Some statistical methods for nonlinear mixed effects models

This thesis proposes and investigates some statistical methods for the analysis of non-linear mixed effects models. Two-stage estimation method, Monte Carlo EM algorithm and model checking for frailty models are studied.; A general two-stage estimation method for nonlinear mixed effects models is proposed. Asymptotic properties of the two-stage method are studied for a wide class of nonlinear mixed effects models. It is found that validity of the two-stage estimation method depends not only on the number of subjects but also critically, on the number of observations per subject. Both theoretic and simulation results also support this finding.; A particularly important nonlinear mixed effects model, widely used in pharmaco-dynamics studies, is investigated in details. The two-stage estimation method and a Monte Carlo EM algorithm are used to fit the model. The performance of the methods is examined through extensive simulations.; Another important class of nonlinear mixed effects model, known as frailty models, in survival analysis, is also investigated. A new approach for checking the presence/absence of frailty is proposed. The new approach is motivated by an empirical Bayes method which is due to Robbins. It is nonparametric in the sense that its validity does not depend on the frailty distribution assumption. Large sample justification of the method is given. Simulation results are also presented, which show that the proposed method has good power in detecting frailty. Moreover, extension of the method to checking gamma frailty assumption is provided.