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The probability of being identified as an outlier with commonly used funnel plot control limits for the standardised mortality ratio.

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journal contribution
posted on 24.10.2012, 08:56 by Sarah E. Seaton, Bradley N. Manktelow
Background: Emphasis is increasingly being placed on the monitoring of clinical outcomes for health care providers. Funnel plots have become an increasingly popular graphical methodology used to identify potential outliers. It is assumed that a provider only displaying expected random variation (i.e. ‘in-control’) will fall outside a control limit with a known probability. In reality, the discrete count nature of these data, and the differing methods, can lead to true probabilities quite different from the nominal value. This paper investigates the true probability of an ‘in control’ provider falling outside control limits for the Standardised Mortality Ratio (SMR). Methods: The true probabilities of an ‘in control’ provider falling outside control limits for the SMR were calculated and compared for three commonly used limits: Wald confidence interval; ‘exact’ confidence interval; probability-based prediction interval. Results: The probability of falling above the upper limit, or below the lower limit, often varied greatly from the nominal value. This was particularly apparent when there were a small number of expected events: for expected events ≤50 the median probability of an ‘in-control’ provider falling above the upper 95% limit was 0.0301 (Wald), 0.0121 (‘exact’), 0.0201 (prediction). Conclusions: It is important to understand the properties and probability of being identified as an outlier by each of these different methods to aid the correct identification of poorly performing health care providers. The limits obtained using probability-based prediction limits have the most intuitive interpretation and their properties can be defined a priori. Funnel plot control limits for the SMR should not be based on confidence intervals.

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Citation

BMC Medical Research Methodology, 2012, 12 : 98

Version

VoR (Version of Record)

Published in

BMC Medical Research Methodology

Publisher

BioMed Central Ltd

eissn

1471-2288

Copyright date

2012

Available date

24/10/2012

Publisher version

http://www.biomedcentral.com/1471-2288/12/98

Notes

PMCID: PMC3441904

Language

eng

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