Background and Objectives: I investigated the use of sensitivity analyses in assessing statistical results or analytical approaches in three different statistical issues: (1) accounting for within-subject correlations in analyzing discrete choice data, (2) handling both-armed zero-event studies in meta-analyses for rare event outcomes, and (3) incorporating external information using Bayesian approach to estimate rare-event rates. Methods: Project 1: I empirically compared ten statistical models in analyzing correlated data from a discrete choice survey to elicit patient preference for colorectal cancer screening. Logistic and probit models with random-effects, generalized estimating equations or robust standard errors were applied to binary, multinomial or bivariate outcomes. Project 2: I investigated the impacts of including or excluding both-armed zero-event studies on pooled odds ratios for classical meta-analyses using simulated data. Five commonly used pooling methods: Peto, Mantel-Haenszel fixed/random effects and inverse variance fixed/random effects, were compared in terms of bias and precision. Project 3: I explored the use of Bayesian approach to incorporate external information through priors to verify, enhance or modify the study evidence. Three study scenarios were derived from previous studies to estimate inhibitor rates for hemophilia A patients treated with rAHF-PFM: 1) a single cohort of previously treated patients, 2) individual patient data meta-analysis, and 3) an previously unexplored patient population with limited data. Results and Conclusion: Project 1: When within-subject correlations were substantial, the results from different statistical models were inconsistent. Project 2: Including both-armed zero-event studies in meta-analyses increased biases for pooled odd ratios when true treatment effects existed. Project 3: Through priors, Bayesian approaches effectively incorporated different types of information to strengthen or broaden research evidence. Through this thesis I demonstrated that when analyzing complicated health research data, it was important to use sensitivity analyses to assess the robustness of analysis results or proper choice of statistical models. / Dissertation / Doctor of Philosophy (PhD)