Expected Value of Sample Information

Concept

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Theoretically, Expected Value of Sample Information (EVSI) is a value of information measure that quantifies the expected benefit of collecting additional imperfect information before making a healthcare decision. It is founded on Bayesian decision theory and estimates the improvement in decision-making that would result from conducting a proposed research study with a specified design and sample size. In health economics, EVSI is used to determine the value of future research and to optimise study design before new evidence is collected.

Mathematically, EVSI is calculated as the difference between the expected net benefit obtained after updating current knowledge with information from a future sample and the maximum expected net benefit based on existing evidence alone. Unlike Expected Value of Perfect Information, EVSI recognises that real studies provide only partial reductions in uncertainty because sample information is incomplete.

In practice, EVSI is estimated using probabilistic sensitivity analysis combined with Bayesian updating, nested Monte Carlo simulation or computational approximation methods. Population EVSI is obtained by multiplying the per-person EVSI by the expected number of patients affected during the decision relevance period. EVSI is routinely used to determine whether proposed research is worthwhile and to optimise trial sample sizes within health technology assessment.

Purpose

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Used to quantify the expected value of collecting additional imperfect evidence, supporting research prioritisation, study design and efficient allocation of research resources.

Mathematical Formulae

Primary Formula

EVSI = E[max(E(NMB|Data))] ? max(E(NMB))

where:

NMB = Net Monetary Benefit

Data = future sample information

Supporting Formulae

Net Monetary Benefit:

NMB = ?E ? C

Population EVSI:

Population EVSI = EVSI ? N

where:

N = affected population over the decision relevance period

Relationship:

0 � EVSI � EVPI

Related Mathematical Methods

• Expected Value of Perfect Information
• Expected Value of Partial Perfect Information
• Expected Net Benefit of Sampling
• Bayesian Decision Theory
• Probabilistic Sensitivity Analysis
• Monte Carlo Simulation
• Value of Information Analysis

Example

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A proposed clinical trial is expected to reduce uncertainty surrounding treatment effectiveness. The EVSI is estimated as �260 per patient. If the intervention is expected to affect 30,000 patients during the decision relevance period, the population EVSI is:

Population EVSI = �260 ? 30,000 = �7.8 million

If the projected research cost is substantially less than �7.8 million, the proposed study is expected to provide worthwhile information for decision-making.

Excel Implementation

Function	Example Formula	Health Economics Application
AVERAGE	=AVERAGE(ResultRange)	Estimate expected net monetary benefit from simulated posterior results.
MAX	=MAX(B2:D2)	Identify the optimal decision following simulated sample information.
SUMPRODUCT	=EVSI_per_patient*Population	Calculate the population EVSI.
IF	=IF(B2>C2,"Research worthwhile","Research not worthwhile")	Compare EVSI with expected research costs during study planning.

VBA (Optional)

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VBA can automate nested Monte Carlo simulations, estimate EVSI for alternative trial designs and compare the value of additional research across candidate sample sizes.

Sources

• Ades AE, Lu G, Claxton K. Expected value of sample information calculations in medical decision modelling. Medical Decision Making. 2004;24(2):207?227.
• Heath A, Manolopoulou I, Baio G. Efficient Monte Carlo estimation of the Expected Value of Sample Information using moment matching. Medical Decision Making. 2018;38(2):163?173.
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
• ISPOR Value of Information Good Practice Reports.
• NICE. NICE Health Technology Evaluations: The Manual.