This thesis compares statistical methods for addressing selection bias in cost-effectiveness analyses (CEA) that use observational data. The thesis has four objectives: (1) to critically appraise currently recommended statistical methods, (2) to consider alternative statistical methods for CEA, (3) to compare propensity score (PS) approaches and Genetic Matching (GM) for estimating subgroup-effects in CEA, and (4) to compare methods that combine regression with PS approaches, for CEA. I developed a new checklist for critically appraising statistical methods for addressing selection bias in CEA, and applied it in a systematic review of published CEA. Most studies used regression or matching methods, and did not assess their underlying assumptions, such as the correct specification of the PS or the endpoint regression model. I identified methods that can make less restrictive assumptions: GM, a multivariate matching method that can directly balance covariates, double-robust (DR) methods, regression-adjusted matching, and machine learning estimation of the PS and the endpoint regression. I compared these methods across a range of typical CEA circumstances, using simulations and case studies. In the first case study, where cost-effectiveness estimates for subgroups were of interest, I found that the cost-effectiveness results differed according to the statistical approach. The accompanying simulation study found that GM was relatively robust to the misspecification of the PS, and provided the least biased and most precise estimates of cost-effectiveness for each subgroup. The second simulation study considered DR methods and regression-adjusted matching for estimating overall cost-effectiveness and found that regression-adjusted matching was relatively robust to misspecification of the PS and the regression model. The third study extended these approaches with machine learning estimation of the PS and the endpoint regression, and found that bias due to misspecification could be further reduced. This thesis concludes that those approaches that relax the assumption that the statistical model for addressing selection bias is correctly specified, can give more accurate and precise estimates of cost-effectiveness than previously recommended methods. Findings from this thesis can improve the quality of CEA that use patient-level observational data, to help future studies provide a sounder basis for policy making.