A second-order semiparametric method for survival analysis, with application to an acquired immune deficiency syndrome clinical trial study

Motivated by the recent acquired immune deficiency syndrome clinical trial study A5175, we propose a semiparametric framework to describe time-to-event data, where only the dependence of the mean and variance of the time on the covariates are specified through a restricted moment model. We use a second-order semiparametric efficient score combined with a non-parametric imputation device for estimation. Compared with an imputed weighted least squares method, the approach proposed improves the efficiency of the parameter estimation whenever the third moment of the error distribution is non-zero. We compare the method with a parametric survival regression method in the A5175 study data analysis. In the data analysis, the method proposed shows a better fit to the data with smaller mean-squared residuals. In summary, this work provides a semiparametric framework in modelling and estimation of survival data. The framework has wide applications in data analysis.