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A STATISTICAL REVIEW OF THE EPA REPORT: HEALTH EFFECTS OF PASSIVE SMOKING: ASSESSMENT OF LUNG CANCER IN ADULTS AND RESPIRATORY DISORDERS IN CHILDREN (EPA/600/6-90/00)64 - EXTERNAL REVIEW DRAFT) Prepared for: The R. J. Reynolds Tobacco Company Prepared by: George Howard, Dr. PH Statistical Analysis Center September 1990 R. J. Reynolds Tobacco Company Comments - RJR Appendix A

Introduction The conclusion by EPA that ETS exposure is related to lung cancer is based on a statistical analysis of data presented in Tables 3.5 and 3.6 of the EPA report. That analysis appears to over-interpret the available data and to employ inconsistent statistical methods. For Table 3.5, the postulated association between ETS and lung cancer is evaluated using three statistical methods: (1) a binomial test to examine whether the proportion of "significant" studies is above the 5% which would occur by chance alone, (2) a Wilcoxon test examining whether the 'S" statistics (log of the odds ratio divided by its standard error) are significantly above zero, the null hypothesis of no association between ETS and lung cancer, and (3) a Mantel-Haenszel estimate. As performed by EPA, these tests suggest that spousal smoking is statistically associated with lung cancer in the studies contained in Tables 3.5 and 3.6 of the report. This report reexamines five aspects of the EPA's analysis of the epidemiologic data: I. Whether the collective studies reported in Table 3.5 are statistically significant under a Wilcoxon analysis after adjustment for misclassification and publication bias. II. The impact of including in the analysis studies that were omitted by EPA. III. The results of restricting EPA's analysis to: (a) Sex-specific risks, (b) U.S. data only, (c) Asian data, and (d) Studies not reviewed by the Surgeon General or NRC. IV. Whether the epidemiologic data as a whole demonstrate a dose-response relationship. V. Whether the statistics reported in Table 3.6 are internally consistent. GD ~ ~ ~ F+ O A1 N

I. Whether the Gollective studies reported in Table 3.5 are statistically sign#icant ander a Wilcoxon analysis after adjustment for muclassif:cation and publication bias. Interpretation of the association identified by EPA's Wilcoxon analysis of the association between ETS exposure and lung cancer depends on, among other things, whether the data examined are free from bias. The effect of misclassification of smoking status and publication bias are both in the direction of increasing the observed relationship of ETS to cancer (overestimating its effect). The EPA report adjusts for the effect of misclassification bias in Chapter 4, by deflating the estimate by a factor of 14% (which is EPA's estimate of the association that would be induced by the expected misclassification). The EPA report totallv discounts publication bias on the basis of reports by Vandenbroucke and Wells, and does not make any quantitative adjustment for that bias source. It should be noted that Vandenbroucke and Wells conclude that publication bias does not account for the total observed difference; they do not conclude that it plays no role at all. As such, the EPA's failure to make an adjustments for publication vias may be viewed as liberal. The EPA should have adjusted for misclassification and publication bias in the analysis of the significance of the association of ETS and cancer in Tables 3.5 and 3.6. If the result is nonsignificant, the analysis in Chapter 4 estimating magnitude of the effect would not be warranted. We will examine the sensitivity of the significance of the ETS/cancer relationship to adjustments for these two biases prior to the analysis of the association. This will be performed in two stages, first adjusting for the effect of misclassification bias, and then examining the effect of publication bias on that adjusted estimate. A2

