Objective: Cost-effectiveness analysis (CEA) on trial-based data has played an important role in pharmacoeconomics. A regression model can be used to account for patient-level heterogeneity throughout covariates adjustment in CEA. However, the estimates from CEA could be biased if ignoring the censoring issue on effectiveness and costs. This study is to propose a regression model to account for both time-to-event effectiveness and cost. Methods: A bivariate regression model was proposed to analyze both effectiveness and cost simultaneously, while censored observations were also taken into account. The regression coefficients were estimated using a Bayesian approach by drawing a random sample from their posterior distribution derived from the Markov chain Monte Carlo (MCMC) method. The proposed method was illustrated using empirical data of anti-platelet therapies to the management of cardiovascular diseases for those patients with high risk of gastrointestinal (GI) bleeding, where cost-effectiveness between different therapies was analyzed under both censored and non-censored circumstances, where the effectiveness was defined as the time to re-hospitalization due to GI complications, and the cost was measured by the total drug expenditure. Results: Under censored circumstances, aspirin plus proton-pump inhibitors (PPIs) was considered more cost-effective than clopidogrel with/without PPIs, as shown in the cost-effectiveness acceptability curve, and clopidogrel was preferred to aspirin for a willingness-to-pay of 89 NTD for delaying 1 day to hospitalization due to GI complications. Conclusions: Ignoring censoring problems could possibly bias the results in CEA. This study has provided an appropriate method to conduct regression-based CEA to improve the estimation which serves its purpose for CEA concerns. Limitations: The normality assumption for the cost and effectiveness in the bivariate normal regression needs to be examined, and the conclusions may be biased if this assumption is violated. However, when sample size is sufficiently large, a slight deviation from normality would not be a serious problem.