Net reclassification improvement (NRI) is an index that attempts to quantify how well a new model reclassifies subjects - either appropriately or inappropriately - as compared to an old model. While c-statistics or AUC has been the standard metric for quantifying improvements over the last few decades, several studies have analyzed the limitations of this metric including lack of clinical relevance and difficulty in interpretation of small magnitude changes. This limitation can be best seen in the example of HDL and Framingham Risk Score (FRS). When a models with and without HDL were analyzed with AUC regarding effect of HDL of modifying FRS, HDL was found not to have a statistical significant effect. However, when analyzed in terms of outcomes, HDL was found to be a significant predictor of heart disease and thus should affect FRS. To overcome this limitation the concept of reclassification, that is how well a new model correctly reclassifies cases, was introduced through the metric of NRI.
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Basic Concept
NRI attempts to quantify how well a new model correctly reclassifies subjects. Typically this comparison is between an original model (e.g. hip fractures as a function age and sex) and a new model which is the original model plus one additional component (e.g. hip fractures as a function of age, sex, and weight). NRI is composed of two components, subjects without events and subjects with events. Subject without (with) events who were correctly reclassified lower (higher) are assigned a +1. Subjects without (with) events who were incorrectly classified as higher (lower) are assigned a -1. Subjects not reassigned are assigned a 0. Sum the scores in each group and divide by the number of subjects in that group. The sum of these two values is the NRI.
Example
In a perfect test, all subjects with events would be classified as abnormal and all subjects without events would be classified as normal. Bold indicates subjects correctly classified by both tests. White indicates subjects incorrectly classified by both tests. Green indicates subjects correctly reclassified by test 2. Red indicates subjects incorrectly reclassified by test 2. NRIe = (4-2)/30 = 0.067. NRIne = (8-4)/70 = 0.057. NRI is the sum which is approximately 0.12.
Limitations
NRI limitations including determining whether a subject has been "correctly" reclassified and issues when the models results are not binary (e.g. low, medium, and high risk).