Adapting portfolio theory for the evaluation of multiple investments in health with a multiplicative extension for treatment synergies

Portfolio theory is central to the analysis of risk in many areas of economics but is seldom used appropriately in health economics. This contribution examines the use of portfolio theory in the context of cost-effectiveness analysis (CEA). A number of modifications are needed to apply portfolio analysis to the economic evaluation of health care interventions. First, the method of reporting the results of a CEA, and consequently some of the underlying assumptions, needs to be modified. Second, portfolio theory needs to be expressed in terms of effects on individuals aggregated to a population. Finally, one needs to allow for the possibility of synergy between the various health interventions. This paper derives a general formula for a portfolio of health care interventions that allows for synergies between interventions where the population effects are aggregated from individual effects. A number of special cases are also derived to highlight the nature of the formulation of the modified portfolio theory. We conclude that, while modified portfolio theory adds a theoretical foundation to health care evaluations, it may not be operational until estimates of the correlation between interventions are available, and the question of uncertainty is resolved in health care evaluation. Also, while a synergy may be present at the individual level, when aggregated over a large population it may not be significant given the standard assumption of constant returns to scale.