Semiparametric analysis of nonparametric proportional hazards models with mixed dependent censored data

Abstract

To construct a nonparametric proportional hazards (PH) model for mixed informative interval-censored failure time data for predicting the risks in heart transplantation surgeries. Based on the complexity of mixed informative interval-censored failure time data, we considered the interdependent relationship between failure time process and observation time process, constructed a nonparametric proportional hazards (PH) model to describe the nonlinear relationship between the risk factors and heart transplant surgery risks and proposed a two-step sieve estimation maximum likelihood algorithm. An estimation equation was established to estimate frailty variables using the observation process model. Ⅰ-spline and B-spline were used to approximate the unknown baseline hazard function and nonparametric function, respectively, to obtain the working likelihood function in the sieve space. The partial derivative of the model parameters was used to obtain the scoring equation. The maximum likelihood estimation of the parameters was obtained by solving the scoring equation, and a function curve of the impact of risk factors on the risk of heart transplantation surgery was drawn. Simulation experiment suggested that the estimated values obtained by the proposed method were consistent and asymptotically effective under various settings with good fitting effects. Analysis of heart transplant surgery data showed that the donor's age had a positive linear relationship with the surgical risk. The impact of the recipient's age at disease onset increased at first and then stabilized, but increased against at an older age. The donor-recipient age difference had a positive linear relationship with the surgical risk of heart transplantation. The nonparametric PH model established in this study can be used for predicting the risks in heart transplantation surgery and exploring the functional relationship between the surgery risks and the risk factors.