Joint Modeling with Censored Data and Group-based Trajectory Clustering

Trajectories of data are collected in a variety of settings and offer insight into the evolution of a disease in the fields of biomedical, human genetic, and public health research. However, trajectories based on serum biomarkers are often subjected to censoring due to the low sensitivity of the bioassay used to measure the marker. A joint modeling approach incorporating a binary outcome and bivariate normal longitudinal markers which subject to left-censoring is proposed as a method to understand the relationship between two longitudinal outcomes and a binary outcome. The binary outcome is fitted by a logistic regression model, and the bivariate correlated longitudinal data are modeled using a linear mixed model. The binary outcome and bivariate measurements are then joined through the random coefficients that are present in both models. A clinical example from the GenIMS study is given. The public health significance is that the proposed method examined the relationship of the two censored longitudinal biomarkers and the binary outcome in a joint modeling approach which provided for direct inference on the effects of the two censored longitudinal marker measurements on the evolution of the disease outcome in public health. \ud Secondly, latent group-based trajectory modeling has been widely used to categorize individuals into several homogeneous trajectory groups. If there exist a small number of individuals who have unique trajectory patterns that are not similar to those observed in the rest of the population, the latent group-based trajectory modeling may end up identifying a larger number of latent trajectory groups with several groups containing very few individuals. Further analysis treating latent groups as a covariate may then cause unstable estimates of standard errors. The second part of this dissertation applies the idea of the tight clustering method in the human genetic field into group-based trajectory analysis to classify latent trajectory groups that are more efficient, and to classify miscellaneous individuals or outliers whose trajectory patterns are dissimilar to the patterns in the rest of the population. We used the Bayesian information criterion as the criterion for model selection. A clinical example from the Normal Aging PiB study is provided. The public health relevance is that this innovative method is able to identify latent trajectory groups and outliers making it widely applicable in any public health setting where longitudinal trajectories are of interest