[Parameter estimation using time-dependent Weibull proportional hazards model for survival analysis with partly interval censored data]

Abstract

OBJECTIVE: To assess the validity and effectiveness of parameter estimation using a time-dependent Weibull proportional hazards model for survival analysis containing partly interval censored data and explore the impact of different covariates on the results of analysis. METHODS: We established a time-dependent Weibull proportional hazards model using the Weibull distribution as the baseline hazard function of the model which incorporated time-varying covariates. Maximum likelihood estimation was employed to estimate the model parameters, which were obtained by optimization of the likelihood function. RESULTS AND CONCLUSION: Numerical simulation results showed that with higher proportions of precise observations across different sample sizes and parameter settings, the proposed model resulted in improved accuracy of parameter estimation with coverage probabilities approximating the theoretical expectation of 95%. As the sample sizes increased, the parameter biases of the model tended to decrease. Experiments with empirical data further validated the effectiveness of the model. Compared with the failure time data for each precisely observed individual, additional interval-censored data helped to obtain more effective estimates of the regression parameters. Comparison with the Cox model that included time-varying covariates further demonstrated the effectiveness of the time-dependent Weibull proportional hazards model for parameter estimation in survival analysis with partly interval censored data.

Keywords: Weibull proportional hazards model; likelihood function; maximum likelihood estimation; partly interval-censored data; time-dependent covariates.