A Comparative Analysis On Estimating Methods Of Quantile Difference Between Two Populations

In survival analysis,sometimes people are concerned about the difference between two populations.For example,in clinical trials,in order to verify whether a new treatment plan is more effective,it is usually necessary to compare the population's distribution of the new treatment group with that of the traditional treatment group.Since the quantile is more robust than other distribution characteristics,the quantile difference can be used to compare the distribution differences between two populations at the same probability level.In this paper,we conduct a comparative analysis on the estimating methods of the quantile difference between two populations.First,the semiparametric model and the estimating equation method are used to estimate the quantile difference between the two populations.A sample from one population is a length biased and right censored data,another sample from another population is a right censored data.We construct two inverse probability weights to establish the estimating equation,and improve the estimators in the sense of mean square error and asymptotic variance respectively.In addition,we also establish the consistency and asymptotic normality of these estimators.Then we construct the confidence interval of the quantile difference by normal approximation.In the numerical simulation,we verify the effectiveness of the proposed methods,and then we compare the semi-parametric method with the non-parametric method,and compare the proposed estimating methods.Finally,these methods are applied to the Oscar data.