A simple construction of optimal estimation in multivariate marginal Cox regression

The multivariate extension of the Cox model proposed by Wei, Lin and Weissfeld in 1989 has been widely used for analyzing multivariate survival data. Under the model assumption, failure times from an individual are assumed to marginally follow their respective proportional hazards regression relation, leaving the joint distribution completely unspecified. This paper presents a simple approach to efficiency improvement through segmentation of stochastic integrals in the marginal estimating equations and incorporation of the limiting covariance structure. It is shown that when partition of the time interval is done at a suitable rate, the resulting estimator is consistent and asymptotically normal. Through the reproducing kernel Hilbert space arising from the covariance function of the limiting Gaussian process, it is also shown that the proposed estimator is asymptotically optimal within a reasonable class of estimators under marginal specification. Simulations are conducted to assess the finite-sample performance of the proposed method.