Study Of Hierarchical Quantile Regression Model And Its Application In Health-related Quality Of Life Of Older People Living Alone

Backgrounds:In large-scale special investigations,multi-stage sampling is often used,and the data obtained is often hierarchical.For hierarchical data,individuals in the same hierarchical unit have a certain commonality.For example,in the health services survey,the city is divided into counties.Because of the economic development,health services,policy and other factors,individuals in different counties may have different health service demands.When a traditional regression model is used to analyze data with hierarchical structure,the model parameters would compromise effectiveness and may results in bias,because the fitted residual error does not involve hierarchy.Therefore,a hierarchical model shall be used.A linear regression model is usually widely used to investigate and explain the impacts of independent variables on conditional mean of dependent variables.However,it is required that the dependent variable obey normal distribution and homogeneity of variance,and the fitting effect will be worse when the condition is not satisfied.Quantile regression expands the linear regression model to estimating conditional quantile of dependent variable,and doesn't make the assumptions of distribution of dependent variables and homogeneity of variance,and it is more conducive to the study of the general appearance of the conditional distribution of dependent variables.Since quantile regression is invented,it is more and more popular from researchers because of its good robustness.It has been rapidly developed with the computer-based large scale computing.Aims:Based on the data of hierarchical structure,this study evaluates the application effect of layered quantile regression model with different covariates and sample distribution,and explores its applicability.We then applied it on the study of the effects of physical exercise on the health related life quality of the elderly living alone based on the health survey data,so as to provide reference and help for the research of relevant fields.Methods:This study adopts the method of combination of simulation study and practical application.First,the hierarchical data is simulated by using the simplest hierarchical quantile regression model.In order to compare the superiorities of hierarchical quantile regression with quantile regression in different data structure,the simulations were divided into three kinds of situations: single independent variable,multiple independent variables,multiplerelated independent variables.In multiple independent variables situation,independent variables were set as interval variables,two-categorical variables,ordinalvariables.The coefficients are set to the same and different conditions in multiple related independent variables situation.In order to cover various sample size,take two levels for example,in the case of a total sample size of 1500 cases,setting the number of observation in first level×second level are 100×15,10×150 and 300×5 three combinations.Random intercepts and random errors consider the different combinations of four random distribution types,including normal distribution,t distribution,Chi-square distribution and asymmetric Laplace distribution.In each case,500 data sets are simulated.Bias,absolute bias and standard deviation were calculated to evaluate the accuracy and stability of both model.Finally,the simulation results are applied to the actual health services survey data to analyze the influence of physical exercise on the health related life quality of the elderly living alonein Shanghai to solve the practical problems and to provide methodological support to thestatistical analysis of health services survey hierarchical data.Results:The simulation results show that in the case of single independent variable,the bias of the intercept of the hierarchical quantile regression and quantile regression are both small,and the fittings are accurate.The intercept estimation of the hierarchical quantile regression is relatively better than that of the quantile regression.In the case of the same total sample size,as the number of units in the second layer increases,that is,the sample in each unit is reduced,the intercepts fitted in the hierarchical quantile regression is better than the quantile regression.The estimated bias of coefficient in hierarchical quantile regression is smaller than the bias in the quantile regression in most random distributions,but in some distributions,the estimated bias of coefficient in hierarchical quantile regression and quantile regression are both large.The coefficients of are both large and less stable.In the case of multiple independent variables,the intercept and coefficient estimation bias of the hierarchical quantile regression and quantile regression are both smaller,and better fitting in.In comparison,whether the coefficient of independent variables are consistent,whether the independent variables are related,whether the type of variables,the intercept's estimation biasof the hierarchical quantile regression are less than quantile regression in the most random distribution,so hierarchical quantile regression are better than quantile regression in accuracy.But the standard deviation of hierarchical quantile regression are larger than quantile regressionso quantile regression are better than hierarchical quantile regression in stability.The estimation bias and standard deviation of coefficients of the hierarchical quantile regression are less than quantile regression in the most random distribution,so hierarchical quantile regression are better than quantile regression in accuracy and stability.In the case study,the data of health-related quality of life of old people who are living alone in Shanghai are analyzed using hierarchical quantile regressionand quantile regression to study influence of physical exercise.We find that the influence of physical exercise on the health-related life quality of the elderly people living alone under different quantile can be comprehensively described and analyzed by using hierarchical quantile regression.For different scores of EQ-VAS of the elderly people,the effect of physical exercise frequency are not all the same,which shall be used to give different health guidance and intervention according to different health quality.Conclusions:Based on the simulation of single independent variable,the intercept of the hierarchical quantile regression is relatively better than that of the quantile regression,and the coefficients in hierarchical quantile regression are more fitted than the quantile regression in most random distributions,but when the random intercept and random error distributions are Chi-AL?Chi-N?Chi-Chi?Chi-t,the estimated bias of coefficient in hierarchical quantile regression and quantile regression are both large and badly fitted.In multiple independent variables,the estimated bias of the intercept and coefficient of hierarchical quantile regression are both smaller than that of quantile regression.In dealing with hierarchical data,using hierarchical quantile regression is better in most cases.Hierarchical quantile regression consider the hierarchical structure in the application,and the influence can be comprehensively described and analyzed to fully find the effects.