Estimating equations for hazard ratio parameters based on correlated failure time data

Weighted partial likelihood estimating equations are proposed for the estimation of marginal hazard ratio parameters based on correlated failure time data. Asymptotic distribution theory is derived for the solution to such equations using martingale convergence results and inverse function theory. Simulation studies and theoretical efficiency calculations indicate that the inclusion of weights in the estimating equation produces important efficiency gains only if the dependencies among the failure times are strong.