Multivariate One-sided Tests For Mixed Effects Models With Missing Covariates

Multivariate one-sided test problems often appear in practice.Based on some scientific theories and practical studies,statistical model parameters of real data often have certain constraints.For example,parameters such as the rate of viral decay during anti-HIV therapy should be non-negative,and the growth rate of children can be expected to be positive.Therefore,adding natural constraints to the parameters of the model in the hypotheses test will get more effective results than the corresponding unconstrained test.In addition,there are often missing data problems in actual studies.In this case,the test based on complete data may not be applicable,and the use of prefect case method to delete all incomplete observed data may cause deviations in the results.This paper considers the multivariate one-sided test problem of the semiparametric nonlinear mixed effects model with the missing covariates are missing at random and non-ignorable.And applies them to the research of HIV treatment,by testing whether the virus decay rates are strictly positive or not,it provides a basis for the effectiveness of treatment.The main research is as follows:1.For the multivariate one-sided test of the semi-parametric nonlinear mixed effects model with the missing covariates are missing at random.Firstly,use multiple imputation method to impute the data to obtain complete data sets for statistical inference.Secondly,two multivariate one-sided tests are proposed based on the results of multiple imputation:(1)Combine several complete data test statistics,and then propose the overall test;(2)Combine parameter estimation of complete data,and then propose a single test statistic based on the combined estimation;Their asymptotic null distribution is derived.Finally,the validity of the two test statistics is proved by HIV case analysis and simulation study.2.For the multivariate one-sided tests of semi-parametric nonlinear mixed effects models with the missing covariates are non-ignorable,the missing not at random mechanism is incorporated into the joint model.Firstly,two kinds of multivariate one-sided tests are proposed based on likelihood method:(1)Missing data and inequality constraints were processed separately.The parameter estimates were obtained by ignoring inequality constraints,and then the Wald type test was constructed for complete data.(2)Missing data and onesided inequality constraints were processed at the same time.Secondly,their asymptotic zero distribution is derived.Finally,the validity of the two test statistics is verified.