CORRESPONDENCE More About: Involuntary Smoking and Lung Cancer: a Case–Control Study

I was interested to see the letter of Wells and Henley (1) concerning errors in the 95 % confidence limits that were presented in an article by Garfinkel et al. (2) on the effects of environmental to-bacco smoke (ETS). I wrote to Garfinkel in 1985 to point out my concerns about the accuracy of some of these confi-dence limits. He replied that he had checked all of the limits very carefully and that he had used a program by Roth-man and Boice (3)—with which I was not familiar—to calculate them. When using data from the study by Garfinkel et al. in meta-analyses, I have relied on the cell counts where they were pro-vided, as has the Environmental Protec-tion Agency (4); but I accepted the data as they were, in the absence of further information for those end points for which only the relative risks and confi-dence intervals (CIs) were given. However, the comments made by Wells and Henley made me look at the issue further, and I began to realize that, instead of using the standard formula— var logeR 4 1/a + 1/b + 1/c + 1/d—for the variance of the logarithm of the rela-tive risk (where a, b, c, and d are the cell counts in the 2 × 2 table, and R is the relative risk), the Rothman and Boice program had incorrectly multiplied this expression by R2/(1.96)2. This leads me to draw two conclusions: First, research-ers ’ attention should be drawn to the possibility of error in their calculated confidence limits if they used this pro-gram (or at least the version of it current at that time). Second, even where Garfinkel et al. did not present the 2 × 2 table of counts, it should be possible to correct the confidence limits. For child-hood exposure to ETS, for example, the estimates that they presented of R 4 0.91 (95 % CI 4 0.74–1.12) should pre-sumably be R 4 0.91 (95 % CI 4 0.58– 1.42). Fortunately, use of these corrected data does not affect the general results of fixed-effects meta-analyses of the over-all evidence on the association between passive smoking and lung cancer, namely, that there is a significant asso-ciation for smoking by the husband (R 4 1.16 [95 % CI 4 1.08–1.23], based on 47 estimates) but no significant asso-ciation with either workplace exposur