Indiana University-Purdue University Indianapolis (IUPUI) / Dementia studies often collect multiple longitudinal neuropsychological measures in order to examine patients' decline across a number of cognitive domains. Dementia patients have shown considerable heterogeneities in individual trajectories of cognitive decline, with some patients showing rapid decline following diagnoses while others exhibiting slower decline or remain stable for several years. In the first part of this dissertation, a multivariate finite mixture latent trajectory model was proposed to identify longitudinal patterns of cognitive decline in multiple cognitive domains with multiple tests within each domain. The expectation-maximization (EM) algorithm was implemented for parameter estimation and posterior probabilities were estimated based on the model to predict latent class membership. Simulation studies demonstrated satisfactory performance of the proposed approach. In the second part, a simulation study was performed to compare the performance of information-based criteria on the selection of the number of latent classes. Commonly used model selection criteria including the Akaike information criterion (AIC), Bayesian information criterion (BIC), as well as consistent AIC (CAIC), sample adjusted BIC (SABIC) and the integrated classification likelihood criteria (ICLBIC) were included in the comparison. SABIC performed uniformly better in all simulation scenarios and hence was the preferred criterion for our proposed model. In the third part of the dissertation, the multivariate finite mixture latent trajectory model was extended to situations where the true latent class membership was known for a subset of patients. The proposed models were used to analyze data from the Uniform Data Set (UDS) collected from Alzheimer's Disease Centers across the country to identify various cognitive decline patterns among patients with dementia.

The astonishing progress of molecular biology, engineering and computer science has resulted in mature technologies capable of examining multiple cellular components at a genome-wide scale. Protein-protein interactions are one example of such growing data. These data are often organised as networks with proteins as nodes and interactions as edges. Albeit still incomplete, there is now a substantial amount of data available and there is a need for biologically meaningful methods to analyse and interpret these interactions. In this thesis we focus on how to compare protein interaction networks (PINs) and on the rela- tionship between network architecture and the biological characteristics of proteins. The underlying theme throughout the dissertation is the use of small subgraphs – small interaction patterns between 2-5 proteins. We start by examining two popular scores that are used to compare PINs and network models. When comparing networks of the same model type we find that the typical scores are highly unstable and depend on the number of nodes and edges in the networks. This is unsatisfactory and we propose a method based on non-parametric statistics to make more meaningful comparisons. We also employ principal component analysis to judge model fit according to subgraph counts. From these analyses we show that no current model fits to the PINs; this may well reflect our lack of knowledge on the evolution of protein interactions. Thus, we use explanatory variables such as protein age and protein structural class to find patterns in the interactions and subgraphs we observe. We discover that the yeast PIN is highly heterogeneous and therefore no single model is likely to fit the network. Instead, we focus on ego-networks containing an initial protein plus its interacting partners and their interaction partners. In the final chapter we propose a new, alignment-free method for network comparison based on such ego-networks. The method compares subgraph counts in neighbourhoods within PINs in an averaging, many-to-many fashion. It clusters networks of the same model type and is able to successfully reconstruct species phylogenies solely based on PIN data providing exciting new directions for future research.