  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.
