Methods for analysis of multiple longitudinal outcomes and for testing multiple endpoints

Clinical trials often involve multiple binary or continuous outcomes that are repeatedly measured, in order to assess the safety and efficacy of drug therapies. However, there are limitations to available statistical methods for multi-outcome longitudinal data. First, there is debate regarding the most appropriate approach for binary data, even when the binary outcomes are considered separately. Next, if the multiple outcomes are considered simultaneously, an approach based on generalized estimating equations (GEE) (Liang and Zeger, 1986) is available that models the association between multiple outcomes over time via a Kronecker product correlation structure; However, this method is only applicable for balanced data, with an equal number of measurements per outcome within subjects. Finally, multiple tests will usually be conducted in analysis of clinical trials that involve multiple longitudinal outcomes; However, this will result in inflation of the overall type I error rate, i.e. the probability of falsely rejecting any true null hypothesis. This thesis proposes approaches that address the limitations described above and is based on the following two considerations: (i) Before any adjustment for multiple testing, appropriate statistical methods should be implemented for analysis of any binary outcomes and to properly address the multi-dimensional structure of the data; and (ii) A powerful and efficient multiple testing procedure should be applied to account for multiplicity, once the initial analysis has been conducted. We propose methods for longitudinal binary data and unbalanced multivariate longitudinal data in the framework of GEE. Further, we develop a theoretical framework for constructing a class of efficient and powerful multiple testing procedures for the control of overall type I error rate at the prespecified level of significance. The thesis consists of three parts: Part I describes our methods for single binary and multiple continuous or categorical longitudinal outcomes (Kim, Shults and Hilbe, 2008a; Kim et al., 2008b); Part II discusses the implementation of single and multiple longitudinal outcomes in our user-written SAS software (Kim and Shults, 2008c,d); and lastly, Part III describes a unified approach for constructing multiple testing procedures in the closure framework (Kim, Entsuah and Shults, 2008e)