Background. Investing efficiently in future research to improve policy decisions is an important goal. Expected value of sample information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of a range of different studies. Estimating EVSI with the standard nested Monte Carlo algorithm has a notoriously high computational burden, especially when using a complex decision model or when optimizing over study sample sizes and designs. Recently, several more efficient EVSI approximation methods have been developed. However, these approximation methods have not been compared, and therefore their comparative performance across different examples has not been explored. Methods. We compared 4 EVSI methods using 3 previously published health economic models. The examples were chosen to represent a range of real-world contexts, including situations with multiple study outcomes, missing data, and data from an observational rather than a randomized study. The computational speed and accuracy of each method were compared. Results. In each example, the approximation methods took minutes or hours to achieve reasonably accurate EVSI estimates, whereas the traditional Monte Carlo method took weeks. Specific methods are particularly suited to problems where we wish to compare multiple proposed sample sizes, when the proposed sample size is large, or when the health economic model is computationally expensive. Conclusions. As all the evaluated methods gave estimates similar to those given by traditional Monte Carlo, we suggest that EVSI can now be efficiently computed with confidence in realistic examples. No systematically superior EVSI computation method exists as the properties of the different methods depend on the underlying health economic model, data generation process, and user expertise.