• Gene–environment interaction;
  • Joint genetic and environmental effects;
  • Maternal genetic effect;
  • Mother–child pair design;
  • Offspring genetic effect;
  • Profile likelihood;
  • Semiparametric maximum likelihood

Summary Case-control mother–child pair design represents a unique advantage for dissecting genetic susceptibility of complex traits because it allows the assessment of both maternal and offspring genetic compositions. This design has been widely adopted in studies of obstetric complications and neonatal outcomes. In this work, we developed an efficient statistical method for evaluating joint genetic and environmental effects on a binary phenotype. Using a logistic regression model to describe the relationship between the phenotype and maternal and offspring genetic and environmental risk factors, we developed a semiparametric maximum likelihood method for the estimation of odds ratio association parameters. Our method is novel because it exploits two unique features of the study data for the parameter estimation. First, the correlation between maternal and offspring SNP genotypes can be specified under the assumptions of random mating, Hardy–Weinberg equilibrium, and Mendelian inheritance. Second, environmental exposures are often not affected by offspring genes conditional on maternal genes. Our method yields more efficient estimates compared with the standard prospective method for fitting logistic regression models to case-control data. We demonstrated the performance of our method through extensive simulation studies and the analysis of data from the Jerusalem Perinatal Study.