Volume 44 - Article 35 | Pages 853–864  

Outsurvival as a measure of the inequality of lifespans between two populations

By James W. Vaupel, Marie-Pier Bergeron-Boucher, Ilya Kashnitsky

Response Letter

04 August 2022 | Response Letter

A Note on the Outsurvival Statistic

by David Hand

One of the distinguishing features of statistics as a discipline is that it is ubiquitous: it is applied everywhere. A consequence of this is that statistical tools are often redeveloped or rediscovered by researchers in various domains, unaware that the tools and their properties have already been developed and explored elsewhere. When this is the case it can be useful to draw attention to the fact, so as to avoid duplication of effort and so that potential users can better understand the properties of the tool.

A recent paper in Demographic Research by Vaupel et al. (2021) illustrates this. The authors propose an "outsurvival statistic" "that measures the probability that an individual from a population with low life expectancy will live longer than an individual from a population with high life expectancy." However, the measure is more generally interpreted as indicating the probability that a randomly chosen object from one distribution will have a smaller value than a randomly chosen object from another distribution, as the authors note in Section 5 of their paper. But as such it is an extremely widely-used measure, with a very large literature in which it is most commonly known as the Area Under the Curve (AUC) or Area Under the ROC Curve (AUROC), where the curve in question is the "Receiver Operating Characteristic". It is often the measure of choice in evaluating diagnostic instruments in medicine, in signal detection, in machine learning, and in credit scoring, and is described in countless standard texts. See, for example, Altman (1991), Senn (1997), Zhou et al. (2002), Krzanowski and Hand (2009), Webb and Copsey (2011), Anderson (2007), Zou et al. (2012). In 2013, Hand and Anagnostopoulos (2013) estimated that the statistic was used in around 6000 scientific papers per year, and it has been generalised and extended in various directions.


Altman, D.. (1991). Practical Statistics for Medical Research. Chapman and Hall, London.

Anderson, R. (2007) The Credit Scoring Toolkit. Oxford University Press, Oxford.

Hand, D.J. and Anagnostopoulos, C. (2013). When is the area under the receiver operating characteristic curve an appropriate measure of classifier performance? Pattern Recognition Letters 34: 492–496.

Krzanowski, W.J. and Hand, D.J. (2009). ROC Curves for Continuous Data. London: CRC Press.

Senn, S. (1997). Statistical Issues in Drug Development. Chichester: John Wiley and Sons.

Vaupel, J.W., Bergeron-Boucher, M-P, and Kashnitsky, I. (2021). Outsurvival as a measure of the inequality of lifespans between two populations. Demographic Research 44(35): 853–864.

Webb, A.R. and Copsey, K.D. (2011). Statistical Pattern Recognition (3rd ed.). Chichester: John Wiley and Sons.

Zhou, X-H., Obuchowski, N.A., and McClish, D.K. (2002). Statistical Methods in Diagnostic Medicine. Chichester: John Wiley and Sons.

Zou, K.H., Liu, A., Bandos, A.I., Ohno-Machado, L., and Rockette, H.E. (2012). Statistical Evaluation of Diagnostic Performance. London: Chapman and Hall.

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