Opportunity Loss

Concept

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Theoretically, Opportunity Loss is the expected loss incurred when a decision made under uncertainty differs from the decision that would have been chosen if the true state of nature were known. It is a fundamental concept in Bayesian decision theory and decision analysis and represents the value forgone by selecting a suboptimal alternative. In health economics, opportunity loss quantifies the consequences of decision uncertainty and underpins value of information analysis and reimbursement decision-making.

Mathematically, opportunity loss is calculated as the difference between the net benefit of the optimal decision under perfect information and the net benefit achieved by the decision selected using current information. The expected opportunity loss is obtained by averaging this difference across all possible parameter values according to their probability distribution. This quantity is numerically equivalent to the Expected Value of Perfect Information on a per-person basis.

In practice, opportunity loss is estimated using probabilistic sensitivity analysis by comparing the optimal intervention for each simulation with the intervention selected using current evidence. Health economists use opportunity loss to quantify the consequences of uncertainty, identify decisions associated with the greatest potential regret and prioritise additional research where the expected loss from uncertainty is greatest.

Purpose

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Used to quantify the expected consequences of making decisions under uncertainty, evaluate the cost of imperfect information and support research prioritisation in health economic evaluation.

Mathematical Formulae

Primary Formula

Opportunity Loss = max(NMB) ? NMB(selected)

where:

NMB = Net Monetary Benefit

NMB(selected) = net monetary benefit of the intervention chosen using current information

Supporting Formulae

Expected Opportunity Loss:

EOL = E[max(NMB)] ? max(E[NMB])

Net Monetary Benefit:

NMB = ?E ? C

Relationship:

EOL = EVPI

where:

EVPI = Expected Value of Perfect Information

Related Mathematical Methods

• Expected Value of Perfect Information
• Expected Value of Partial Perfect Information
• Expected Value of Sample Information
• Expected Net Benefit of Sampling
• Net Monetary Benefit
• Bayesian Decision Theory
• Probabilistic Sensitivity Analysis

Example

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A probabilistic sensitivity analysis compares two treatment options. Under one simulated parameter set, Treatment A produces a net monetary benefit of �31,500 while Treatment B produces �29,800. If Treatment B is selected based on current information, the opportunity loss for that simulation is:

Opportunity Loss = �31,500 ? �29,800 = �1,700

Repeating this calculation across all simulations and averaging the results provides the expected opportunity loss, which is equivalent to the per-person Expected Value of Perfect Information.

Excel Implementation

Function	Example Formula	Health Economics Application
MAX	=MAX(B2:C2)	Identify the maximum net monetary benefit for each simulation.
IF	=IF(B2>C2,B2,C2)	Select the optimal intervention under perfect information.
AVERAGE	=AVERAGE(LossRange)	Calculate the expected opportunity loss across simulations.
MAX	=MAX(AVERAGE(B2:B10001),AVERAGE(C2:C10001))	Determine the maximum expected net monetary benefit under current information.

VBA (Optional)

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VBA can automate opportunity loss calculations across probabilistic sensitivity analyses and summarise expected opportunity loss for competing healthcare interventions.

Sources

• Claxton K. The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics. 1999;18(3):341?364.
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
• Raiffa H, Schlaifer R. Applied Statistical Decision Theory. Harvard University Press.
• ISPOR Value of Information Good Practice Reports.
• NICE. NICE Health Technology Evaluations: The Manual.