Likelihood Inference for Unified Transformation Cure Model with Interval Censored Data

In this paper, we extend the unified class of Box-Cox transformation (BCT) cure rate models to accommodate interval-censored data. The probability of cure is modeled using a general covariate structure, whereas the survival distribution of the uncured is modeled through a proportional hazards structure. We develop likelihood inference based on the expectation maximization (EM) algorithm for the BCT cure model. Within the EM framework, both simultaneous maximization and profile likelihood are addressed with respect to estimating the BCT transformation parameter. Through Monte Carlo simulations, we demonstrate the performance of the proposed estimation method through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. Also considered is the efficacy of the proposed EM algorithm as compared to direct maximization of the observed log-likelihood function. Finally, data from a smoking cessation study is analyzed for illustrative purpose.