Cost Effectiveness Analysis with and Without Stochastic Uncertainty

Abstract

Objective: To evaluate the optimal allocation of health care treatments when treatment costs and outcomes are uncertain.Background: In the context of perfectly certain health care costs and outcomes, Weinstein and others have demonstrated that optimal treatment allocation requires a comparison of all potential incremental cost effectiveness ratios (ICERs) against a decision-maker willingness-to-pay (WTP) ratio (cutoff threshold) using either linear programming methods, treatment ‘prioritization’ rules or incremental net monetary benefits (NMB) assessment. Thus far, stochastic treatment allocation evaluation has focused primarily on two-treatment comparisons where the uncertainty in the increment cost effectiveness ratio (ICER) is plotted on the cost-QALY plane and the stochastic properties are characterized in terms of WTP confidence intervals, incremental NMB plots, or cost effectiveness acceptability curves (CEAC). The decision rules and the characterization of global optimal treatment allocation under uncertainty has not been previously fully elucidated. Results: With uncertain costs and outcomes, using NMB methods, it is demonstrated that if the decision- maker is only concerned about maximizing expected QALYs for a given budget (or in the dual optimization program, minimizing the expected cost of providing a fixed number of expected QALYs to the beneficiary population) all of the standard ‘perfect certainty’ results about optimal treatment allocation carry through. However, to the extent that the decision-maker is concerned about treatment cost and outcome variability (e.g., the decision-maker is risk averse) the optimal treatment allocation will necessarily involve a portfolio of treatment strategies involving tradeoffs between treatment risks and benefits. Unless all treatments are perfectly positively correlated, there will nearly always be some gain by using a mixed treatment strategy rather than characterizing certain treatments as ‘dominant’ or ‘dominated.’ The mathematics of modern portfolio theory apply directly to this problem and demonstrate 1: (Separation Theorem) — the optimal treatment portfolio efficiency frontier is independent of the decision-makers willingness-to-pay for health care treatments; 2: (Market Beta Analysis) the decision as to whether a new treatment should be added to the optimal treatment portfolio depends on the tradeoff between the new treatment incremental NMB and its covariance with the current optimal treatment portfolio risk. Conclusions: Decision-makers using ICER methods to optimally allocate health care treatments under stochastic uncertainty will consider not only the NMB expected return to treatment but also treatment cost and outcome variability. This leads to the more realistic result that a portfolio of mixed treatment strategies will generally be preferable to one where only those treatments with the highest expected returns are implemented. This finding has substantial implications for formulary decision-making, comparative effectiveness research and the interpretation and characterization of stochastic ICERs.