Group sequential methods for nonlinear models in clinical trials with applications to prenatal research on twin births

Group sequential methods are often chosen in a randomized clinical trial for ethical reasons and economic benefits. A nonlinear model is sometimes desirable for the inherent nonlinear relationship between the response and the parameters. For example, fetal growth or birth weight can be best described using a nonlinear function, such as the Gompertz function, of gestational age. Currently, group sequential methods are mainly applied to linear models. In this thesis, group sequential methods for nonlinear models are developed. Particular emphasis is given to establish the underlying independent increments structure of sequentially computed test statistics, since standard group sequential methods can be directly applied under the structure in designing and monitoring a clinical trial. Simulation studies were conducted to examine the small sample properties of the covariance matrix of the sequentially computed test statistics. The methods are further developed to include nonnormally distributed responses. Twins are at higher risk than singletons for poor fetal growth and adverse birth outcomes. As a first step toward designing a randomized clinical trial to evaluate an appropriate intervention to enhance twin fetal growth, a conceptual model describing twin fetal growth and birth outcomes is also derived to identify critical factors that can improve twin fetal growth since most studies rely on simplistic models and fail to present a coherent picture.