Drew, Clara2022-11-142022-11-142022-08https://hdl.handle.net/11299/243182University of Minnesota Ph.D. dissertation. August 2022. Major: Biostatistics. Advisor: Cavan Reilly. 1 computer file (PDF); vii, 114 pages.Understanding the long term effects of infectious disease can help clinicians anticipate, predict, and treat adverse health outcomes that may arise. To discern the natural history of an infectious disease, analyzing imperfect observational data is often the only available course of action. Two motivating examples are explored in this dissertation. The first example addresses the persistence of Ebola viral RNA in semen of survivors. We introduce methodology to robustly estimate the proportion of persistent viral shedders and the likelihood of continued positive tests over time by approximating a latent class model. The second motivational example in this dissertation pertains to the causes of increased cardiovascular disease (CVD) risk among those who are HIV positive. We implement nonlinear Mendelian randomization using the generalized method of moments to estimate how certain proteins can causally increase risk of CVD. We focus on the selection of genetic variants to use as instrumental variables in order to mitigate bias associated with this methodology.enThesis or Dissertation