AN EXPLORATION OF THE IMPACT OF NON-DIVISIBILITY, DIMINISHING MARGINAL RETURNS TO SCALE AND NON-MARGINAL BUDGET IMPACT ON THE COST-EFFECTIVENESS THRESHOLD USING A SIMULATION MODELLING APPROACH

Purpose: The optimal cost-effectiveness threshold has been subject to much debate. In the standard model, technologies are assumed to be divisible and exhibit constant returns to scale. The threshold is plotted as a linear function through the origin of the cost-effectiveness (CE) plane, implying a single threshold in all circumstances. We consider the implications of departures from the assumptions underlying the standard model, including the possibility of diminishing marginal returns to scale or non-divisibility of technologies. We also consider if the optimal threshold is dependent upon a new technology’s budget impact and whether the new technology constitutes a net investment or net disinvestment.

Method: We conducted simulations using a de novo model of a hypothetical health care system. The model comprises three stages: allocation of an initial budget among a pool of initial technologies, consideration of a new technology, and reallocation of resources among initial technologies if the new technology is adopted. The optimal threshold ensures that new technologies are adopted only if the net incremental benefit of adoption and reallocation is positive. Three scenarios were considered: divisible technologies exhibiting constant returns; divisible technologies exhibiting diminishing returns; and non-divisible technologies. For each scenario we estimated the optimal thresholds for net investments and net disinvestments across a range of possible budget impacts. We repeated each scenario using three different initial budgets.

Result: The standard exposition of the cost-effectiveness threshold holds under the following conditions: (a) initial technologies are divisible and exhibit constant returns to scale; (b) a single initial technology remains partially adopted following initial allocation; and (c) the budget impact of each new technology is sufficiently small that reallocation involves expanding or contracting only the partially adopted initial technology. In all other cases, the threshold depends upon whether the new technology is a net investment or net disinvestment and the magnitude of the budget impact. The threshold curve is a piecewise linear function under divisibility and constant returns, a concave function under divisibility and diminishing returns, or a step function under non-divisibility.

Conclusion: The standard exposition of the cost-effectiveness threshold is a special case that holds only under specific conditions. Under other conditions, threshold curves take a different functional form that reduces the scope for new technologies to appear cost-effective.