<p>In this thesis, we perform a survival analysis for right-censored data of populations with a cure rate. We consider two cure rate models based on the Geometric distribution and Poisson distribution, which are the special cases of the Conway-Maxwell distribution. The models are based on the assumption that the number of competing causes of the event of interest follows Conway-Maxwell distribution. For various sample sizes, we implement a simulation process to generate samples with a cure rate. Under this setup, we obtain the maximum likelihood estimator (MLE) of the model parameters by using the gamlss R package. Using the asymptotic distribution of the MLE as well as the parametric bootstrap method, we discuss the construction of confidence intervals for the model parameters and their performance is then assessed through Monte Carlo simulations.</p> / Master of Science (MSc)

Model-based clustering is a probabilistic approach that views each cluster as a component in an appropriate mixture model. The Gaussian mixture model is one of the most widely used model-based methods. However, this model tends to perform poorly when clustering high-dimensional data due to the over-parametrized solutions that arise in high-dimensional spaces. This work instead considers the approach of combining dimension reduction techniques with clustering via a mixture of generalized hyperbolic distributions. The dimension reduction techniques, principal component analysis and factor analysis along with their extensions were reviewed. Then the aforementioned dimension reduction techniques were individually paired with the mixture of generalized hyperbolic distributions in order to demonstrate the clustering performance achieved under each method using both simulated and real data sets. For a majority of the data sets, the clustering method utilizing principal component analysis exhibited better classi cation results compared to the clustering method based on the extending the factor analysis model. / Thesis / Master of Science (MSc)

Anticipations of personalized medicine are primarily attributed to the recent advances in computational science and high-throughput technologies that enable the ever-more realistic modeling of complex diseases. These diseases result from the interplay between genes and environment that have limited our ability to predict, prevent, or treat them. While many envision the utility of integrated high-dimensional patient-specific information, basic research towards developing accurate and reliable frameworks for personalized medicine is relatively slow in progress. This thesis provides a state-of-the-art review of current challenges towards personalized medicine. There is a need for global investment in basic research that includes 1) cost-effective generation of high-quality high-throughput data, 2) hybrid education and multidisciplinary teams, 3) data storage and processing, 4) data integration and interpretation, and 5) individual and global economic relevance; to be followed by global investments into public health to adopt routine personalized medicine. This review also highlights that unknown or unadjusted interactions result in true heterogeneity in the effect and relevance of patient data. This limits our ability to integrate and reliably utilize high-dimensional patient-specific data. This thesis further investigates the true heterogeneity in marginal effects of known BMI genetic variants. This involved the development of the novel statistical method, meta-quantile regression (MQR), to identify variants with potential gene-gene / gene-environment interactions. Applying MQR on public and local data (75,230 European adults) showed that FTO, PCSK1, TCF7L2, MC4R, FANCL, GIPR, MAP2K5, and NT5C2 have potential interactions on BMI. In addition, a gene score of 37 BMI variants shows that the genetic architecture of BMI is shaped by gene-gene and gene-environment interactions. The computational cost of fitting MQR models was greatly reduced using unconditional quantile regression. The utility of MQR was further compared to variance heterogeneity tests in identifying variants with potential interactions. MQR tests were found to have a higher power of detecting synergetic and antagonistic interactions for skewed quantitative traits while maintaining nominal Type I error rates compared to variance heterogeneity tests. Overall, MQR is a valuable tool to detect potential interactions without imposing assumptions on the nature of interactions. / Thesis / Doctor of Philosophy (PhD) / The anticipations of personalized medicine are largely due to the recent advances in computational science and our capabilities to rapidly measure and generate biological data. These developments have enhanced our understanding of complex diseases, and should theoretically enable us to predict, prevent and treat such cases in a proactive personalized context. This thesis provides a state-of-the-art review of the challenges and opportunities that explain the relatively slow progress towards personalized medicine. It identifies data integration and interpretation as the main bottleneck and proposes a novel method, termed Meta-Quantile Regression (MQR), to identify genetic variations with potential interactions. Analyzes were conducted on a total of 75,230 individuals with European ancestry, and the genetic architecture of obesity was shown to be shaped by genetic interactions. Lastly, the computational cost of MQR was substantially reduced using linear approximations, and MQR was further shown to have better performance in identifying potential interactions compared to classic variance tests.

This thesis studies the problem of frequentist model averaging over a set of multiple $\epsilon$-support vector regression (SVR) models, where the support vector machine (SVM) algorithm was extended to function estimation involving continuous targets, instead of categorical ones. By assigning weights to a set of candidate models instead of selecting the least misspecified one, model averaging presents a strong alternative to model selection for tackling model uncertainty. Not only do we describe the construction of smoothed BIC/AIC model averaging weights, but we also propose a Mallows model averaging procedure which selects model weights by minimizing Mallows' criterion. We conduct two studies where the set of candidate models can either include or not include the true model by making use of simulated random samples obtained from different data-generating processes of analytic form. In terms of mean squared error, we demonstrate that our proposed method outperforms other model averaging and model selection methods that were tested, and the gain is more substantial for smaller sample sizes with larger signal-to-noise ratios. / Thesis / Master of Science (MSc)

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