Robust logistic regression of family data in the presence of missing genotypes

Large cohort studies are commonly launched to study the risk effect of genetic variants or other risk factors on a chronic disorder. In these studies, family data are often collected to provide additional information for the purpose of improving the inference results. Statistical analysis of the family data can be very challenging due to the missing observations of genotypes, incomplete records of disease occurrences in family members, and the complicated dependence attributed to the shared genetic background and environmental factors. In this article, we investigate a class of logistic models with family-shared random effects to tackle these challenges, and develop a robust regression method based on the conditional logistic technique for statistical inference. An expectation–maximization (EM) algorithm with fast computation speed is developed to handle the missing genotypes. The proposed estimators are shown to be consistent and asymptotically normal. Additionally, a score test based on the proposed method is derived to test the genetic effect. Extensive simulation studies demonstrate that the proposed method performs well in finite samples in terms of estimate accuracy, robustness and computational speed. The proposed procedure is applied to an Alzheimer's disease study.