  Family studies provide an important tool for understanding etiology of
diseases, with the key aim of discovering evidence of family aggregation and to
determine if such aggregation can be attributed to genetic components.
Heritability and concordance estimates are routinely calculated in twin studies
of diseases, as a way of quantifying such genetic contribution. The endpoint in
these studies are typically defined as occurrence of a disease versus death
without the disease. However, a large fraction of the subjects may still be
alive at the time of follow-up without having experienced the disease thus
still being at risk. Ignoring this right-censoring can lead to severely biased
estimates. We propose to extend the classical liability threshold model with
inverse probability of censoring weighting of complete observations. This leads
to a flexible way of modeling twin concordance and obtaining consistent
estimates of heritability. We apply the method in simulations and to data from
the population based Danish twin cohort where we describe the dependence in
prostate cancer occurrence in twins.
