Comparative Analysis Of Quantile Difference Estimators For Two Samples With Length-Biased And Right-Censored Data

When comparing the effects of implementation of the two treatment regimens,data observed by the existing treatment regimen were usually right-censored data,and data observed by the new treatment regimen were usually length-biased and right-censored data.In statistical inference,in order to remove the influence of outliers,the inference method based on quantiles is usually used.Combined with the comparison of treatment effects,the parameter of interest in this paper is the difference of quantiles between the two populations.Through the difference of quantiles of the two populations,the difference between the two treatment schemes is analyzed.At present,statistical inference based on the difference of quantiles between two populations with right-censored data and length-biased and right-censored data is mostly applied by semiparametric method: assuming that the population distribution information corresponding to right-censored data is sufficient,non-parametric methods such as maximum likelihood weight equation and inverse probability weight equation are used,assuming that the global distribution information corresponding to the length-biased and right-censored data is insufficient.These parametric methods and non-parametric methods are integrated in different ways to form various semi-parametric inference methods.However,different integration methods will bring different results,because the parametric methods have the risk of model misjudgment,and the nonparametric methods have slower convergence speed.By comparing several estimation methods,this paper analyzes the misjudgment cost of parametric methods in the sense of goodness of fit and the inferential advantage of nonparametric methods in the sense of mean square error.The information carried by covariates is likely to be useful for statistical inference.In this paper,the Cox proportional hazards model is used to make statistical inference.In practical application,the acquisition of covariate information needs to pay extra cost,even high cost.This paper compares the estimation results without covariates and with covariates,and analyzes the improvement of the estimation results after the introduction of covariates.