Optimal Allocation of Research Funds under a Budget Constraint

Purpose. Health economic evaluations that include the expected value of sample information support implementation decisions as well as decisions about further research. However, just as decision makers must consider portfolios of implementation spending, they must also identify the optimal portfolio of research investments. Methods. Under a fixed research budget, a decision maker determines which studies to fund; additional budget allocated to one study to increase the study sample size implies less budget available to collect information to reduce decision uncertainty in other implementation decisions. We employ a budget-constrained portfolio optimization framework in which the decisions are whether to invest in a study and at what sample size. The objective is to maximize the sum of the studies' population expected net benefit of sampling (ENBS). We show how to determine the optimal research portfolio and study-specific levels of investment. We demonstrate our framework with a stylized example to illustrate solution features and a real-world application using 6 published cost-effectiveness analyses. Results. Among the studies selected for nonzero investment, the optimal sample size occurs at the point at which the marginal population ENBS divided by the marginal cost of additional sampling is the same for all studies. Compared with standard ENBS optimization without a research budget constraint, optimal budget-constrained sample sizes are typically smaller but allow more studies to be funded. Conclusions. The budget constraint for research studies directly implies that the optimal sample size for additional research is not the point at which the ENBS is maximized for individual studies. A portfolio optimization approach can yield higher total ENBS. Ultimately, there is a maximum willingness to pay for incremental information that determines optimal sample sizes.