Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models

Abstract.  Multivariate failure time data arises when each study subject can potentially ex‐perience several types of failures or recurrences of a certain phenomenon, or when failure times are sampled in clusters. We formulate the marginal distributions of such multivariate data with semiparametric accelerated failure time models (i.e. linear regression models for log‐transformed failure times with arbitrary error distributions) while leaving the dependence structures for related failure times completely unspecified. We develop rank‐based monotone estimating functions for the regression parameters of these marginal models based on right‐censored observations. The estimating equations can be easily solved via linear programming. The resultant estimators are consistent and asymptotically normal. The limiting covariance matrices can be readily estimated by a novel resampling approach, which does not involve non‐parametric density estimation or evaluation of numerical derivatives. The proposed estimators represent consistent roots to the potentially non‐monotone estimating equations based on weighted log‐rank statistics. Simulation studies show that the new inference procedures perform well in small samples. Illustrations with real medical data are provided.