Semiparametric analysis of dependent interval-censored data based on the Newton-MI algorithm

Interval-censored data is a common type of failure time data in survival analysis. However, in practice, there is often a dependent relationship between the failure time and the observation time, and ignoring this dependency can lead to biased inferences. To address this issue, this study describes the dependent relationship between the failure time and the observation time using the copula model and establishes a copula-based joint model. Existing research on dependent censored data has focused on cases where covariate effects take relatively simple forms, however, in practical studies, it has been observed that the effects of covariates are more complex. Consequently, this study assumes that the failure time follows an additive-multiplicative hazards model, which includes covariates with multiplicative effects as well as covariates with additive effects, providing greater flexibility. Additionally, we propose a penalized sieve maximum likelihood estimation method. Furthermore, a Newton Multiple Iteration (Newton-MI) algorithm, adept at handling parameter non-negativity constraints, is employed to estimate the model parameters. Extensive simulations validate the proposed method's favorable statistical properties. Finally, we apply the proposed model and methods to a tumor dataset.