Partially linear transformation models with varying coefficients for multivariate failure time data

This paper studies the estimation and inference of varying coefficients and parameters in the partially linear transformation models for multivariate failure time data. A profile martingale-based estimating method that includes global and local estimating equations is proposed. Asymptotic properties of the estimators are established. Some numerical simulations are given to show the performance of the estimation method in finite-sample situation. In order to reduce the computational burden, a simple and useful one-step estimator method is used. We further suggest a delete-a-group jackknife method to estimate asymptotic variance of estimators. A real data set from the Busselton Population Health Surveys is analyzed to illustrate the proposed methods.