A semiparametric inverse-Gaussian model and inference for survival data with a cured proportion

This work focuses on a semiparametric analysis of a cure rate modelling approach based on a latent failure process. In clinical and epidemiological studies, a Wiener process with drift may represent a patient's health status and a clinical endpoint occurs when the process first reaches an adverse threshold state. The first-hitting-time then follows an inverse-Gaussian distribution. On the basis of the improper inverse-Gaussian distribution, we consider a process-based lifetime model that allows for a positive probability of no event taking place in finite time. Model flexibility is achieved by leaving a transformed time measure for disease progression completely unspecified, and regression structures are incorporated into the model by taking the acceleration factor and the threshold parameter as functions of the covariates. When applied to experiments with a cure fraction, this model is compatible with classical two-mixture or promotion-time cure rate models. We develop an asymptotically efficient likelihood-based estimation and inference procedure and derive the large-sample properties of the estimators. Simulation studies demonstrate that the proposed method performs well in finite samples. A case study of stage-III soft tissue sarcoma data is used as an illustration.