Semi-Parametric Accelerated Failure Time Model And Its Appliaction In Medical Field

In survival analysis, the semi-parametric accelerated failure time model is a linear regression model in which the responses are the logarithms of survival times and the error term distribution is unspecified. It provides a useful alternative model to the Cox proportional hazards model for analyzing censored survival data.Many people have studied a rank based estimation method in the accelerated failure time model with censored data. A broad class of rank-based monotone estimating functions is developed for the semi-parametric accelerated failure time model with censored observations. The corresponding estimators can be obtained by minimizing a convex objective function through a standard linear programming technique. But it is difficult to estimate the variance of the rank-based estimator well by conventional methods. We introduce the method which is proposed by Zhou—an empirical likelihood testing procedure for the censored rank regression estimator where the likelihood is defined as the censored empirical likelihood of the error variables. He used the empirical likelihood method to derive a test and thus a confidence interval based on the rank estimators of the regression coefficient in the accelerated failure time model. The limiting distribution of the log empirical likelihood ratio is a central chi-squared distribution under null hypothesis. Standard chi-squared distributions are used to calculate the p-value and to construct the confidence interval.The empirical likelihood method avoids the need to estimate the variance; instead one must carry out a constrained maximization of the censored empirical likelihood, which can be done reliably. Furthermore, to test one hypothesis or obtain a p-value, the empirical likelihood method involves solving only one optimization problem. Simulations and examples show that the chi-squared approximation to the distribution of the log empirical likelihood ratio performs well, and has some advantages over the existing methods.We introduce another semi-parametric procedure which is proposed by Arnost Komarek to estimate parameters of an accelerated failure time model. The motivation for this method stems from exploiting penalized B-splines to smooth the error density f(e). To express the density of the error distribution, he used the P-spline (B-splines with penalties) smoothing technique of Eilers and Marx (1996). To accommodate error densities with infinite support and for other reasons, he replaced the B-splines with their limits as the degree of the B-spline goes to infinity; namely, with normal densities. The spline coeffcients as well as any number of regression parameters are quickly and accurately estimated via penalized maximum likelihood. He used the Pseudo-variance for drawing accurate inferences based on penalized MLE. The method directly provides predictive survival distributions for fixed values of covariates while allowing for left-, right-, and interval-censored data.We use R statistics software as platform to handle the analysis of our example.