Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data

Doubly truncated data arise when a failure time T is observed only if it falls within a subject-specific, possibly random, interval [U,V], where U and V are referred to as left- and right-truncation times, respectively. In this article, we consider the problem of fitting semiparametric transformation regression models to doubly truncated data. Most of the existing approaches in literature, which adjust for double truncation in regression models, require independence between failure times and truncation times, which may not hold in practice. To relax the independence assumption to conditional independence given covariates, we consider a conditional likelihood approach and develop the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of models. Based on score equations for the regression parameter and the infinite-dimensional function, we propose an iterative algorithm for obtaining the cMLE. The cMLE is shown to be consistent and asymptotically normal. Simulation studies indicate that the cMLE performs well and outperforms the existing estimators when an independence assumption holds. Applications to an AIDS dataset is given to illustrate the proposed method.