This study consists of the sensitivity analysis for two previously developed tumor growth models: Gompertz model and quotient model. The two models are considered in both continuous and discrete time. In continuous time, model parameters are estimated using least-square method, while in discrete time, the partial-sum method is used. Moreover, frequentist and Bayesian methods are used to construct confidence intervals and credible intervals for the model parameters. We apply the Markov Chain Monte Carlo (MCMC) techniques with the Random Walk Metropolis algorithm with Non-informative Prior and the Delayed Rejection Adoptive Metropolis (DRAM) algorithm to construct parameters' posterior distributions and then obtain credible intervals.

In this dissertation we propose novel Bayesian methods of analysis of patterns of neuropsychological testing. We first focus attention to situations in which the goal of the analysis is to discover risk factors of cognitive decline using longitudinal assessment of tests scores. Variable selection in the Bayesian setting is still challenging, particularly for analysis of longitudinal data. We propose a novel approach to selection of the fixed effects in mixed effect models that combines a backward selection algorithm and a metrics based on the posterior credible intervals of the model parameters. The heuristic of this approach is based on searching for those parameters that are most likely to be different from zero based on their posterior credible intervals, without requiring ad hoc approximations of model parameters or informative prior distributions. We show via a simulation study that this approach produces more parsimonious models than other popular criteria such as the Bayesian deviance information criterion. We then apply this approach to test the hypothesis that genotypes of the APOE gene have different effects on the rate of cognitive decline of participants in the Long Life Family Study. In the second part of the dissertation we shift focus on analysis of neuropsychological tests administered using emerging digital technologies. The challenge of analyzing these data is that for each study participant the test is a data stream that records time and spatial coordinates of the digitally executed test and the goal is to extract some useful and informative summary univariate variables that can be used for analysis. Toward this goal, we propose a novel application of Bayesian Hidden Markov Models to analyze digitally recorded Trail Making Tests. Applying the Hidden Markov Model enables us to perform automatic segmentation of the digital data stream and allows us to extract meaningful metrics that correlate the Trail Making Tests performance to other cognitive and physical function test scores. We show that the extracted metrics provide information in addition to the traditionally used scores. / 2023-10-06T00:00:00Z