SEMIPARAMETRIC TRANSFORMATION MODELS WITH MULTILEVEL RANDOM EFFECTS FOR CORRELATED DISEASE ONSET IN FAMILIES.

Large cohort studies are commonly launched to study risk of genetic variants or other risk factors on age at onset (AAO) of a chronic disorder. In these studies, family history data including AAO of disease in family members are collected to provide additional information and can be used to improve efficiency. Statistical analysis of these data is challenging due to missing genotypes in family members and the heterogeneous dependence attributed to both shared genetic back-ground and shared environmental factors (e.g., life style). In this paper, we propose a class of semiparametric transformation models with multilevel random effects to tackle these challenges. The proposed models include both proportional hazards model and proportional odds model as special cases. The multilevel random effects contain individual-specific random effects including kinship correlation structure dependent on the family pedigree, and a shared random effect to account for unobserved environment exposure. We use nonparametric maximum likelihood approach for inference and propose an expectation-maximization algorithm for computation in the presence of missing genotypes among family members. The obtained estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient. Simulation studies demonstrate that the proposed method performs well with finite sample sizes. Finally, the proposed method is applied to study genetic risks in an Alzheimer's disease study.