Multi-Response Nonlinear Mixed Effects Models for Longitudinal Data Analysis

摘要

This thesis presents a method for analyzing multi-response nonlinear longitudinaldata. Currently, the methods used to handle multi-response nonlinear longitudinal data usually involve a two stage approach. First, nonlinear functions for each variable are fit to each subject. Second, the parameters from stage one are then used to estimate population average parameters, estimate parameter correlations, conduct hypothesis tests, etc. This two stage approach is often cumbersome because it involves modeling each individual separately. Sometimes the two stage approach is impossible because there might be inadequate data to fit a nonlinear function to certain subjects. This thesis presents a unified approach for fitting multi-response nonlinear mixed effects models (MNLMEM) to longitudinal data. Essentially the nonlinear aspect of the model is handled by Taylor series expansion. Once the model has been linearized, a multi-response analog of the Laird and Ware model (Biometrics 38: 963-974,1982.) that has been developed by Zucker, Zerbe, and Wu (Biometrics, in press) is then applied. In addition, if the errors in the model are additive and the model has been linearized, it is also possible to use an algorithm discussed by Hocking (The Analysis of Linear Models, 1985). Using either approach it is possible to obtain estimates of the fixed effects, variance components, and Fisher's information matrix for both the fixed effects and variance components. This makes it possible to conduct asymptotic hypothesis tests and build asymptotic confidence intervals about functions of the fixed effects and variance components. The methods are very general and allow for missing and unequally spaced data.