Number needed to test: quantifying risk stratification provided by diagnostic tests and risk predictions

Risk stratification is the ability of a test or model to separate those at high vs. low risk of disease. There is no risk stratification metric that is in terms of the number of people requiring testing, which would help with considering the benefits, harms, and costs associated with the test and interventions. We introduce the expected number needed to test (NNtest) to identify one more disease case than by randomly selecting people for disease ascertainment. We show that NNtest measures risk stratification, allowing us to decompose NNtest into components that contrast the increase in risk upon testing positive (‘concern’) versus the decrease in risk upon testing negative (‘reassurance’). A graph of the reciprocals of concern vs. reassurance have linear contours of constant NNtest, visualizing the relative importance and tradeoff of each component to better understand the properties of risk thresholds with equal NNtest. We apply NNtest to the controversy over the risk threshold for who should get testing for BRCA1/2 mutations that cause high risks of breast and ovarian cancers. We show that risk thresholds between 0.78% and 5% optimize NNtest. At these thresholds, people will require risk-model evaluation to find one more mutation-carrier. However, these thresholds of equal NNtest provide very different concern and reassurance, with 0.78% providing much more reassurance (and thus much less concern) than 5%. Given that genetic testing costs are declining rapidly, the greater reassurance provided by the 0.78% threshold might be deemed more important than the greater concern provided by the 5% threshold.