Affiliation of authors: Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD.
Correspondence to: Sholom Wacholder, Ph.D., National Institutes of Health, EPS 8046, 6120 Executive Blvd., Bethesda, Md 20892 (e-mail: Wacholder{at}nih.gov).
Dr. Millikan's letter raises the question of how to assess the bias from population stratification in a particular study that did not account for race or ethnicity. We show here that, even in the most extreme situation, where a genotype is virtually universal in one group and absent in the other, the bias factor must lie between the ratio of disease rates in the two groups and its reciprocal. To see this, one must remember that the confounding risk ratio, CRR, which is a measure of the bias, depends on the ratio of the disease rates among those with the at-risk genotype and its frequency in the two groups, P1b and P1w (1). When the rates or genotype frequencies are equal (RR = 1 or P1b = P1w), CRR is 1. If RR is greater than 1, then the confounding is positive, and CRR is greater than 1 when P1b is greater than P1w (2); CRR is below 1 (negative confounding) results when P1b is less than P1w. When P1b = 1 and P1w = 0, CRR equals RR; when P1b = 0 and P1w = 1, CRR equals 1/RR. Thus, the bias factor CRR must lie between the rate ratio RR and its reciprocal 1/RR, regardless of the differences in frequency of the at-risk genotype. Table 1 shows the CRR for various genotype frequencies when there are two groups split 20%80%.
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In addition to a wide range of cancer rates and genotype frequencies among the groups, there are two requirements for important bias from population stratification when race or ethnicity is ignored (1). The genotype frequencies and cancer rates must vary together; clearly, with only two groups, they do so here. The differences in rates must remain after adjustment for known risk factors; while the North Carolina study collected information on all known breast cancer risk factors (3), it is unclear how much, if any, of the rate difference they explain.
In contrast to breast cancer, the ratio of incidence rates of prostate cancer in black and white males from 1993 through 1997 is near 1.7 in the Surveillance, Epidemiology, and End Results Program.1 In Table 1, the column for RR = 1.7 shows that failure to adjust for race in a study of genotypes with an extreme difference in frequency and prostate cancer is likely to have a greater impact than for breast cancer.
NOTES
1 SEER is a set of geographically defined, population-based, central cancer registries in the United States, operated by local nonprofit organizations under contract to the National Cancer Institute (NCI). Registry data are submitted electronically without personal identifiers to the NCI on a biannual basis, and the NCI makes the data available to the public for scientific research.
REFERENCES
1
Wacholder S, Rothman N, Caporaso N. Population stratification in epidemiologic studies of common genetic variants and cancer: quantification of bias. J Natl Cancer Inst 2000;92:11518.
2 Boivin JF, Wacholder S. Conditions for confounding of the risk ratio and of the odds ratio. Am J Epidemiol 1985;121:1528.[Abstract]
3 Newman B, Moorman PG, Millikan R, Qaqish BF, Geradts J, Aldrich TE, et al. The Carolina Breast Cancer Study: integrating population-based epidemiology and molecular biology. Breast Cancer Res Treat 1995;35:5160.[Medline]
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