Signature
EVPI_pop = EVPI * sum_(t=0)^T [N_t / (1+r)^t]
| Inputs | Definition | Unit |
|---|---|---|
EVPI | Expected value of perfect information for one person facing the decision | currency per person |
N_t | Number of people whose treatment choice is informed by the decision in period t, listed across periods | people per period |
r | Rate used to discount the value to people facing the decision in later periods | proportion per year |
t | Time of each period from the start of the decision, listed across periods | years |
EVPI_pop | Expected value of perfect information for everyone expected to face the decision over its lifetime | currency |
|---|
TLast period in which the decision is expected to remain relevant (years)
Function
Value of information function
Maps the joint distribution of net benefit across the options in a decision to the expected gain from resolving some or all of the uncertainty before choosing, compared with choosing the option with the highest expected net benefit on current information.
Try this function
Implementations
Excel
Population EVPI from a period table
With the numbers of people in the named range Population, the period times in Period and the discount rate in Rate, SUMPRODUCT discounts each cohort and Excel multiplies the total by per-person EVPI.
=EVPI*SUMPRODUCT(Population/(1+Rate)^Period)
Assumptions
Stated timing and horizon
The first period is t equal to 0 and is not discounted; if the first cohort is to be discounted, t starts at 1. The time horizon stands in for future changes in technologies, prices and evidence, so it is stated and justified.
Only people who can benefit are counted
N_t excludes people whose treatment is decided before new evidence could be available, and it can be reduced for incomplete adoption. Per-person EVPI is assumed to apply unchanged to every period.
Worked examples
1,000 people a year for five years
Per-person EVPI is £200, and 1,000 people a year face the decision for five years, from t equal to 0 to 4, with future cohorts discounted at an illustrative 3.5% a year. The discounted population is about 4,673 people, so population EVPI is about £934,616. The figures are illustrative.
EVPI = 200; T = 4; t = [0,1,2,3,4]; N_t = [1000,1000,1000,1000,1000]; r = 0.035; EVPI_pop = 934615.84
Undiscounted population of 20,000
Per-person EVPI is £1,800 and 2,000 patients a year face the decision for ten years, with discounting ignored for simplicity. The 20,000 patients give a population EVPI of £36 million, matching the worked example on the expected net benefit page.
EVPI = 1800; T = 9; t = [0,1,2,3,4,5,6,7,8,9]; N_t = [2000,2000,2000,2000,2000,2000,2000,2000,2000,2000]; r = 0; EVPI_pop = 36000000
Common errors
Scaling by everyone with the condition indefinitely
Multiplying per-person EVPI by all current and future patients, with no time horizon or exclusion of those treated before evidence arrives, overstates the value of research.
Sources
Time horizons for research decisions
Philips Z, Claxton K, Palmer S. The half-life of truth: what are appropriate time horizons for research decisions? Medical Decision Making. 2008;28(3):287-299.
ISPOR introduction to value of information
Fenwick E, Steuten L, Knies S, Ghabri S, Basu A, Murray JF, Koffijberg HE, Strong M, Sanders Schmidler GD, Rothery C. Value of information analysis for research decisions: an introduction. Report 1 of the ISPOR Value of Information Analysis Emerging Good Practices Task Force. Value in Health. 2020;23(2):139-150.
Canonical Identity
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