Multivariate One-Sided Tests for Nonlinear Mixed-Effects Models with Incomplete Data

Nonlinear mixed-effects (NLME) models are widely used in the analysis of longitudinal studies. The parameters in an NLME model typically have meaningful scientific interpretations, and these parameters may have some natural order restrictions such as being strictly positive. The problems of testing parameters with order restrictions are known as multivariate one-sided hypothesis testing. However, multivariate one-sided testing problems in NLME models have not been discussed thoroughly.

In many longitudinal studies, the inter-individual variation can be partially explained by the time-varying covariates which, however, may be measured with substantial errors. Moreover, censoring and non-ignorable missingness in response are very common in practice. Standard testing procedures ignoring covariate measurement errors and/or response censoring/missingness may lead to biased results. We propose multiple imputation methods to address the foregoing data complication. The multiple imputation methods allow us to use existing "complete-data" hypothesis testing procedures for parameters with order restrictions. In this thesis, we propose testing statistics for the multivariate one-sided testing problems in NLME models with: (i) mis-measured covariates, (ii) both mis-measured covariates and left-censored response, and (iii) both mis-measured covariates and non-ignorable missing response, which are discussed in Chapters 2-4, respectively. Some asymptotic null distributions of the proposed test statistics are derived. The proposed methods are illustrated by HIV data examples and evaluated by simulation studies under different scenarios. Simulation results have shown the power advantage of the proposed testing statistics over the commonly used ones.