Estimation research on panel count data and interval-censored data

In survival analysis, interval-censored data and panel count data are two important types of incomplete data. The proportional hazard model is one of the most commonly used models for analyzing censored data, and in order to fully consider the nonlinear effects of covariates, the article extends the traditional proportional hazard model to a nonparametric proportional hazard model. The article will discuss the joint estimation analysis of interval censored data and panel count data under this general model. Assuming that the failure time obeys the nonparametric proportional hazard model, a fragile term is introduced to characterize the correlation between the failure time and the counting process, and then the joint likelihood function is maximized using the sieve method based on Bernstein polynomials to estimate the parameters. Finally, extensive numerical simulations are performed and the proposed estimation method is applied to skin cancer example data.