Health economic decision models compare costs and health effects of different interventions over the long term and usually incorporate survival data. Since survival is often extrapolated beyond the range of the data, inaccurate model specification can result in very different policy decisions. However, in this area, flexible survival models are rarely considered, and model uncertainty is rarely accounted for. In this article, various survival distributions are applied in a decision model for oral cancer screening. Flexible parametric models are compared with Bayesian semiparametric models, in which the baseline hazard can be made arbitrarily complex while still enabling survival to be extrapolated. A fully Bayesian framework is used for all models so that uncertainties can be easily incorporated in estimates of long-term costs and effects. The fit and predictive ability of both parametric and semiparametric models are compared using the deviance information criterion in order to account for model uncertainty in the cost-effectiveness analysis. Under the Bayesian semiparametric models, some smoothing of the hazard function is required to obtain adequate predictive ability and avoid sensitivity to the choice of prior. We determine that one flexible parametric survival model fits substantially better than the others considered in the oral cancer example.