Statistical techniques for analyzing irregular and sparse cyclical longitudinal data with applications to bipolar disorder

Bipolar disorder is an illness characterized by abnormal mood swings encompassing both mania and depression, often with irregular longitudinal patterns. The variable and cyclical episodic nature of the disease presents many challenges for statistical analyses. These complex features make it difficult to characterize the data, define disease improvement measures, and develop appropriate statistical models. This is particularly problematic among rapid cycling bipolar disorder patients whose disease is defined by highly erratic and frequent mood shifts. In this dissertation, I present two approaches to analyzing data from bipolar disorder studies. The first approach focuses on the time spent in various mood states. Using longitudinal mood severity rating scale scores, data are transformed into a sequence of mood states. These sequences are analyzed as a Markov chain and stationary distributions are used to measure within- and between-group differences. The non-parametric bootstrap is employed to test for differences. The second approach focuses on features of the mood episodes. Mood severity rating scale scores are modeled as a longitudinal function of episodes and patient-specific characteristics. Episodes are parameterized by their durations, peak severities (amplitudes), and times of occurrence (locations). This flexible parametric model is fit to the data using a global iterative search algorithm known as Particle Swarm Optimization. To reduce the dimensional space of the search algorithm, an episode detection method is proposed. Estimates are derived for each patient and are used as inputs in secondary statistical models. These approaches are applied to a three-arm randomized trial of rapid cycling bipolar disorder patients. Mechanisms of these approaches are tailored to address sparsity and small sample size issues present in the data. Simulations are used to assess the statistical performance and agreement of these approaches, and recommendations for clinical application are presented.