Algorithm 5.
Double-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 target parameter(s) sampled in step 2. |
| 4. Update the prior distribution of the target parameter(s) with the plausible dataset from step 2 to form the posterior distribution for the target parameter(s). Sample a value from this posterior distribution, which may require Markov chain Monte Carlo sampling if the prior and likelihood are not conjugate. |
| 5. Sample a value from the prior distribution of the remaining uncertain parameters. |
| 6. Evaluate the utility function for each decision option using the parameter values from steps 4 and 5 and store the results. |
| 7. Repeat steps 4 to 6 J times. This represents the inner loop of simulation. |
| 8. Calculate the mean of the utility values across all J samples for each decision option in step 7 and store. |
| 9. Repeat steps 2 to 8 for K values from the prior distribution of the parameters. This represents the outer loop of simulation. |
| 10. Calculate the mean utility values for each decision option across all K samples of the output stored in step 9, i.e., the mean of the inner loop averages. |
| 11. Choose the maximum of the expected utility values in step 10 and store. This is the expected utility with current knowledge. |
| 12. Calculate the maximum utility of the decision options (i.e. the maximum of the inner loop means) for each of the K samples of the output stored in step 9. |
| 13. Calculate the mean of the K maximum utility values generated in step 12. This is the expected utility with new sample information about the target parameter(s) of interest. |
| 14. Calculate the EVSI as the difference between the expected utility with new sample information (step 13) and the expected utility with current knowledge (step 11). |
| 15. Repeat steps 1-14 to calculate EVSI for different study designs (e.g., studies with different sample sizes or lengths of follow-up). |