Funnel plots for institutional comparisons
We introduce -funnelcompar-, a Stata routine that performs the analysis suggested by David J. Spiegelhalter (Funnel plots for comparing institutional performance, Statistics in Medicine, Volume 24 Issue 8, 1185-1202). The basic idea in funnel plot is to plot performance indicators against a measure of their precision in order to detect outliers. A scatter plot of an indicator level is plotted together with a baseline and control limits, that shrinks as the sample size gets bigger. Our command performs funnel plots for binomial (proportion) poisson (crude and standardized rates) and normal (means) distributed variables. The baseline (and stan- dard errors in case of normal variables) can either be specified by the user (for instance as literature reference) or be estimated from the data as a weighted or non-weighted mean of the data. By default confidence limits are plotted at 2 and 3 standard error, in order to detect alarm and alert signals, as recommended by statistical process control theory. Options have been implemented to mark single institutions, groups of institutions or those institutions lying outside control limits. These plots are increasingly used to report performance indicators at institutional level. Classical league tables imply the existence of ranking between institutions and implicitly support the idea that some of them are worse/better than others. A different approach is possible using statistical process control theory: all institutions are part of a single system and perform at the same level. Observed differences can never be completely eliminated and are explained by chance (common cause variation). If ob- served variation exceed that expected, special-cause variation exists and requires further explanation to identify its cause.
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