Statistical Analysis of Biomedical Data

This dissertation is done in two parts. In the first part of the dissertation, our goal was to analyze Log-Rank and generalized Wilcoxon tests and see how well they perform under various conditions using data derived by measuring concentration levels of various miRNAs in cancer patients. This analysis was done by simulating multiple sets of data for each type of initial conditions, then using the simulated data to see how the tests perform. In the end, we have concluded that while Log-Rank test performs better there are still drawbacks. To deal with the drawbacks, we modified the Log-Rank test to give us a robust p-value. The modification was then checked to see how it performs under the same conditions as the original test. The results show that while the modification fixes the drawbacks of the original test, under certain conditions the modified test had worse performance than the original Log-Rank test. In the end, the decision whether to use the original or modified Log-Rank test should be made on the basis what drawback is a lesser one based on the user’s needs.

In the second part, our goal was to analyze brain activity levels and level of connectivity between pairs of cortex regions, using time-series data obtained from a series of fMRI images for 32 young epileptic patients; then we use the results to differentiate between different groups of epileptic patients. We got the best group separations when analyzing results from a mutual information calculation. Mutual information is a non-linear, distribution independent measure of connectivity between two-time-series. Results of this calculation allow us to perfectly separate four diagnosis groups that have more than one patient. To be robust, this type of data-driven results should be derived from analysis of a larger group of patients.