CORRESPONDENCE

Re: All-Cause Mortality in Randomized Trials of Cancer Screening

Mitchell H. Gail, Hormuzd A. Katki

Affiliation of authors: Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD.

Correspondence to: Mitchell H. Gail, M.D., Ph.D., National Cancer Institute, 6120 Executive Blvd., Rm. 8032, Bethesda, MD 20892–7244 (e-mail: gailm{at}exchange.nih.gov).

Misclassification biases can affect cause-specific mortality, as pointed out by Black et al. (1). One should not infer from their Table 1, however, that such biases are operating in these screening trials. There is simply too much noise to draw any inference about bias in "direction" or "magnitude," as indicated by the confidence intervals in Table 1. The editorial (2) also makes much of the "major inconsistencies" between results for cause-specific and all-cause mortality. We, therefore, report the results of a simulation in which no biases are operating to demonstrate that these inconsistencies can be easily explained by chance effects, not by bias.

The simulations were based on the data in Table 1 from Black et al. (1) and the references therein. From the references, we obtained the numbers of deaths Ds, Dc, Dts, and Dtc observed in each trial. These correspond to screened (Ds), control cause-specific (Dc), screened (Dts), and control all-cause (Dtc) deaths, respectively. From the corresponding rates in the same table (1), Rs, Rc, Rts, and Rtc, we calculated the person-years (PY) (x 104) from the equation PYs = Dts/Rts and PYc = Dtc/Rtc. To eliminate all bias in our simulations, we then set Rts = Rtc + Rs Rc. We defined the expected Poisson counts for cause-specific and other deaths as Es = Rs x PYs, Ec = Rc x PYc, Eother,s = (RtsRs) x PYs, and Eother,c = (RtcRc) x PYc. Proceeding in this way for each of the 11 trials with confidence intervals in Table 1 from Black et al. (1), we generated four independent Poisson death counts with the expectations above, computed the estimated cause-specific and all-cause rates by dividing deaths by PYs or PYc as appropriate, and determined how many "inconsistencies" there were in direction or magnitude by using the criteria described by Black et al. (1).

In 10 000 such simulations, the average number of inconsistencies of direction was 3.61 with a standard deviation of 1.55. The average number of inconsistencies of magnitude was 1.64 with a standard deviation of 1.09. Thus, the numbers of inconsistencies of direction (five of 11) and magnitude (two of 11) reported by Black et al. are entirely consistent with chance. In fact, 26.84% of the simulated trials had five or more inconsistencies in direction, and 52.00% had two or more inconsistencies in magnitude. One does not need to invoke "sticky diagnosis" bias or "slippery linkage" bias or any other bias to explain the results in Table 1.

Estimates of a difference in all-cause mortality rates are much less precise than in cause-specific mortality rates. To get the same precision, the all-cause mortality study would need to be larger (or longer) by a factor equal to the ratio of the sum of the screened and control all-cause mortality rates to the sum of the corresponding cause-specific mortality rates. For the Swedish Two-County Study, the all-cause mortality study would need to be 37.6 times larger (or longer). Clearly, studies of all-cause mortality that are sufficiently large to have the required precision would not be feasible in many situations.

REFERENCES

1 Black WC, Haggstrom DA, Welch HG. All-cause mortality in randomized trials of cancer screening. J Natl Cancer Inst 2002;94:167–73.[Abstract/Free Full Text]

2 Juffs HG, Tannock IF. Screening trials are even more difficult than we thought they were. J Natl Cancer Inst 2002;94:156–7.[Free Full Text]



             
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