Estimation And Application Of Additive Residual Quantile Regression Model With Covarite Threshold Effect

The effect of change-point refers to the change of the basic structure or relevant distribution of the model before and after the point of change.Only accurately identify the impact of the change point,can get the right result.The application of change-point is very extensive,involving biomedicine,economy finance,meteorology and so on many research fields.In the field of survival analysis,most studies on the change-point effect are based on Cox proportional hazards model.Cox proportional hazards model is an important model in survival analysis for failure risk modeling.The residual life model studied in this paper is also one of the important models for survival analysis,in which the residual life refers to the time that an individual can survive after time T.Compared with Cox model for risk function modeling,residual life model for residual life modeling can directly obtain the influence of various factors on survival time.In recent years,scholars' researches on residual life model mainly focus on mean residual life model and quantile residual life regression model.There are many related articles,but few of them consider the point of change effect.In the actual data,for individuals at different stages of development,the degree of influence of covariates on the residual life may be different.If this difference is ignored,biased or even opposite conclusions may be drawn.Therefore,this paper considers the residual life model with covariate threshold effect.Moreover,compared with the mean value,quantile can describe the actual distribution of residual life more comprehensively,and is not easily affected by outliers.Therefore,this paper discusses the quantile residual life model with covariate threshold effect.Finally,because the survival analysis of the data is often incomplete.This paper also considered right censoring.To sum up,this paper studies the quantile residual life model with covariate threshold effect under right censored data.First of all,the smoothing method of kernel estimation was used to reduce the estimation difficulties caused by the demonstrative function;second,the inverse probabilistic weighting method was used to deal with the right deletion data;finally,the minimum absolute deviation method(LAD)was used to estimate the parameters of the quantile regression model.What's more,this paper carries out numerical simulation under different sample sizes and different window widths,showing the application of the model under different data.At the end of the paper,we applied the proposed model to the clinical data of patients with primary biliary cirrhosis(PBC data)and explained the results.