Semiparametric inference for the accelerated life model with time-dependent covariates

The accelerated life model assumes that the failure time associated with a multi-dimensional covariate process is contracted or expanded relative to that of the zero-valued covariate process. In the present paper, the rate of contraction/expansion is formulated by a parametric function of the covariate process while the baseline failure time distribution is unspecified. Estimating functions for the vector of regression parameters are motivated by likelihood score functions and take the form of log rank statistics with time-dependent covariates. The resulthlg estimators are proven to be strongly consistent and asymptotically normal under suitahle regularity conditions. Simple methods are derived for making inference about a subset of regression parameters while regarding others as nuisance quantities. Finite-sample properties of the estimation and testing procedures are investigated through Monte Carlo simulations. An illustration with the well-known Stanford heart transplant data is provided. ,4 M S Suh/ec t Class[Ocation: Primary 62J05: secondary 60F05, 62F12, 62G05 K e y words: Accelerated failure time model: Censoring; Log rank statistic: Minimum dispersion statistic: Rank regression; Survival data: Time-varying covariates