Effect of Misclassification Bias on the Wilcoxon Ana_ is The odds ratios T-bk r~Analysis olOddy Radm Proaucdin Tabk 3s reported in Table 3.5 are reported in Table I of this report under the column h e a i n OBSER YED g ODDS RATIO. Taking the natural log of. these odds ratios serves to standardize (normalize) the scale (note: odds STUDY oBSERVM OR 1,OG OBS OR Aw LOG OR aw OR AKIB 1.52 0.41871 028768 133333 BROW 1.52 0.41871 029769 133333 BUFF 0.81 -0.21072 -034175 0.71053 CHAN 0.75 -0.26768 -0.41871 0.65789 CORR 2.07 0.72755 039652 181579 GAO 1.19 0.17395 0.04293 1.04386 GARF 131 027003 0.13900 1.14912 GENG 2.16 0.77011 0.6.9908 1$9474 HUMB 2.34 0.85015 0.71912 2.05263 INOU 02795 -0.23572 0-036675 0.6929a KOO 1.55 0.43625 030723 135965 LAMT 1.65 0s007a 0.36975 1.44737 LAMW 2.01 0.69813 0.36711 1.76316 LEE 1.03 0.02956 -0.10147 0.90351 PERS 1.28 0.24686 0.11583 1.12281 SVEN 1.26 0.23111 0.10008 1.10526 TRIC 2.13 0.75612 0.62509 1.86642 WU 1.41 034359 021256 1.2.'i684 ratios of 0.5 and 2.0 imply equal positive and negative association, and taking the log converts these to equal distances from the log of the no effect point of 1.0). The result of this calculation is provided under the column heading LOG OBS ODDS RATIO (i.e., the log of the observed odds ratio). A Wilcoxon signed-rank analysis of the summary log odds ratio (the third column) provides a p-value of 0.0015, the value reported in the EPA report as a measure of the significance of the association between spousal smoking and lung cancer. However, the EPA report concludes that misclassification bias causes an overestimation of the odds ratio by approximately 14% (a 14% increase over the expected 1.00 given no association). For purposes of analysis, this estimate was adopted as the standard. Each of the observed odds ratios was then adjusted to reflect a 14% A3

misclassification bias. This is done by subtracting log(1.14) = 0.131 from each of the values in the second column, resulting in the AD1 LOG ODDS RATIO (column 4 of the Table) estimates. The exponential of this value can be taken to provide the ADJUSTED ODDS RATIO (column 5), which represents the odds ratio after adjustment for the misclassification basis. A Wilcoxon analysis of the fifth column provides a p-value of 0.02, which while significant, represents a more marginal association of ETS and lung cancer (a 2/100 chance that the observed association happened by chance alone). The EPA's determination that misclassification bias spuriously elevates the observed odds ratios by 14% is only one possible assumption. Different assumptions regarding the relevant parameters would produce different estimates of Probability at Various Levels of Misclassificotion Adjustment TeM. J-S 1.00 1.05 1.10 1.15 120 Odds Rotio Cut Point 1.25 1.30 the significance after adjustment. F'P^` 1= "koO1 Poba6ary °f EnkO--C'°°0^ -° ft-c°OR of dw+iwol odjuwnenr Jor mexlasufieaoon bint In order to examine the sensitivity of the observed association of ETS and lung cancer to the assumed misclassification value for adjustment, a similar analysis was conducted for misclassification effect values ranging from 1.00 (no adjustment) to 130, with results provided in Figure 1. A4

For adjustments above 1.24 the association between ETS and cancer becomes statistically nonsignificant. Table II provides a similar analysis for the odds ratios provided in Table 3.6 of the EPA report. Again, a Wilcoxon analysis of the LOG ODDS RATIO, as performed in the report, is significant (p = 0.014), the analysis of the log odds ratio (ADJ LOG RATIO) is only marginally significant (p = 0.04). The sensitivity of rabk rt: A-5ds of Odds Rados haeuea in Tabk 16 the observed association between ETS and lung cancer to variations in the assum tion of the level of p the odds ratio attributable to misclassification bias is STUDY OBSERVED OR - LoG oBS OR ADJ I.OG OR ADJ OR BROW 1.68 051679 0.38777 1.47368 GAO 1.70 0.53063 039960 1.49123 GARF 1.70 053063 039960 1.49123 HUMB 1.20 0.1B242 0.05129 1.05263 INOU 3.09 1.12917 099714 271053 KOO 1.19 0.17395 0.04293 1.04386 W"W 1.00 0.00000 -0.13103 0sn19 LEE 240 0.87547 0.74444 210526 PERS 1.90 0.64185 031063 1.66667 VARE 0.94 -0•ob18s -0•1sz9o 022436 WU 1.20 0.1B232 0.05129 1.05263 provided in Figure 2. This shows that for adjustments above an odds ratio of 1.20 for misclassification bias the association becomes statistically insignificant. Effect of adjustment for publication bias Because statistically nonsignificant studies and/or studies providing no basis for rejecting the null hypothesis are difficult to publish, meta analyses of the published literature are biased towards overestimating an effect. The magnitude of the size of the overestimation is a function of: (1) the number of "unreported" studies, and (2) the size of and the results of the studies. That is, the more studies which are not reported, and/or the A5

