Mahalanobis distance under non-normality

Tiku, M. L.; Islam, M. Qamarul; Qumsiyeh, Sahar B.

doi:10.1080/02331880903043223

Cited by 3 publications

(1 citation statement)

References 31 publications

(66 reference statements)

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“…This shows not only how powerful M is as a metric on its own, but it also aides in providing further insight about the interpretation and clinical usefulness of all presented metrics. Since M as a measure of discrimination is quite robust to departures from normality, 48 metrics dependent only on M may also be considered robust. ΔAUC and NRI(y) under normality depend only on the Mahalanobis distances of the two models.…”

Section: Resultsmentioning

confidence: 99%

Measures for evaluation of prognostic improvement under multivariate normality for nested and nonnested models

Enserro

Demler

Pencina

et al. 2019

Statistics in Medicine

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When comparing performances of two risk prediction models, several metrics exist to quantify prognostic improvement, including the change in the area under the Receiver Operating Characteristic curve, the Integrated Discrimination Improvement, the Net Reclassification Index at event rate, the change in Standardized Net Benefit, the change in Brier score, and the change in scaled Brier score. We explore the behavior and interrelationships between these metrics under multivariate normality in nested and nonnested model comparisons.We demonstrate that, within the framework of linear discriminant analysis, all six statistics are functions of squared Mahalanobis distance, a robust metric that properly measures discrimination by quantifying the separation between the risk scores of events and nonevents. These relationships are important for overall interpretability and clinical usefulness. Through simulation, we demonstrate that the performance of the theoretical estimators under normality is comparable or superior to empirical estimation methods typically used by investigators. In particular, the theoretical estimators for the Net Reclassification Index and the change in Standardized Net Benefit exhibit less variability in their estimates as compared to their empirically estimated counterparts. Finally, we explore how these metrics behave with potentially nonnormal data by applying these methods in a practical example based on the sex-specific cardiovascular disease risk models from the Framingham Heart Study. Our findings aim to give greater insight into the behavior of these measures and the connections existing among them and to provide additional estimation methods with less variability for the Net Reclassification Index and the change in Standardized Net Benefit.

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Section: Resultsmentioning

confidence: 99%