An empirical Bayes method for genetic association analysis using case-control mother-child pair data

Case-control mother-child pair data are often used to investigate the effects of maternal and child genetic variants and environmental risk factors on obstetric and early life phenotypes. Retrospective likelihood can fully utilize available information such as Mendelian inheritance and conditional independence between maternal environmental risk factors (covariates) and children’s genotype given maternal genotype, thus effectively improving statistical inference. Such a method is robust to some extent if no relationship assumption is imposed between the maternal genotype and covariates. Statistical efficiency can be considerably improved by assuming independence between maternal genotype and covariates, but false-positive findings would be inflated if the independence assumption was violated. In this study, two empirical Bayes (EB) estimators are derived by appropriately weighting the above retrospective-likelihood-based estimators, which intuitively balance the statistical efficiency and robustness. The asymptotic normality of the two EB estimators is established, which can be used to construct confidence intervals and association tests of genetic effects and gene-environment interactions. Simulations and real-data analyses are conducted to demonstrate the performance of our new method.