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APPENDIX B 284 Appendix B Method of Combining Data from Studies of Environmental Tobacco Smoke Exposure and Lung Cancer Consider the following kinds of data that might be reported in an epidemiological study of chronic exposure to environmental tobacco smoke (ETS) and lung cancer: Lung Cancer Total Yes No Exposure to ETS Yes a b m1 No c d m2 Total: m3 m4 T Therefore, T is the total number of people in the study, a is the number of people chronically exposed to ETS who also have lung cancer, b is the number of people chronically exposed to ETS who do not have lung cancer, c is the number of people not chronically exposed to ETS who have lung cancer, and d is the number of people not chronically exposed to ETS who do not have lung cancer. The marginal totals are m1=a+b, m2=c+d, m3=a +c, and m4=b+d. The data that correspond to these variables from all of the studies examined in Chapter 12 are shown in Table B-1. CASE-CONTROL STUDIES In a case-control design, the subjects are chosen on the basis of the health outcome, and their exposure history is assessed.
APPENDIX B 285 TABLE B-1 Passive Smoking and Lung Cancer: Observed Numbers Used to Calculate Values in Table 12â4a Type of Study Authors Sex Spouse Smoker Spouse Nonsmoker Risks Study Cases (a) Controls Cases (c) Controls Computed Published (b) (d) CC Chan and Fung, F 34 66 50 73 0.75 â 1982 CC Trichopoulos et F 38 81 24 109 2.13 2.4, 3.4 al., 1983 CC Correa et al., F 14 61 8 72 2.03 2.00 1983 M 2 26 6 154 2.29 2.07 CC Kabat and F 13 15 11 10 0.79 â Wynder, 1984 M 5 5 7 7 1.00 â CC Buffler et al., F 33 164 8 32 0.80 0.78 1984 M 5 56 6 34 0.50 0.52 CC Garfinkel et al., F 92 266 42 136 1.12 1.12 1985 CC Pershagen et al., F 33 150 34 197 1.28 1.2 in press CC Akiba et al., F 73 188 21 82 1.48 1.5 1986 M 3 9 16 101 2.45 1.8 CC Koo et al., 1985 F 51 66 35 70 1.54 1.64 CC Lee et al., 1986 F 22 45 10 21 1.03 1.00 M 8 14 7 16 1.30 1.30 PRO Garfinkel, 1981 F 88 127,164 65 49,422 â 1.27, 1.10 PRO Gillis et al., F 6 1,388 2 521 â 1.00 1984 M 4 306 2 515 â 3.25 PRO Hirayama, 1984 F 146 69,287 37 21,858 â 1.45, 1.91 M 7 1,003 57 19,222 â 2.25 ABBREVIATIONS: CC=Case-Control PRO=Prospective aFor the calculations, (a) through (d) are used for case-control studies and published RR are used for prospective studies.
APPENDIX B 286 The expected number of people who are exposed to environmental tobacco smoke and develop lung cancer is given by: Expected numbers for each of the studies are shown in Table 12â4. The difference between observed and expected numbers of people with lung cancer who are exposed to ETS can be calculated, and the variance of this difference is given by: Therefore, the natural logarithm of the odds ratio (Ï) can be estimated by: and the variance of this estimate is given by: Variance of Ï=[(Variance(ObservedâExpected)]â1 (Yusuf et al., 1985). The odds ratio is estimated by exp[Ï] and is shown in Tables 12â4 (and B-1) with its 95% confidence intervals for each of the studies. PROSPECTIVE (OR COHORT) STUDIES In prospective studies, also known as cohort studies, the subjects are classified (or chosen) on the basis of exposure and the health endpoint is then assessed. In all of the articles the authors have estimated the relative risk, adjusting for such variables as age. Therefore, the published relative risk values were used in the following calculations rather than the estimates of the crude relative risk that could be calculated from the data given in the text. For those studies where a relative risk estimate was given for different levels of smoking by the spouse (Garfinkel et al, 1981; Hirayama, 1984), a combined estimate of the relative risk was calculated using the method given below for combining the prospective studies. The number of people who are exposed to ETS who are expected, under the null hypothesis of no effect, to develop lung cancer is:
APPENDIX B 287 where E is the expected number for m3, based on the published relative risk (RR), that is: The approximate variance of the observed minus expected numbers of people with lung cancer who are exposed to environmental tobacco smoke is: The variance of the natural logarithm of the relative risk was calculated using the published confidence limits for the estimate of the relative risk, except for one study (Gillis et al., 1984), where the method given above for the case-control studies use used since no confidence limits were available. SUMMING OVER STUDIES The overall values for the case-control studies were calculated by adding the values of ObservedâExpected (i.e., OâE) and their variance for the individual studies as follows: and for the variance: (Yusuf et al., 1985). For the prospective studies, the overall value for the ln RR was calculated as: and for the variance: (Kleinbaum et al., 1982). The overall value, for all of the studies combined, was obtained
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