On dependence estimation using correlated failure time data from case-control family studies

Correlated failure time data arise routinely in case-control family studies. To measure the dependence between bivariate failure times, a cross ratio, i.e. conditional hazard ratio, function has been used. Many approaches, ranging from estimating equations to likelihood score equations, have been proposed for the estimation of parameters in the cross ratio function from prospective family data. However, the adaptation of these approaches to case-control family data appears too complicated and computationally intensive to be practical. In this paper, a connection is established between the cross ratio function and the relative risk function in a stratified proportional hazards model, leading to the development of a set of partial-likelihood-based estimating equations. A simulation study is conducted to evaluate the performance of this estimation procedure, and two datasets are analysed to illustrate this method.