Semiparametric analysis of the additive hazards model with dependent right-censored data

In the researches of censored failure time data, most of them focus on the study which failure time and censored failure time are independent. In practice, there exists a dependent relationship between the failure time and the observation time. If we ignore the relationship, a biased inference process or even wrong conclusion may be drawn. To deal with this, assumed the failure time follows additive hazards model and the dependent censored failure time follows proportional hazards model, and we employ the copula model to describe the relationship between failure time and observation time, then we could get a copula joint model. In order to obtain the parameter estimation, based on spline function approximation and quadratic penalty function, we develop a penalty sieve maximum likelihood estimation of copula joint model. Newton-MI algorithm, which has advantage of solving the positivity constraint of parameters, is used to solve the model parameters. A large number of numerical simulations have verified the good statistical properties of the proposed method. In addition, we apply the proposed method to a ovarian tumor data, an some meaningful conclusions were obtained.