Secondary Phenotype Analysis in Ascertained Family Designs: Application to the Leiden Longevity Study

The case-control design is often used to test associations between the case-control status and genetic variants. In addition to this primary phenotype, a number of additional traits, known as secondary phenotypes, are routinely recorded, and typically, associations between genetic factors and these secondary traits are studied too. Analysing secondary phenotypes in case-control studies may lead to biased genetic effect estimates, especially when the marker tested is associated with the primary phenotype and when the primary and secondary phenotypes tested are correlated. Several methods have been proposed in the literature to overcome the problem, but they are limited to case-control studies and not directly applicable to more complex designs, such as the multiple-cases family studies. A proper secondary phenotype analysis, in this case, is complicated by the within families correlations on top of the biased sampling design. We propose a novel approach to accommodate the ascertainment process while explicitly modelling the familial relationships. Our approach pairs existing methods for mixed-effects models with the retrospective likelihood framework and uses a multivariate probit model to capture the association between the mixed type primary and secondary phenotypes. To examine the efficiency and bias of the estimates, we performed simulations under several scenarios for the association between the primary phenotype, secondary phenotype and genetic markers. We will illustrate the method by analysing the association between triglyceride levels and glucose (secondary phenotypes) and genetic markers from the Leiden Longevity Study, a multiple-cases family study that investigates longevity.