Semiparametric Analysis of Additive–Multiplicative Hazards Model with Interval-Censored Data and Panel Count Data

In survival analysis, interval-censored data and panel count data represent two prevalent types of incomplete data. Given that, within certain research contexts, the events of interest may simultaneously involve both data types, it is imperative to perform a joint analysis of these data to fully comprehend the occurrence process of the events being studied. In this paper, a novel semiparametric joint regression analysis framework is proposed for the analysis of interval-censored data and panel count data. It is hypothesized that the failure time follows an additive–multiplicative hazards model, while the recurrent events follow a nonhomogeneous Poisson process. Additionally, a gamma-distributed frailty is introduced to describe the correlation between the failure time and the count process of recurrent events. To estimate the model parameters, a sieve maximum likelihood estimation method based on Bernstein polynomials is proposed. The performance of this estimation method under finite sample conditions is evaluated through a series of simulation studies, and an empirical study is illustrated.