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Title: | Unbiasedness and efficiency of non-parametric and UMVUE estimators of the probabilistic index and related statistics | Authors: | VERBEECK, Johan DELTUVAITE-THOMAS, Vaiva BERCKMOES, Ben BURZYKOWSKI, Tomasz AERTS, Marc THAS, Olivier BUYSE, Marc MOLENBERGHS, Geert |
Issue Date: | 2020 | Publisher: | SAGE PUBLICATIONS LTD | Source: | Statistical Methods in Medical Research, p. 747-768 | Abstract: | In reliability theory, diagnostic accuracy, and clinical trials, the quantity PðX > YÞ þ 1=2PðX ¼ YÞ, also known as the Probabilistic Index (PI), is a common treatment effect measure when comparing two groups of observations. The quantity PðX > YÞ À PðY > XÞ, a linear transformation of PI known as the net benefit, has also been advocated as an intuitively appealing treatment effect measure. Parametric estimation of PI has received a lot of attention in the past 40 years, with the formulation of the Uniformly Minimum-Variance Unbiased Estimator (UMVUE) for many distributions. However, the non-parametric Mann-Whitney estimator of the PI is also known to be UMVUE in some situations. To understand this seeming contradiction, in this paper a systematic comparison is performed between the non-parametric estimator for the PI and parametric UMVUE estimators in various settings. We show that the Mann-Whitney estimator is always an unbiased estimator of the PI with univariate, completely observed data, while the parametric UMVUE is not when the distribution is misspecified. Additionally, the Mann-Whitney estimator is the UMVUE when observations belong to an unrestricted family. When observations come from a more restrictive family of distributions, the loss in efficiency for the non-parametric estimator is limited in realistic clinical scenarios. In conclusion, the Mann-Whitney estimator is simple to use and is a reliable estimator for the PI and net benefit in realistic clinical scenarios. | Keywords: | Completeness;relative efficiency;net benefit;probabilistic index;UMVUE;unbiased;Wilcoxon-Mann-Whitney | Document URI: | http://hdl.handle.net/1942/33025 | ISSN: | 0962-2802 | e-ISSN: | 1477-0334 | DOI: | 10.1177/0962280220966629 | ISI #: | 000634854900008 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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