Censored Regression Quantiles Model And Its Application In Survival Analysis

Censored regression quantiles, the extension of median regression, models the linear relationship of the conditional quantiles of a censored distribution and a set of covariates. Different form traditional linear model which regresses the conditional mean, it regresses the conditional quantiles of response variable. The model has attracted a great deal of interest in the recent literature due to its robustness to distributional misspecification of the error term and unknown conditional heteroscedaticity. In the area of survival analysis, we are often interested in survival time which is a censored distribution due to withdraws of patients amongst other reasons. Because of the complicated substances of human disease, it is often very difficult to determine the distribution of survival time, furthermore, there is plenty of data which can't satisfy the assumption of proportional hazards. Censored regression quantiles doesn't need to specify the distribution of error item, and relaxes the application conditions, so it is applicable under wider situations. In addition, as might be expected, unusually large and small quantiles often depend on the independent variables quite differently from the median response. So censored regression quantiles model has great application potential in survival analysis. In this paper, the author explored the structure of censored regression quantiles model, its estimation and inference of parameters .The paper describes a recursively reweighted estimator of the regression quantile process and it can be viewed as a direct generalization of the Kaplan–Meier estimator. The estimates of regression parameters can be obtained by linear programming method. In order to carry out valid statistical inferences for censored regression quantiles models, it is necessary to provide consistent estimators for the asymptotic variance-covariance matrices. However, the asymptotic variance-covariance matrices are difficult to estimate reliably since they involve conditional densities of error terms. The difficulty may be avoided by applying the bootstrap method. Simulation studies and examples suggest the strong potential of the method as an alternative to the use of Cox model. Here, we use R statistics software as platform to handle the analysis of our simulation experiments and application example.