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Net benefit
Net benefit is calculated as a weighted combination of true and false positives, where is the threshold probability, true and false positives are count variables and N is the total number of observations.
Decision curve analysis evaluates a predictor for an event as a probability threshold is varied, typically by showing a graphical plot of net benefit against threshold probability. By convention, the default strategies of assuming that all or no observations are positive are also plotted.
Decision curve analysis is distinguished from other statistical methods like receiver operating characteristic (ROC) curves by the ability to assess the clinical value of a predictor. Applying decision curve analysis can determine whether using a predictor to make clinical decisions like performing biopsy will provide benefit over alternative decision criteria, given a specified threshold probability.
Threshold probability is defined as the minimum probability of an event at which a decision-maker would take a given action, for instance, the probability of cancer at which a doctor would order a biopsy. A lower threshold probability implies a greater concern about the event (e.g. a patient worried about cancer), while a higher threshold implies greater concern about the action to be taken (e.g. a patient averse to the biopsy procedure). Net benefit is a weighted combination of true and false positives, where the weight is derived from the threshold probability. The predictor could be a binary classifier, or a percentage risk from a prediction model, in which case a positive classification is defined by whether predicted probability is at least as great as the threshold probability.
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