Open AccessSpecifying the Probability Characteristics of Funnel Plot Control Limits: An Investigation of Three Approaches
Author(s) -
Bradley N Manktelow,
Sarah E Seaton
Publication year - 2012
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0045723
Subject(s) - control limits , outlier , probability distribution , interpolation (computer graphics) , limit (mathematics) , statistics , empirical probability , funnel plot , funnel , mathematics , computer science , bayesian probability , posterior probability , control chart , confidence interval , mathematical analysis , engineering , artificial intelligence , process (computing) , motion (physics) , mechanical engineering , publication bias , operating system
Background Emphasis is increasingly being placed on the monitoring and comparison of clinical outcomes between healthcare providers. Funnel plots have become a standard graphical methodology to identify outliers and comprise plotting an outcome summary statistic from each provider against a specified ‘target’ together with upper and lower control limits. With discrete probability distributions it is not possible to specify the exact probability that an observation from an ‘in-control’ provider will fall outside the control limits. However, general probability characteristics can be set and specified using interpolation methods. Guidelines recommend that providers falling outside such control limits should be investigated, potentially with significant consequences, so it is important that the properties of the limits are understood. Methods Control limits for funnel plots for the Standardised Mortality Ratio (SMR) based on the Poisson distribution were calculated using three proposed interpolation methods and the probability calculated of an ‘in-control’ provider falling outside of the limits. Examples using published data were shown to demonstrate the potential differences in the identification of outliers. Results The first interpolation method ensured that the probability of an observation of an ‘in control’ provider falling outside either limit was always less than a specified nominal probability ( p ). The second method resulted in such an observation falling outside either limit with a probability that could be either greater or less than p , depending on the expected number of events. The third method led to a probability that was always greater than, or equal to, p . Conclusion The use of different interpolation methods can lead to differences in the identification of outliers. This is particularly important when the expected number of events is small. We recommend that users of these methods be aware of the differences, and specify which interpolation method is to be used prior to any analysis.