A Power Transformation-based Compositional Data Analysis Approach with Application to Physical Activity Epidemiology

Abstract

Compositional data arise in many scientific fields, where relative proportions of different parts of a whole are basic units of data. An example is physical activity (PA) epidemiology, where one is often interested in composition of various PA intensity categories within 24-hour activity cycles based on objective measurements such as accelerometry. Although a few compositional data analysis approaches have been applied to modeling PA data, they have drawbacks that are often overlooked. In this master's thesis, we propose a power transformation-based framework for analyzing PA compositional data, which is more flexible and directly addresses the drawbacks of existing approaches. We first review current compositional data analysis approaches and their applications to PA data. Next, we present the proposed model for compositional data in the absence of zero values and investigate its theoretical properties, estimation, and inference. Moreover, we extend our power transformation-based model to account for compositional data in the presence of exact zeros. Two estimation strategies, constrained maximum likelihood estimation and modified likelihood procedures, are proposed. Extensive simulation studies were conducted to evaluate the finite sample properties of the proposed approaches. Finally, we applied these methods to study the compositional effects of sedentary behavior, light intensity PA and moderate to vigorous PA in relationship to health outcomes from the National Health and Nutrition Examination Survey (NHANES) data.