Purpose: There has been increasing demand that measures of uncertainty be presented alongside point estimates when reporting cost-effectiveness analyses. However, a number of methodological studies have argued that optimal strategies can be identified using expected value alone, and that the probability distribution of the cost-effectiveness metric is irrelevant to this choice. Under this reasoning, the distributional information is only useful for determining the expected value of future research, decisions about which are seen as independent from the strategy choice. I examine the conditions under which it is appropriate to choose optimal strategies based solely on the expected value of the cost-effectiveness metric, and issues that arise when these conditions do not exist.
Method: In reality, decision-makers face an ongoing sequence of decisions, with new information becoming available periodically, and each occasion allowing us to update prior beliefs and revise earlier decisions. A simple mathematical model is developed to demonstrate the consequences of making decisions using expected value alone versus using the joint distribution of incremental costs and outcomes. In this model the decision-maker chooses between two strategies at t0 based on probabilistic information about costs and outcomes. Consequences of the chosen strategy accrue until t1, when, with probability p, new information on costs and outcomes becomes available. The decision-maker can then revise their strategy choice, and consequences continue to accrue until t2. The decision-maker’s goal is to maximize total expected utility.
Result: I find an important condition for choosing strategies based solely on expected value is that the strategy set available at future decisions—and pay-offs—are independent of the current decision. If independence holds, each decision becomes a one-shot game, and decisions based on expected value will maximize overall outcomes. However, independence does not hold in two common situations – where changing strategy incurs transition costs, and where decision-makers are unwilling to consider cost-effective strategies that produce worse health outcomes. In these scenarios, I find that decisions made using the joint probability distribution of incremental costs and outcomes will achieve (weakly) greater total expected utility compared to using expected value alone, and that decisions about optimal strategy cannot be made independently from decisions about optimal research investment.
Conclusion: In two commonly encountered situations, making decisions based on expected value alone can lead to suboptimal outcomes.
Candidate for the Lee B. Lusted Student Prize Competition