Optimal weight functions for marginal proportional hazards analysis of clustered failure time data

The choice of weights in estimating equations for multivariate survival data is considered. Specifically, we consider families of weight functions which are constant on fixed time intervals, including the special case of time-constant weights. For a fixed set of time intervals, the optimal weights are identified as the solution to a system of linear equations. The optimal weights are computed for several scenarios. It is found that for the scenarios examined, the gains in efficiency using the optimal weights are quite small relative to simpler approaches except under extreme dependence, and that a simple estimator of an exchangeable approximation to the weights also performs well.