Expected Value of Partial Perfect Information

Expected Value of Partial Perfect Information in Research Prioritisation

In health economic evaluation, the expected value of partial perfect information (EVPPI) shows which uncertain inputs of a cost-effectiveness model are potentially worth researching. It takes the cost of decision uncertainty that the expected value of perfect information measures for the whole model and asks how much of it would disappear if one parameter, or one group of parameters that a single study could inform, were known exactly. The ISPOR Value of Information Task Force places it as the second stage of a value of information analysis, after EVPI and before the expected value of sample information for a specific study. It is also called partial EVPI or the expected value of perfect parameter information.

From the whole model to groups of parameters

In Bayesian decision theory a risk-neutral decision maker adopts the option with the highest expected net benefit, and value of information analysis asks whether more evidence would change that choice enough to justify its cost. EVPI answers this for all parameter uncertainty at once. EVPPI splits the parameters into a set of interest, which is resolved, and a complementary set, which stays uncertain.

The first ISPOR report sets EVPPI as the step that follows a population EVPI large enough to make research potentially worthwhile. Its good practice recommendations are to estimate EVPPI for groups of parameters that a new study would inform together, and to compare population EVPPI with the expected cost of research on each group. The second report adds that a population EVPPI below the cost of research is sufficient to rule that research out, while one above it is necessary but not sufficient. It also states that the EVPPI for a set of parameters is an upper limit on the EVSI of any study informative about them, and the value of a real design net of its cost is the expected net benefit of sampling.

The EVPPI formula and the order of its operations

The second ISPOR report writes EVPPI as the difference between two expected values. The first is the expected value of deciding after the parameters of interest are known, and the second is the expected value of deciding now.

$$\text{EVPPI}(\theta_i) = E_{\theta_i}\left[ \max_{d} E_{\theta_c \mid \theta_i}\{NB(d, \theta_i, \theta_c)\} \right] - \max_{d} E_{\theta}\{NB(d, \theta)\}$$

where $\theta_i$ is the set of parameters of interest, $\theta_c$ is the remaining parameters, $\theta$ is all parameters, $d$ is a decision option, $NB$ is net benefit (the report writes a utility function $U$), and each $E$ is an expectation over the current distribution of the parameters in its subscript, where $\theta_c \mid \theta_i$ conditions on the parameters of interest.

Inside the brackets, the parameters of interest are treated as known, the remaining uncertainty is averaged out and the best option for that value is chosen. The outer expectation averages over the values the parameters of interest might take, because they are unknown when the research decision is made. The second term is the expected net benefit of the option chosen on current evidence, as in EVPI.

Net benefit is usually expressed as net monetary benefit or net health benefit at a stated cost-effectiveness threshold, so EVPPI changes with the threshold, and the first ISPOR report recommends presenting results for a range of thresholds. Two bounds follow from the definition. EVPPI cannot be negative, because the option chosen on current evidence remains available whatever is learnt, and it cannot exceed EVPI, because knowing every parameter is worth at least as much as knowing some of them. EVPPI is zero when no plausible value of the parameters of interest would change the decision.

Why the most uncertain parameter is not always the most valuable

The first ISPOR report notes that the parameters with the highest EVPPI will not necessarily be the most uncertain ones. EVPPI is high only where parameter uncertainty drives decision uncertainty, and resolving a very uncertain parameter that cannot change the decision has no value to the decision maker.

A one-way sensitivity analysis and its tornado diagram rank inputs by their effect on the result. The 2026 HEMA report on uncertainty in economic evaluation notes that tornado diagrams examine inputs individually and generally do not preserve correlations, and that their findings should be read alongside probabilistic analysis and, where appropriate, EVPI or EVPPI.

The first ISPOR report recommends calculating EVPPI for the whole group when one study would inform several parameters, because EVPPI is typically not additive. Strong, Oakley and Brennan defined their case-study groups by the study that could inform them, such as effectiveness parameters for a trial and duration-of-response parameters for long-term follow-up.

