Signature
D = (1 + r) * (1 - (1 + r)^(-Y)) / r; EVSI_pop = EVSI * N * D
| Inputs | Definition | Unit |
|---|---|---|
r | Annual rate used to discount the value to later cohorts, entered as a proportion above zero, with a value such as 0.000001 standing in for no discounting | proportion per year |
Y | Number of years, counted from year 0, over which the study result informs treatment choices | years |
EVSI | Expected value of sample information per patient from HE-FM-EVSI-001 or HE-FM-EVSI-003 | currency per patient |
N | Number of patients a year whose treatment the study result would inform | patients per year |
D | Present value of one patient a year in years 0 to Y minus 1 at rate r, which tends to Y as r approaches zero | years |
|---|---|---|
EVSI_pop | Expected value of sample information for everyone whose treatment the study result would inform over the decision's lifetime | currency |
Function
Expected value of sample information function for a proposed study design
Maps the current uncertainty about a decision model's parameters, the sampling distribution of the data a proposed study would collect and the net benefit of each option to the expected gain from choosing after the study reports rather than now. EVSI equals the expectation, over the datasets X the study could produce, of the largest posterior expected net benefit among the options, less the largest expected net benefit on current evidence, the form given as equation 10 of the second ISPOR value of information report and equation 2 of Kunst and colleagues. It replaces the perfect knowledge of a parameter subset in EVPPI (HE-FM-VOI-003) with the data of a study of stated design and size, so it is never negative and does not exceed EVPPI for the parameters the study informs or per-person EVPI (HE-FM-VOI-001). This package gives the exact form for a study with two possible results, the normal preposterior variance, closed-form EVSI for two options and population EVSI over the decision's lifetime on the basis used for population EVPI (HE-FM-VOI-002). The expected net benefit of sampling, population EVSI less the cost of the study, has its own package. Notation follows the Expected Value of Sample Information article.
Try this function
Implementations
Excel
Population EVSI with the beneficiary factor from Excel PV
With per-person EVSI in a cell named EVSIPerPerson, the annual population in AnnualPop, the rate in DiscountRate and the lifetime in DecisionYears, PV with type 1 returns D, the present value of one patient a year with the first in year 0.
=EVSIPerPerson*AnnualPop*PV(DiscountRate,DecisionYears,-1,0,1)
Assumptions
Constant beneficiary population able to act on the result from year 0
N patients a year face the decision and every cohort from year 0 benefits from the result. Because benefits arrive only when the study reports, the first ISPOR report notes that the beneficiary population is usually adjusted for the time a study takes, which here means starting the sum at the year the result is available.
Justified decision lifetime explored in scenarios
Y stands in for future changes such as patent expiry, new comparators and other research. The first ISPOR report recommends justifying the effective time horizon and exploring alternatives in scenario analyses, because value of information results can be highly sensitive to it.
Worked examples
Population EVSI of study S1 for 2,000 patients a year over five years at 3.5%
With an illustrative 2,000 patients a year for five years, the 10,000 future patients of the article's example, and an illustrative discount rate of 3.5% a year, D is about 4.6731 and the GBP 73 per-patient EVSI of S1 gives a population EVSI of about GBP 682,270.
EVSI = 73; N = 2000; Y = 5; r = 0.035; D = 4.673079; EVSI_pop = 682269.56
Population EVSI of study S2 for 2,000 patients a year over five years at 3.5%
On the same illustrative basis the GBP 171 per-patient EVSI of S2 gives a population EVSI of about GBP 1.60 million.
EVSI = 171; N = 2000; Y = 5; r = 0.035; D = 4.673079; EVSI_pop = 1598193.09
Undiscounted population EVSI of study S1 approximated with a near-zero rate
With a rate of 0.000001, D is within 0.0001 of 5 and population EVSI is about GBP 0.73 million, the undiscounted figure for 10,000 patients in the article, a limiting case that checks the factor.
EVSI = 73; N = 2000; Y = 5; r = 0.000001; D = 4.99999; EVSI_pop = 729998.54
Common errors
Per-patient EVSI compared with the total cost of a study
Setting S1's GBP 73 per patient against an illustrative study cost of GBP 0.4 million makes the study look far too expensive, while its population EVSI over 10,000 future patients is about GBP 0.73 million undiscounted. Per-person values are scaled to the beneficiary population before any comparison with study cost.
Counting patients treated before the study reports in population EVSI
If S1 takes two years to report, only the last three of the five annual cohorts can benefit, and population EVSI at 3.5% is about GBP 395,207 instead of GBP 682,270. Counting every cohort from year 0 overstates the value of a slow study.
Sources
ISPOR task force equation for the population value of research
Rothery C, Strong M, Koffijberg HE, Basu A, Ghabri S, Knies S, Murray JF, Sanders Schmidler GD, Steuten L, Fenwick E. Value of information analytical methods. Report 2 of the ISPOR Value of Information Analysis Emerging Good Practices Task Force. Value in Health. 2020;23(3):277-286. Equation 15 gives population value of information as the per-person value times the sum over periods t from 0 to T of the incidence I_t divided by (1+d)^t, and the text states that the value of research is discounted over the time horizon and that its benefits are realised only when the study findings are reported.
ISPOR task force recommendation on the effective time horizon for population VOI
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. The section on the beneficiary population and Good Practice Recommendation 3 ask analysts to justify the effective time horizon and explore alternatives in scenario analyses, because VOI estimates can be highly sensitive to it, and note that the beneficiary population is usually adjusted for the time a study takes to finish.
Canonical Identity
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