Title: On Compositional Data Modeling and Its Biomedical Applications
Description: Compositional data occur naturally in biomedical studies which investigate changes in the proportions of various components of a combined medical measurement. The statistical method to analyze this type of data is underdeveloped. Currently the multivariate logitnormal model seems to be the only model routinely used in analyzing compositional data, and its application is mainly in geology and has yet to be known to the biomedical elds. In this dissertation, we propose the multivariate simplex model as an alternative method of modeling compositional data, either cross-sectional or longitudinal and develop statistical methods to analyze such data. We suggest three approaches to making a fair comparison between the multivariate simplex models and the multivariate logit-normal models. The simulations indicate that our proposed multivariate simplex models often outperform the multivariate logit-normal models.