Case-control mother–offspring pair design has been widely adopted for studying early-life and women’s pregnancy health. It allows assessment of pre-and perinatal environmental risk factors as well as both maternal and offspring genetic risk factors. Data arising from this design is routinely analyzed using standard prospective logistic regression. Such data has two unique fea-tures: the offspring genotypes are not correlated with maternal environmental risk factors given maternal genotypes, and offspring and maternal genotypes are related through mendelian transmission. In this work, built upon a novel regression model relating maternal genotypes to environmental risk factors, we proposed a novel retrospective likelihood method that effectively utilized the two data features to increase statistical efficiency for detecting maternal and offspring genetic effects. The inference procedure was based on a profile likelihood derived using the Lagrange multiplier method, but we replaced the multipliers with their large sample limits to enable highly efficient and computationally stable estimation. We showed that our proposed estimates of odds ratio association parameters are consistent and asymptotically normally distributed and demonstrated the finite sample performance through exten-sive simulation studies and application to genetic association studies of birth weight and gestational diabetes mellitus.
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Acknowledgments. We thank the editor, associate editor and three reviewers for their insightful comments. The first author was supported in part by NIH grants R21-ES020811 and R01-ES016626 and NSFC grant 11771096. The second author was supported in part by NIH grants R21-ES020811. The sixth author was supported in part by NIH grants R21-ES020811 and R01-ES016626.
© Institute of Mathematical Statistics, 2020.
- Case-control mother–offspring pair design
- Genetic association
- Profile likelihood
- Retrospective likelihood
- Saddle point problem