Longitudinal datasets that contain the same variables at multiple time occasions from a given subject are frequently observed in current medical studies.

Research has been done to develop method to analyze such data and make meaningful inferences. In this dissertation, we use hidden Markov models (HMM) and a modied reversible jump Markov chain Monte Carlo algorithm to analyze the longitudinal medical data .

For an eye tracking data of participants looking at chest X-rays with a potential cancerous nodule, we use the HMM model to nd out what areas on the images attract participants attention more, how their eyes jump among these areas, and which scan pattern is related to an eective detection of the nodule. We estimated the total number of areas of interest (AOIs) on each image, as well as their centers,

sizes and orientations. We use pixel luminance as prior information, as nodules are often brighter and luminance may thus aect the AOIs. Dierences in scan patterns between those who found the nodule and those who didn't, are discussed.

For a HIV clinical trial data, we use the hidden Markov model to estimate the health states each patient at dierent time points, compare the states with physical phenomena in HIV clinical trials, and predict health development patterns.