more nonsignificant the nonreported studies are, the more likely meta analysis is to overestimate the size of the association. In this section, the effect of: (1) the number of unincluded papers, and (2) the size of the Probability at Various Levels of Misclossificotion Adjustment 0.25 1 effect in these papers which were Fir- 2: ~~0~ pva/uc ojETSIC-rer efje+a as a funcrion oJnce iiac of adjTUanrnt for mitdaay'ficari- biac not included is examined. This will be considered after the above adjustment for misclassification bias (assuming the value of 1.14 in the EPA report) as discussed in the previous section. In Figure 3 the effect of from one to five unreported studies on the analysis of Table 3.5 is examined. The vertical axis shows the Wilcoxon p-value and the horizontal the significance of the unreported studies. Each of the lines represents the relationship of the p-value for a specific number of Probability After Adding Additional Nonsignificont Studies 040 , 0.30 ~ ~ 0 0.20 1 .0 --1 OOQI p . L ------• '~-- -- Y oddt. a --- 3 o0dt. ---- ----- . OOdt. : 0.10 • - ~ .. - S o0al. - - - _ - ~ ~ - - - - - -~•_i{~L. 0.00 0.70 0.79 0.L8 0.97 1.06 1.15 Odds Ratio Cut Point Figwr 3: EJJWa o/pudficariori biat ae Tabk 15 ~ A6

unreported studies, ranging from one to five. In addition, there is a horizontal line representing the alpha = 0.05 level. As can be seen, if there are three unreported studies showing no effect (odds ratio of 1.00), the analysis of Table 3.5 would have concluded that there is no effect. Figure 4 shows the effect of publication bias on the Wilcoxon statistic in the analysis of Table 3.6, again after adjustment for misclassification. If there is a single unreported study showing no effect, the analysis would have concluded that there was no ETS/lung- cancer relationship. If there are four unreported studies having odds ratios as great as 1.10 it would still be concluded that there was no relationship between ETS and cancer. Conclusions Misclassification and publication bias both tend to spuriously elevate the overall observed association between spousal smoking and lung cancer. Both biases should be corrected for quantitatively in any meta- analysis. The relationship Probability After Adding Additional Nonsignificant Studies - - 1 odal - - 2 odut --- 3 oddt •-°'- 4 OACI_ - 5 oddL 0.3 ....... .................. _.~--•-------- -••-••'"' - - - ' ~ 0.2 . ~ ~I __--'---------------------- 0.1 - - .•------------------ 0.0 0.70 0.79 0.EE 0.97 1.06 1.15 Odds Ratio Cut Point Figun I.• EJjoa ojnli:damfuadon biar on Tabk 16 between ETS and cancer, as evaluated in Tables 3.5 and 3.6, is at best only marginal after adjustments for misclassification and publication bias. If Table 3.5 is adjusted for an odds ratio of 1.14, and if there are as many as 3 unpublished papers showing no effect, then the A7

