Adaptive designs can improve the efficiency of drug development, but further research is needed before some are more widely implemented. One such design is a treatment-selection design, which begins with k treatment arms, but only a subset is carried forward after an interim analysis. The final analysis of the selected arm(s) is then performed using the data from both stages of the study. One issue with this design is ensuring the Type I error rate is controlled, but there have been a number of proposals that largely address this. A second drawback that has not yet been fully addressed is that the maximum likelihood estimate of the selected arm at the final analysis is often biased upward due to the selection method. Unbiased estimators already exist for this design, but methods with an acceptable balance between bias and mean squared error (MSE) are lacking. In this dissertation, two estimation approaches are proposed. The first is a parametric bootstrap resampling method in which the level of bias adjustment applied is driven by a comparison of the observed results to those expected when all arms have equal true means. The second approach is an empirical Bayes estimator that implements a novel limited translation function. These methods are compared to previously proposed approaches with respect to bias and MSE for studies that have either a normal or binomial endpoint. Both proposed methods are shown to exhibit reduced bias with reasonable MSE in some simulated scenarios, but the resampling method consistently shows similar, or improved, performance compared to previous approaches across the examined scenarios. The utility of this resampling method is further demonstrated by showing that it can be implemented when the arm with the second largest mean is selected for stage 2. It is also shown that the resampling method can be extended to when more than one arm is selected in stage 1, when there is a futility analysis, or when the study has a time-to-event endpoint. Recommendations on confidence intervals are also provided. The results demonstrate that the parametric bootstrap resampling method is a viable estimation approach for treatment-selection designs.