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

Large cohort studies are often used to investigate the impact of genetic variants or other risk factors on the age at onset (AAO) of a chronic disorder. These studies collect family history data, including the AAO of a disease in family members, in order to provide additional information and to improve the efficiency of estimating associations. Statistical analyses of these data are challenging owing to missing genotypes in family members and the heterogeneous dependence attributed to both their shared genetic background and shared environmental factors (e.g., lifestyle). Therefore, we propose a class of semiparametric transformation models with multilevel random effects to address these challenges. The proposed models include both the proportional-hazards model and the proportional-odds model as special cases. The multilevel random effects contain individual-specific random effects, including the kinship correlation structure dependent on the family pedigree, and a shared random effect to account for any unobserved exposure to the environment. We use a nonparametric maximum-likelihood approach for our inferences and propose an expectation-maximization algorithm for the 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, we apply the proposed method to examine genetic risks in an Alzheimer's disease study.