relationship between ETS and cancer (as measured by the Wilcoxon statistic) becomes insignificant. In Table 3.6, if a similar adjustment is made for misclassification bias and of there is a single unreported paper showing no effect, then it would be concluded that there was no relationship between ET'S and cancer. As such, when one considers (only) misclassification and publication bias the relationship between ET3 and cancer appears marginal under the Wilcoxan analysis. If one were also to consider confounders the relationship would appear weaker still. 11. The impact of including in the analysis studies that were omitted by EPA. For inclusion in Table 3.5, the EPA required that a study report "raw" frequencies. This restriction was placed to allow the use of Mantel-Haenszel statistic for the estimation of the ETS/lung cancer relationship. This restriction removed a number of studies from consideration. Including these studies could affect the estimated odds ratio or the significance of the relationship. Notably, the study by Varela was omitted, a large case/control study where the overall estimated effect was nonsignificantly pyotective. Including this study, and other studies omitted from Table 3.5 may modify the estimated odds ratio. An alternative statistical procedure can be adopted to allow for the incorporation of the studies not providing raw data. The data used in this analysis is described in Table III, where the estimated odds ratio, log of odds ratio and the variance of the log-odds ratio are provided. Because the log of the odds ratio is normally distributed (under the central limit A8

theorem), estimation can be performed using weighted general linear models, where the weights are the inverse of the variance of the log of the odds ratio. A plot of the weight (inverse of the variance) versus the log odds ratio is provided in Figure 5. This figure clearly shows that those studies with a large log risk ratio (and hence, large estimated RR) all have a relatively small weight. Conversely, the three studies with the largest weights {Varela (M), Varela (F), and Garfinkel ('81)}, each with a weight above 60, have estimated logRR very near zero. Two of these three studies were Tab1e III: Fadmattd RR JDVRR and OJ IOaRR SOURCE ox LOG OR varianx t.oo OR US. studia &ownson (E) 1S2 0.42121 0.48452 Brownson (M) 136 031945 1.21591 Buf(kr (F) 0.80 -021706 0.19265 Butner (M) 031 -0.68131 0.41394 c«,= (F) 2.07 0.72541 0.22671 C.ortea (M) 1.97 0.68024 0.71162 Garfink.el '85 131 0.27061 0.04429 Garfinlcd '81 1.17 0.15700 0.01364 Humbk 2.34 0.85043 0.29174 Kabat (F) 0.79 -0.z39a 033450 Kabat (M) 1.00 0.00000 0.69571 vurla (F & M) 0.96 -0.98490 0.00691 w° 1.41 034175 0x+950 ~ European ~ GiAic (F) 1.00 0.00°00 0.67176 Gillis (M) 3.25 1.17865 0.75656 Lee (F)- 1.03 0.02632 0.21530 Loe (M) 131 0.26706 0.40179 Pershasea 1.27 0.24272 0.07146 Svenason 1.26 0.2.3361 0.16711 Trichopoubs 2.13 0.75643 0.0895° Asian stuaia Akiba (F) 1S2 0.41632 0.°7883 Akiba (M) 2.10 0.74392 0s1685 Chan & Fun6 0.75 -0.28486 0.07826 Gao 1.19 0.17341 0.03636 Ge"E z16 0.76630 0.12303 Hirayama (F) 1.45 037156 0.03304 Hirayama (M) 2.28 0.82418 0.16086 lnoix 2S5 0.93609 039771 lcoo 1s5 0.43532 0.07762 Lam 1.65 0.49972 0.03264 Lam & Cheng 2.01 0.69957 O.o9e63 Shimizu 1.08 0.07946 0.07042 Sobue 0.94 -0.06188 0.04857 omitted from the EPA analysis and will have a very heavy weight in the estimated risk ratio. Estimated risk ratios, weighted by the inverse of the variance, and shown for subgroups (as in the previous question), are shown in Table IV. When these three studies are included in the analysis, there is no significant effect between ETS and lung cancer overall or in any subgroup. The Asian studies yield a significantly different summary risk ratio than the U. S. studies (p = 0.0224). A9