  Background: The Expected Value of Sample Information (EVSI) determines the
economic value of any future study with a specific design aimed at reducing
uncertainty in a health economic model. This has potential as a tool for trial
design; the cost and value of different designs could be compared to find the
trial with the greatest net benefit. However, despite recent developments, EVSI
analysis can be slow especially when optimising over a large number of
different designs. Methods: This paper develops a method to reduce the
computation time required to calculate the EVSI across different sample sizes.
Our method extends the moment matching approach to EVSI estimation to optimise
over different sample sizes for the underlying trial with a similar
computational cost to a single EVSI estimate. This extension calculates
posterior variances across the alternative sample sizes and then uses Bayesian
non-linear regression to calculate the EVSI. Results: A health economic model
developed to assess the cost-effectiveness of interventions for chronic pain
demonstrates that this EVSI calculation method is fast and accurate for
realistic models. This example also highlights how different trial designs can
be compared using the EVSI. Conclusion: The proposed estimation method is fast
and accurate when calculating the EVSI across different sample sizes. This will
allow researchers to realise the potential of using the EVSI to determine an
economically optimal trial design for reducing uncertainty in health economic
models. Limitations: Our method relies on some additional simulation, which can
be expensive in models with very large computational cost.
