Value of Information Some introductory remarks by Tony O’Hagan Welcome! • Welcome to the second CHEBS dissemination workshop • This forms part of our Focus Fortnight on “Value of Information” • Our format allows plenty of time for discussion of the issues raised in each talk, so please feel free to join in! Uncertainty in models • An economic model tells us the mean cost and effectiveness for each treatment, and so gives their mean net benefits • We can thereby identify the most cost-effective treatment • However, there are invariably many unknown parameters in the model • Uncertainty in these leads to uncertainty in the net benefits, and hence in the choice of treatment Responses to uncertainty • We need to recognise this uncertainty when expressing conclusions from the model › Variances or intervals around estimates of net benefits › Cost-effectiveness acceptability curves for the choice of treatment • We can identify those parameters whose uncertainty has most influence on the conclusions Sensitivity and VoI • One way to identify the most influential parameters is via sensitivity analysis • This is primarily useful to see where research will be most effective in reducing uncertainty • A more direct approach is to quantify the cost to us of uncertainty, and thereby calculate the value of reducing it • Then we should engage in further research wherever it would cost less than the value of the information it will yield Notation • To define value of information, we need some notation › X denotes the uncertain inputs › EX denotes expectation with respect to the random quantity X › t denotes the treatment number › maxt denotes taking a maximum over all the possible treatments › U (t , X ) denotes the net benefit of treatment t when the uncertain inputs take values X Baseline • If we cannot get more information, we have to take a decision now, based on present uncertainty in X • This gives us the baseline expected net benefit maxt EX U (t , X ) • The baseline decision is to use the treatment that achieves this maximal expected net benefit Perfect information • Suppose now that we could gain perfect information about all the unknown inputs X • We would then simply maximise U (t , X ) across the various treatments, using the true value of X • However, at the present time we do not know X and so the expected achieved net benefit is EX maxt U (t , X ) EVPI • The gain in expected net benefit from learning the true value of X is the difference between these two formulae EX maxt U (t , X ) — maxt EX U (t , X ) • We call this the Expected Value of Perfect Information, EVPI Partial information • Now suppose we can find out the true value of Y, comprising one or more of the parameters in X (but not all of them) • Then we will get expected net benefit maxt EX | Y U (t , X ) where now we need to take expectation over the remaining uncertainty in X after learning Y, which is denoted by EX | Y • But because at the present time we do not yet know Y, our present expectation of this future expected net benefit is the relevant measure EY maxt EX | Y U (t , X ) • To calculate this, we need to carry out two separate expectations • To get the value of the partial information, we again subtract the baseline expected net benefit Sample information • In practice, we will never be able to learn the values of any of the parameters exactly • What we can hope for is to do some research that will yield more information relevant to some or all of X • Let this information be denoted by Y • Then the previous formula still holds › Sample information is a kind of partial information Scaling up • All of these formulae have been expressed at a per-patient level • To get the real value of information, we need to multiply by the number of patients to whom the choice of treatment will apply › When comparing with the cost of an experiment to get more information now, the relevant number of patients should be discounted over time Computation • Computing EVPI is quite straightforward › Simple Monte Carlo (MC) sampling from the distribution of X can evaluate the baseline as well as the perfect information expected net benefit • Computing the value of partial or sample information is more complex › Two levels of sampling are needed for MC computation • More sophisticated Bayesian methods are available when the model is too complex for MC
© Copyright 2024 Paperzz