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Objective: Genetic studies of complex human diseases rely heavily on the epidemiologic association paradigm, particularly the population-based case-control designs. This study aims to compare the matching effectiveness in terms of bias reduction between exposure matching and stratum matching., Study Design and Setting: Formulas for population stratification bias were derived. An index of matching effectiveness was constructed to compare the two types of matching., Results: It was found that exposure matching can paradoxically increase the magnitude of population stratification bias sometimes, whereas stratum matching can guarantee to reduce it., Conclusion: The authors propose two simple rules for genetic association studies: (a) to match on anything that helps to delineate population strata such as race, ethnicity, nationality, ancestry, and birthplace and (b) to match on an exposure only when it is a strong predictor of the disease and is expected to have great variation in prevalence across population strata.

The case-only study is a convenient approach and provides increased statistical efficiency in detecting gene-environment interactions. The validity of a case-only study hinges on one well-recognized assumption: The susceptibility genotypes and the environmental exposures of interest are independent in the population. Otherwise, the study will be biased. The authors show that hidden stratification in the study population could also ruin a case-only study. They derive the formulas for population stratification bias. The bias involves three terms: 1) the coefficient of variation of the exposure prevalence odds, 2) the coefficient of variation of the genotype frequency odds, and 3) the correlation coefficient between the exposure prevalence odds and the genotype frequency odds. The authors perform simulation to investigate the magnitude of bias over a wide range of realistic scenarios. It is found that the estimated interaction effect is frequently biased by more than 5%. For a rarer gene and a rarer exposure, the bias becomes even larger (>30%). Because of the potentially large bias, researchers conducting case-only studies should use the boundary formula presented in this paper to make more prudent interpretations of their results, or they should use stratified analysis or a modeling approach to adjust for population stratification bias in their studies.

The case-control study design is popular for genetic association studies of complex human diseases. However, case-control studies may suffer from bias due to population stratification. In this paper, the authors present simple formulas that can set a limit to the havoc population stratification bias can wreak (the lower and upper bounds of the confounding rate ratio and the upper bound of the type I error rate). The authors demonstrate applications of these formulas using two examples. The formulas can help researchers make more prudent interpretations of their (potentially biased) results.