effect lung cancer is occurring. This suggests the possibilitv of a confounding factor being related to ETS in a positive but non linear manner. The second line of evidence is that when an effect of childhood ETS exposure is not adjusted for the relationship becomes only marginal significant. This appears to be primarily due to a deficiency of cases in the exposed as a child but not as an adult control group. Perhaps this might reflect a unconscious bias on the part of lung cancer cases that did not want blame parents if they were not exposed as adults so they did not remember childhood exposure. What ever the true reason for the deficiency of cases, perhaps only random error, it is biologically inconsistent with anv logical cigarette effect model. Because of the noted problems with the ETS lung cancer response data it is highly recommended that a dose response model not be derived from the summary information available in the Fontham et. al. (1994) paper. However this conclusion is based only on partial information. If the detailed information contained in the study was available for analysis an alternative recommendation possibly could be made. References Fontham. T.H.. Correa. P.. Revnolds. P.. Wu-Williams. A.. Bufflor. P.A.. Greenberg, R.S.. Chen. V.W.. Alterman. T.. Boyd. P., Austin. D.F. and J. Liff. 1994. Environmental tobacco smoke and lung cancer in nonsmoking women. JAmer Medical.-issociation. 271:1752-1759. 'vfoolgavkar, S.H.. Luebeck. E.G.. Krewski, D.. and J.M. Zielinski. 1993. Radon. cigarette smoke and lung cancer: a reanalysis of the Colorado Plateau uranium miners' data. Epidemiology. 4:204-217 10