Value of Information for Dose Selection

Why Information Has Value for a Dose Decision

Dose selection is often made while important model parameters remain uncertain. A new study, assay, or interim analysis may reduce that uncertainty. Its value is not simply that parameter estimates become more precise: information is useful for the decision only to the extent that it can change which dose is chosen, and that change improves expected outcomes.

The appropriate comparison is between the best dose chosen with current evidence and the dose that would be chosen after each possible information outcome. This is an expected utility comparison. Utility must represent the consequences relevant to the decision, such as efficacy and toxicity, on a common scale. The numerical utility values below are hypothetical and illustrate the calculations, not clinical recommendations.

The information-generating process matters because it determines both the possible outcomes \(Y\) and how those outcomes change uncertainty about \(\theta\). For each outcome, the decision-maker updates the distribution of \(\theta\), calculates expected utility for every available dose, and selects the best dose for that outcome. The average of those outcome-specific best utilities is then compared with the current best expected utility.

A Small Example: Updating the Dose Choice

Calculating EVSI Carefully

For discrete states and outcomes, the calculation can be organized using the joint probabilities of state and information outcome. For any observed outcome, posterior probabilities are obtained from Bayes' rule. The posterior expected utility of each dose is then compared, and the highest is retained. Importantly, the maximizing dose may differ across outcomes.

Why EVSI Cannot Exceed Perfect Information

Perfect information reveals the uncertain state before the dose is selected. Its expected value is the expected utility of choosing the best dose separately in each state, minus the current best expected utility. It provides an upper bound on the value of any less informative signal under the same dose options, utility function, and timing.

For a finite set of doses, the bound follows from the fact that, for each information outcome, posterior expected utility cannot exceed the posterior expectation of the best dose-specific utility if the state itself were known. Averaging over outcomes gives \(E_Y[\max_d E\{U(d,\theta)\mid Y\}]\leq E_\theta[\max_d U(d,\theta)]\). Also, EVSI is nonnegative when the decision-maker can ignore the information and retain the current dose. Combining these facts gives \(0\leq\operatorname{EVSI}\leq\operatorname{EVPI}\).

The first inequality relies on optional use of the information: if a signal is costly, compulsory, or delays treatment, those consequences must be included separately. The upper bound presumes the same decision options and utility scale on both sides of the comparison.

Information Costs and a Decision Rule

If information costs \(C\) on the same utility scale and does not otherwise affect outcomes, its net expected value is \(\operatorname{EVSI}-C\). A positive value supports acquiring the information under the stated model; a negative value does not. Costs can include more than money: treatment delay, patient burden, or the possibility that information arrives too late can be represented in utility or explicitly subtracted if commensurately measured. Avoid subtracting a cost twice if it is already included in the utility function.

Assumptions, Diagnostics, and Common Pitfalls

An EVSI calculation is only as credible as the decision model and the predictive distribution used in it. The following conditions should be made explicit:

• The candidate doses and feasible actions are defined consistently before and after information arrives.
• The utility function reflects relevant benefits, harms, and preferences, and its scale is comparable across uncertain states and outcomes.
• The current uncertainty distribution and the information model \(P(Y\mid\theta)\) are appropriate. If efficacy and toxicity predictions are dependent, their joint uncertainty must be represented rather than replaced by separate marginal calculations.
• The future result is available before the decision, and the information has no unmodeled effect on the patient or treatment pathway.
• All relevant outcomes, including missing, inconclusive, or harmful information outcomes where applicable, are represented in the predictive calculation.

A useful diagnostic is to inspect the dose selected for every possible outcome. If the same dose is selected after all outcomes, the information has EVSI zero under the specified model: it may improve knowledge without improving this decision. If the dose changes, check that the posterior probabilities for every outcome sum to one, that outcome probabilities sum to one, and that the dose-specific expected utilities use the same utility values and units throughout. A very large EVSI relative to EVPI signals an arithmetic or modeling error, because it violates the upper bound.

Common mistake: using the best dose under the posterior mean parameter as though that were automatically the best dose under uncertainty. This plug-in approach generally differs from maximizing posterior expected utility: in general, \(U(d,E[\theta])\neq E[U(d,\theta)]\). It can therefore misstate both the current decision value and EVSI. The correction is to average utility over the full uncertainty distribution for each dose, then maximize. A related mistake is to average dose choices across outcomes; the correct procedure maximizes expected utility separately for each outcome and then averages those maxima using outcome probabilities.

EVSI also differs from robustness or worst-case decision criteria. It is an expected improvement under a specified probability model and utility function, not a guarantee that the selected dose performs well in every plausible state. Consequently, conclusions may change if prior uncertainty, the information model, utility weights, or access to candidate doses changes. Sensitivity analysis is appropriate when those inputs are consequential, but the calculation itself does not resolve disagreements about which utilities or probability model should be used.