© 2004 by Oxford University Press
© 2004 Oxford University Press
CORRESPONDENCE |
RESPONSE: Re: Assessing the Probability That a Positive Report is False: An Approach for Molecular Epidemiology Studies
Affiliations of authors: Biostatistics Branch (SW, HAK), Core Genotype Facility (SC), Hormonal and Reproductive Epidemiology Branch (MGC), and Occupational and Environmental Epidemiology Branch (NR), Division of Cancer Epidemiology and Genetics, and Pediatric Oncology Branch, Center for Cancer Research (SC), National Cancer Institute, National Institutes of Health, Bethesda, MD; George Washington University, Biostatistics Center, Rockville (LE)
Correspondence to: Sholom Wacholder, PhD, Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Bethesda, MD 20892-7244 (e-mail: wacholder{at}nih.gov)
Dr. Dubben notes that a study with higher statistical power will have a lower false-positive report probability (FPRP) than a study with lower statistical power, as seen in equation 1 and in figures 1 and 2 of our original paper (1). He is puzzled, however, by figure 5 (1), which shows FPRP increasing with increasing statistical power.
Our paper's figure 5 (1) shows the reduction in statistical power with fixed sample size from demanding stronger evidence for calling a study positive, whether by an FPRP or P-value criterion. By contrast, sample size is not fixed in figures 1, 2, and 3 (1), which show the influence of prior probability and of statistical power, manifested through sample size, on FPRP. When sample size is fixed, there is an additional constraint implicit in equation 2 because varying 
has a direct effect on statistical power. On the other hand, all the variables on the right side of equation 1 are free to vary independently when sample size is not fixed.
Figure 1 in this response shows the same curves from the original paper's figure 5 (1) labeled to indicate the P value (in boldface) and the odds ratio (in italics) that corresponds to the P value that would give the FPRP value on the x-axis and statistical power on the y-axis. For example, the figure shows that the greater stringency from imposing an FPRP criterion of 0.2 instead of 0.5 in a study with 1500 case patients and 1500 control subjects does not substantially reduce statistical power for detecting an odds ratio of 1.5 when the prior probability is 0.001 and the allele frequency among the control subjects is 0.3. Under the more stringent criterion, associations with P values below about 0.00023 instead of below 0.0010, or, equivalently an observed odds ratio below 1.33 instead of below 1.29 if the observed allele frequency among controls was 0.3, would be deemed noteworthy for an FPRP of 0.2, based on equation 1 of our original paper (1). In fact, regardless of the preset FPRP criterion, we would report an FPRP value of 0.2 if the observed P value were 0.00023. Although the editorial by Thomas and Clayton called FPRP calculations from P values "inappropriate," we argue that the FPRP value can be interpreted as the lowest FPRP for which the finding meets a preset criterion for noteworthiness, just as the observed P value is the lowest level for which the finding meets the criterion for statistical significance (1).
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We believe that our approach provides both results and conclusions broadly similar to those from more complicated methods, as noted by Thomas and Clayton (2), with the advantage that it can be implemented and understood by a large fraction of the cancer research community. We look forward to further discussions of our work (2,3,4) and related ideas (5) as we study steadily increasing numbers of genes with steadily decreasing prior probabilities in molecular epidemiology studies.
REFERENCES
1 Wacholder S, Chanock S, Garcia-Closas M, El Ghormli L, Rothman N. Assessing the probability that a positive report is false: an approach for molecular epidemiology studies. J Natl Cancer Inst 2004;96:434–42.
2 Thomas DC, Clayton DG. Betting odds and genetic associations. J Natl Cancer Inst 2004;96:421–3.
3 Sellers TA. Genetic ancestry and molecular epidemiology. Cancer Epidemiol Biomarkers Prev 2004;13:499–500.
4 Rebbeck TR, Ambrosone CB, Bell DA, Chanock SJ, Hayes RB, Kadlubar FF, et al. SNPs, haplotypes, and cancer: applications in molecular epidemiology. Cancer Epidemiol Biomarkers Prev 2004;13:681–7.
5 Colhoun HM, McKeigue PM, Davey Smith G. Problems of reporting genetic associations with complex outcomes. Lancet 2003;361:865–72.[CrossRef][Web of Science][Medline]
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J Natl Cancer Inst 2004 96: 1722.
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