Visualizing the value of diagnostic tests and prediction models, part II. Net benefit graphs: net benefit as a function of the exchange rate

Abstract

Background and Objective

In this second of a 3-part series, we move from expected gain in utility (EGU) graphs to net benefit (NB) graphs, which show how NB depends on w = C/B, the treatment threshold odds, equal to the harm of treating unnecessarily (C) divided by the benefit of treating appropriately (B).

Method

For NB graphs, we shift from the perspective of testing individual patients with varying pretest probabilities of disease to the perspective of applying a test or risk model to an entire population with a given prevalence of disease, P₀. As with EGU graphs, we subtract the harm of testing and the expected harm of treating according to the results of a test or model when it is wrong from the expected benefit of treating when it is right. The difference is that for NB graphs, the prevalence is fixed at P₀ , and the x-axis is w. NB graphs show the NB of 3 strategies: 1) “Treat None”; 2) “Test” and treat those with predicted risk greater than the treatment threshold; and 3) “Treat All” in the population regardless of predicted risk.

Results

The “Treat All” line intersects the y-axis at NB = P₀ and the x-axis at w = P₀/(1 − P₀). The “Test” line intersects the “Treat All” line at the Treat–Test threshold value of w; it intersects the x-axis at the Test-No Treat value of w.

Conclusion

When NB is plotted as a function of w, NB graphs can be drawn as straight lines from easily calculated intercepts.