Algorithm 6.

Single loop Monte Carlo scheme for computing EVSI

1. Define the proposed study design (sample size, length of follow-up etc). Determine the data generating distribution (the likelihood) under this design.

2. Sample a value from the prior distribution of the parameter(s) that will be informed by new data.

3. Sample a plausible dataset from the distribution defined in step 1, conditional on the value of the parameter(s) sampled in step 2.

4. Update the prior distribution of the target parameter(s) of interest with the new data in step 3 to form the posterior distribution. Analytically compute the expectation (mean value) of this posterior distribution. This will be possible if the prior and likelihood distributions are conjugate.

5. Evaluate the utility function for each decision option using the posterior mean estimate of the target parameter(s) and the mean values of the remaining uncertain parameters. Store the values.

6. Repeat steps 2 to 5 for N samples from the prior distribution of the target parameter(s) of interest.

7. Calculate the mean utility values for each decision option across all N samples of the output stored in step 5.

8. Choose the maximum of the expected utility in step 7 and store. This is the expected utility with current knowledge about the target parameter(s) of interest.

9. Calculate the maximum utility of the decision options for each of the N samples of the output stored in step 5.

10. Calculate the mean of the N maximum utility values generated in step 9. This is the expected utility with new sample information about the target parameter(s) of interest.

11. Calculate the EVSI as the difference between the expected utility with new sample information (step 10) and the expected utility with current knowledge (step 8).

12. Repeat steps 1-11 to calculate EVSI for different study designs (e.g., studies with different sample sizes or lengths of follow-up).