Partially linear transformation cure models for interval-censored data

There has been considerable progress in the development of semiparametric transformation models for regression analysis of time-to-event data. However, most of the current work focuses on right-censored data. Significantly less work has been done for interval-censored data, especially when the population contains a nonignorable cured subgroup. A broad and flexible class of semiparametric transformation cure models is proposed for analyzing interval-censored data in the presence of a cure fraction. The proposed modeling approach combines a logistic regression formulation for the probability of cure with a partially linear transformation model for event times of susceptible subjects. The estimation is achieved by using a spline-based sieve maximum likelihood method, which is computationally efficient and leads to estimators with appealing properties such as consistency, asymptotic normality and semiparametric efficiency. Furthermore, a goodness-of-fit test can be constructed for the proposed models based on the sieve likelihood ratio. Simulations and a real data analysis are provided for illustration of the methodology.