EM algorithm for change-point additive hazards models with partially interval-censored data

In medical research such as cancer prognosis, a key statistical challenge lies in accurately estimating a change-point for a continuous biomarker threshold beyond which its association with the hazard function undergoes a structural shift. Identifying such a change-point is crucial for uncovering heterogeneous treatment effects and enhancing clinical risk stratification. The paper introduces a novel latent variable approach under the additive hazards model for partially interval-censored data. We formulate a semi-parametric model that explicitly incorporates the structural change-point. To address the associated computational challenges, we develop an efficient Expectation-Maximization algorithm that integrates sieve estimation with Bernstein polynomials. The methodology is built on reformulating the change-point problem as a tractable mixture model via a latent variable, which naturally fits the EM framework. The proposed algorithm stably handles the complexity induced by partial interval-censoring and iteratively refines the estimation of both the change-point location and model parameters. The asymptotic properties of the proposed estimators are established. Extensive simulation studies demonstrate the method's finite- sample performance. Its practical utility is illustrated through an application to a breast cancer study, where it identifies a threshold of clinical significance.