Regression analysis of interval-censored failure time data with change points and a cured subgroup

There exists a substantial body of literature that discusses regression analysis of interval-censored failure time data and also many methods have been proposed for handling the presence of a cured subgroup. However, only limited research exists on the problems incorporating change points, with or without a cured subgroup, which can occur in various contexts such as clinical trials where disease risks may shift dramatically when certain biological indicators exceed specific thresholds. To fill this gap, we consider a class of partly linear transformation models within the mixture cure model framework and propose a sieve maximum likelihood estimation approach using Bernstein polynomials and piecewise linear functions for inference. Additionally, we provide a data-driven adaptive procedure to identify the number and locations of change points and establish the asymptotic properties of the proposed method. Extensive simulation studies demonstrate the effectiveness and practical utility of the proposed methods, which are applied to the real data from a breast cancer study that motivated this work.