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Abstract
This dissertation consists of three papers written on semiparametric mixed-effects analysis in the presence of structural model misspecification. In the first paper, we develop a new semiparametric modeling approach to address potential structural model misspecification. Specifically, we use a set of ordinary differential equations (ODEs) with form x˙ = A(t)x + B( t) where B(t) is a nonparametric function vector estimated using penalized splines. The inclusion of nonparametric functions in ODEs makes identification of structural model misspecification feasible by quantifying the model uncertainty and provides flexibility for accommodating possible structural model deficiencies. The resulting model will be implemented in a nonlinear mixed-effects modeling setup for population analysis. We illustrate the method with an application to cefamandole data and evaluate its performance through simulations.
The second paper proposes an alternative method to the stochastic differential equation (SDE)-based method in developing a proper parametric ODE model. In SDE a Gaussian diffusion term is introduced into an ODE to quantify the system noise. However, in our proposed method B(t) in a system of ODE with form x˙ = A( t)x + B(t) is assumed to be a nonparametric function, which constructs a quantitative measure of model uncertainty so that information on the proper model structure can be derived directly from data. By means of the two examples with simulated data, we find that our method, which is a data-driven, distribution-free and intensive computation-free method, can perform model diagnostic and provide a basis for systematic model development similar to the SDE-based method.
In the third paper, Bayesian analysis is provided for fitting a spline-enhanced ODE mixed model. Since the Lindstrom and Bates' estimation algorithm used in the first paper could perform poorly when the degree of nonlinearity is high, Bayesian analysis without linearization approximation needed is a good alternative for fitting a spline-enhanced ODE mixed model. We illustrate and evaluate Bayesian analysis on our proposed model with an application to cefamandole data and a Ditropan study using simulated data.
