| Summary: | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 147-154). === The growing number of large biomedical databases and electronic health records promise to be an invaluable resource for biomedical researchers. Recent work, however, has shown that sharing this data- even when aggregated to produce p-values, regression coefficients, count queries, and minor allele frequencies (MAFs)- may compromise patient privacy. This raises a fundamental question: how do we protect patient privacy while still making the most out of their data? In this thesis, we develop various methods to perform privacy preserving analysis on biomedical data, with an eye towards genomic data. We begin by introducing a model based measure, PrivMAF, that allows us to decide when it is safe to release MAFs. We modify this measure to deal with perturbed data, and show that we are able to achieve privacy guarantees while adding less noise (and thus preserving more useful information) than previous methods. We also consider using differentially private methods to preserve patient privacy. Motivated by cohort selection in medical studies, we develop an improved method for releasing differentially private medical count queries. We then turn our eyes towards differentially private genome wide association studies (GWAS). We improve the runtime and utility of various privacy preserving methods for genome analysis, bringing these methods much closer to real world applicability. Building off this result, we develop differentially private versions of more powerful statistics based off linear mixed models. === by Sean Kenneth Simmons. === Ph. D.
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