Worked example with two parameters and a combined trial (illustrative)

All numbers in this example are illustrative. A new treatment is compared with standard care at a threshold of GBP 25,000 per QALY, the lower end of the range in the NICE manual (PMG36). The incremental net monetary benefit (INB) of the new treatment depends on two independent parameters, the relative treatment effect A and the health-state utility B. Each is either high or low with probability 0.5, so the four combinations each have probability 0.25.

Step 1 finds the decision on current evidence. Standard care has an INB of zero, so the new treatment is adopted when expected INB is positive.

$$E[\text{INB}] = 0.25 \times (2{,}000 + 1{,}000 + 200 - 2{,}400) = 0.25 \times 800 = 200$$

where 0.25 is the probability of each combination and 200 is the expected INB in GBP per patient, so the new treatment is adopted.

Step 2 computes EVPI. With perfect information the new treatment would be chosen in the first three combinations and standard care, worth zero, in the fourth.

$$\text{EVPI} = 0.25 \times (2{,}000 + 1{,}000 + 200 + 0) - 200 = 800 - 200 = 600$$

where 800 is the expected value with perfect information and 600 is EVPI in GBP per patient.

Step 3 computes EVPPI for A. If A is known to be high, expected INB is the mean of 2,000 and 1,000, which is 1,500, and the new treatment is chosen. If A is known to be low, expected INB is the mean of 200 and -2,400, which is -1,100, so standard care is chosen and the value is zero.

$$\text{EVPPI}(A) = 0.5 \times 1{,}500 + 0.5 \times 0 - 200 = 750 - 200 = 550$$

where 0.5 is the probability of each value of A and 550 is EVPPI for A in GBP per patient.

Step 4 repeats this for B. Given high utility, expected INB is the mean of 2,000 and 200, which is 1,100, and given low utility it is -700, so standard care is chosen.

$$\text{EVPPI}(B) = 0.5 \times 1{,}100 + 0.5 \times 0 - 200 = 550 - 200 = 350$$

where 350 is EVPPI for B in GBP per patient.

Step 5 checks additivity. The two values sum to GBP 900, but EVPPI for A and B together equals EVPI, GBP 600, because these are the only uncertain parameters.

Step 6 adds a third parameter, the unit cost of a rare adverse event, which is very uncertain but moves INB by only GBP 100 up or down with equal probability. Its conditional expected INB is 300 or 100, positive either way, so the decision never changes and its EVPPI is zero.

Step 7 scales to the population, assuming that 2,000 people a year face the choice for 10 years, discounted at 3.5% a year, the PMG36 reference-case rate. The discount factors for years 0 to 9 sum to 8.6077, so the discounted population is about 17,215 people (2,000 x 8.6077 = 17,215.4). Population EVPPI is then about GBP 9.47 million for A, GBP 6.03 million for B and GBP 10.33 million for A and B together.

Step 8 applies the decision rule. A trial of the treatment effect costing GBP 4 million passes the test for A, so the analysis moves on to EVSI. A trial measuring both parameters and costing GBP 11 million would look worthwhile if the separate values were summed (GBP 900 per patient gives about GBP 15.49 million), but it fails against the correct joint value of GBP 10.33 million. At GBP 35,000 per QALY every value would be recomputed from the probabilistic analysis, not rescaled.

Computing EVPPI from a probabilistic analysis

The second ISPOR report notes that an analytic solution rarely exists because the first term contains a nested expectation, so EVPPI is estimated by simulation. The methods differ in how they handle that inner expectation.

The traditional method is a nested double loop. An outer loop draws a value of the parameters of interest, an inner loop runs a probabilistic sensitivity analysis with those values fixed, and the highest mean net benefit is recorded for each outer draw and averaged. With correlated parameters, the inner draws must come from the conditional distribution of the remaining parameters. The second report warns that small inner loops give biased estimates, and Strong, Oakley and Brennan explain that the maximisation step makes the bias upward. An EVPPI estimate above EVPI is therefore a sign of Monte Carlo error, not a finding.

