Expected Value of Perfect Information

You have just done a study comparing the cost-effectiveness of drug A and drug B.  Should you just rest on these laurels or is further research on drug B warranted.  Decision Modelling for Health Economic Evaluation claims that there are 3 criteria that should determine whether or not you decide to collect more information:

  • The expected cost-effectiveness of drug B given current information.  Let us assume that drug A is far superior to drug B.  In this case the value of future information is likely low.  Even if drug B turns out to be somewhat more cost-effective than previous estimates had indicated, because drug A was far superior to drug B, it is unlikely that new information will make drug B better than drug A.  Thus, if the prior information tells us that there is a large difference in the expected cost effectiveness in the two drugs, it is unlikely that additional information will change that decision.
  • The uncertainty surrounding prior cost-effectiveness estimates.  The more uncertain the prior estimates the more valuable is any new information.  If prior estimates are believed to be very accurate, than there is likely little value in collecting more information.
  • The slope of the loss function which values the consequences of an error.  This basically means how important this decision is in the grand scheme of things.   If the drug would be a potential cure for AIDS, then it is very important to get this decision right.  If the treatment is for a very rare, very mild allergy, then additional information would be less valuable than in the AIDS drugs.

EVPI – Normal Distribution

Mathematically, if we assume a normal distribution, we can calculate the expected value of perfect information (EVPI) as follows:

  • EVPI = λ * σ0*L(|η0|/σ0)

 λ is the cost effectiveness threshold, η0 is the prior mean incremental net health benefit, σ02 is the prior variance of the incremental net health benefit, and L(⋅) is the loss function.

EVPI – Nonparametric Approach

To calculate the expected value of perfect information (EVPI) in a non parametric setting, we simply run a simulation based on our prior parameter estimates.  We ask what would be the difference in outcomes based on used the current drug of choice against choosing the perfect drug for each patient for each iteration.

Let us look at an example with 2 treatments.  We see that option B currently has a higher expected value. If we went with option B in every iteration, the expected benefit would be £13.  However, in iterations 2, 4, and 5, option A is actually superior.  If we choose optimally each time (i.e., Treatment A for 2, 4, and 5 and Treatment B for 1 and 3), the expected payoff would be £13.8.  Thus, the value of the additional information would be £0.8 per patient.  If the cost of the research was less than £0.8*number of effected patients, then we should do the research.

We can also look at this situation when there are multiple treatments (see example).  Let us say that using current information, treatment B is still the best choice, but now we also have to consider options C and D.  In this example, option B still has the highest expected value £13.  However, if we choose the optimal drug at each iteration, then our payoff would be £14.4.  Thus the EVPI would be £1.4.  

One item to note in this example: we see that treatment D is never optimal for any iteration.  Thus, it does not pay to do any additional research for treatment D since it is very unlikely to unseat treatment B as the optimal choice.  It may be worthwhile–depending on the cost of the research–to investigate treatment C since it dominates treatment B in iterations 1 and 4.

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