Value of information

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Value of information (VOI) in decision analysis is the amount a decision maker would be willing to pay for information prior to making a decision.<section end=glossary />

Scope

How can value of information be calculated?

Definition

Input

To calculate value of information, you need

• a decision to be made,
• an outcome indicator to be optimised,
• an optimising function to be used as the criterion for the best decision,
• an uncertain variable of interest (optional, needed only if partial VOI is calculated for the variable)

Output

Value of information, i.e. the amount of money that the decision-maker is willing, in theory, to pay to obtain a piece of information.

Rationale

• See Decision theory, Value of information, and Expected value of perfect information.
• There are different kinds of indicators under value of information, depending on what level of information is compared with the current situation:

  EVPI

  Expected value of perfect information (everything is known perfectly)

  EVPPI

  Expected value of partial perfect information (one variable is known perfectly, otherwise current knowledge)

  EVII

  Expected value of imperfect information (things are known better but not perfectly)

  EVPII

  Expected value of partial imperfect information (one variable is known better but not perfectly)

Result

Procedure

EVPI = E(Max(U(di,θ))) - Max(E(U(di,θ))), 

where E=expectation over uncertain parameters θ, Max=maximum over decision options i, U=utility of decision d.

The general formula for EVPII is:

EVPII = Eθ2(U(Max(Eθ2(U(di,θ2))),θ2)) - Eθ2(U(Max(Eθ1(U(di,θ1))),θ2)),

where θ1 is the prior information and θ2 is the posterior (improved) information. EVPPI can be calculated with the same formula in the case where P(θ2)=1 iff θ2=θ1. If θ includes all variables of the assessment, the formula gives total, not partial, value of information.

The interpretation of the formula is the following (starting from the innermost parenthesis). The utility of each decision option d_i is estimated in the world of uncertain variables θ. Expectation over θ is taken (i.e. the probability distribution is integrated over θ), and the best option i of d is selected. The point is that in the first part of the formula, θ is described with the better posterior information, while the latter part is based on the poorer prior information. Once the decision has been made, the expected utility is estimated again based on the better posterior information in both the first and second part of the formula. Finally, the difference between the utility after the better and poorer information, respectively, gives the value of information.

Management

• Analytica file for calculating value of information

How to use the method

Value of information score

The VOI score is the current expected value of perfect information (EVPI) for that variable in an assessment where it is used. If the variable is used is several assessments, it it the sum of EVPIs across all assessments.