A single loop is enough for some models. The second report explains that when the model is linear or multilinear in the remaining parameters, with no correlation between those multiplied together, their means can replace the inner loop, and it prefers single-loop methods where they apply.

Regression methods use only the stored probabilistic sample. Strong, Oakley and Brennan regress each option's net benefit on the parameters of interest, using a generalised additive model or Gaussian process regression, and treat the fitted values as the conditional expected net benefit.

$$\widehat{\text{EVPPI}} = \frac{1}{N} \sum_{n=1}^{N} \max_{d} \hat{g}(d, \theta_i^{(n)}) - \max_{d} \frac{1}{N} \sum_{n=1}^{N} \hat{g}(d, \theta_i^{(n)})$$

where $N$ is the number of probabilistic samples, $\theta_i^{(n)}$ is the value of the parameters of interest in sample $n$ and $\hat{g}(d, \theta_i^{(n)})$ is the fitted net benefit of option $d$ at that value. Using the fitted values in the second term as well exploits the positive correlation between the two terms and improves precision.

In their first case study, with 10,000 model runs, the additive model estimate for two effectiveness parameters had a standard error of about GBP 16 against a reference value of about GBP 248, while a double loop of 10 outer by 1,000 inner runs had a standard error of about GBP 140. The authors add that the additive model is likely to fail with more than about six interacting parameters of interest, where they recommend the Gaussian process. Because it needs only the probabilistic sample, the regression also works for models built in specialist software or owned by someone else. Software is listed on the VOI analysis page.

What EVPPI can support in HTA and research decisions

The HEMA report describes EVPPI as pointing to the parameters where the value of information is highest. It recommends reporting EVPI with every probabilistic analysis, with EVPPI and EVSI used where a research decision is actually in prospect, and does not propose parameter-level analysis as a general requirement.

Its Table 5.1 adds a check. For sampling uncertainty from well-designed, relevant studies, EVPI and EVPPI measure the whole residual, but for estimates from studies at risk of bias the uncertainty is captured only where a bias adjustment has been parameterised, and otherwise EVPI understates the cost of uncertainty.

Limits and common misreadings

Several errors recur in applied work. Each overstates the case for research or points it at the wrong parameter.

1. Summing EVPPIs. Separate values are not additive, so a study informing several parameters needs EVPPI computed for the group.
2. Treating EVPPI as the value of a study. EVPPI assumes the parameters become known exactly. Strong, Oakley and Brennan describe it as only an upper bound on the expected value of research, and EVSI values a real design.
3. Ignoring what is not parameterised. The second ISPOR report notes, discussing minimal models, that EVPPI cannot be computed for quantities not parameterised in the model, so structural choices explored only through scenarios have no EVPPI.
4. Arbitrary grouping. Groups that match no feasible study, or that split correlated parameters, give values no research decision can use.

Sources

• Fenwick E, Steuten L, Knies S, Ghabri S, Basu A, Murray JF, Koffijberg H, 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. https://doi.org/10.1016/j.jval.2020.01.001
• Rothery C, Strong M, Koffijberg H, 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. https://doi.org/10.1016/j.jval.2020.01.004
• Strong M, Oakley JE, Brennan A. Estimating multiparameter partial expected value of perfect information from a probabilistic sensitivity analysis sample: a nonparametric regression approach. Medical Decision Making. 2014;34(3):311-326. https://doi.org/10.1177/0272989X13505910
• Steuten L, Thavorn K, Cipriano LE, Guertin JR, McQueen B, Schmidler G, Sullivan S, Wailoo A, Sculpher M. Methods to Analyze and Present Uncertainty in Economic Evaluation to Support HTA Decisions (HEMA Report 2). Health Economics Methods Advisory; 2026. Sections 4.5, 5.4 and 6.4, and Table 5.1. https://hemamethods.org/wp-content/uploads/2026/10/HEMA-Report-2_For-Publication_100726.pdf
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Sections 4.5.1, 6.3.4 and 6.3.7. https://www.nice.org.uk/process/pmg36