Multiple Imputation For Models Of Mixed Effects With Change Points

According to the World Health Organization(WHO),as of 2019,the number of people living with HIV and AIDS(HIV/AIDS)worldwide has grown to 38 million and is still growing.Currently,AIDS remains one of the biggest public health challenges worldwide.Therefore,an in-depth study of its function and pathogenesis is necessary to help researchers develop effective new therapies against this virus.The existing theoretical models commonly used in HIV/AIDS research are:linear mixed effects(LME)models,nonlinear mixed effects(NLME)models,nonparametric nonlinear mixed effects models,and semiparametric nonlinear mixed effects models.The semiparametric NLME model,on contrast,is a regression model with parameters influenced by random variables,which can estimate both the mean effect of the population and individual differences,having more flexible characteristics and practicality.In this paper,we applied mainly to the semiparametric NLME model.In longitudinal HIV data studies,missing data,covariate measurement errors,left censoring,skewed response distribution,and rebound in viral load(called change points at the moment of rebound)are the most common problems.The article,focuses on the case of simultaneous covariate measurement errors,skewed distribution of response variables and change points in the data.By combining the clinical AIDS data,the corresponding theoretical data analysis models were constructed by applying R language and data analysis software such as Winbugs under the framework of mathematical models.The multiple imputation method was used to estimate the models parameters,and simulation studies were conducted to make the analytical results more convincing and credible.The innovations of this paper are:(1)For longitudinal data with both change points and measurement errors,a semiparametric nonlinear mixed-effects model with change points,a linear mixed-effects model,and a change point model are jointly modeled,discriminant rules for change points are given,and multiple imputation methods are used for parameter estimation when there are missing data.(2)When the data have change points,measurement errors and asymmetry at the same time,a semiparametric nonlinear mixed-effects model with skewed errors is proposed,and then joint modeling and estimation of model parameters are performed.