Ann Thorac Surg 2008;86:349. doi:10.1016/j.athoracsur.2007.12.019
© 2008 The Society of Thoracic Surgeons
Correspondence
Reply
Gary L. Grunkemeier, PhD,
YingXing Wu, MD
Medical Data Research Center, Providence Health System, 9205 SW Barns Rd, Ste 33, Portland, OR 97225
(Email: gary.grunkemeier{at}providence.org).
To the Editor:
We thank Mohammed and Deeks [1] for drawing attention to an alternative method of displaying comparative mortality data [1]. Even though the error-plot is more widely used, the funnel plot as proposed by Spiegelhalter [2] provides an interesting and attractive alternative display. However, the information contained in these two portrayals is—or can be made to be—exactly the same.
Our Figure 1
shows A of Mohammed and Deeks' Figure 1, with the 99% confidence limits included, for comparison with Mohammed and Deeks' Figure 2 funnel plot. Note that the interpretation of Figure 1 is the same as the funnel plot: centers A, B, C and D have observed/expected (O/E) ratios of less than 1, with A near the 99% confidence limit and B and C near the 95% limit. Centers E and F have O/E ratios greater than 1, and neither exceeds the 95% limit.
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Fig 1. Observed to expected (O/E) ratio for each hospital. The squares represent the point estimates, and the areas of the squares are proportional to the expected number of deaths. The vertical lines display confidence intervals. The short inner horizontal bars are 95% confidence limits, and the longer outer horizontal bars are 99% confidence limits.
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Another dimension of information is incorporated into the M&D funnel plot, the number of expected deaths, on the horizontal axis. For binomial data such as operative mortality, we usually encode the number of cases, consistent with the recommendation of Spiegelhalter [2], into the areas of the symbols. But we did not do so in our original article [3], from which Figure 1 of M&D is taken, because the point there was to compare different confidence interval methods, and this would have made the figure too crowded. In Figure 1, we have encoded the expected number of deaths into the areas of the figures, to be consistent with the M&D funnel plot.
Neither of these plots makes an attempt to correct for multiple comparisons; indeed, Spiegelhalter suggests "... allowance for multiple comparisons ... is best carried out separately [2]."
Hence we respectfully differ with the conclusion of M&D that the funnel plot "can produce materially different interpretations [1]." We do think that the funnel plot is an attractive and useful adjunct, perhaps preferred in some cases. However, the figure in our original article [3] was to compare different confidence interval methods, which were almost impossible to put on a funnel plot.
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References
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- Mohammed MA, Deeks JJ. In the context of performance monitoring, the caterpillar plot should be mothballed in favor of the funnel plot(letter) Ann Thorac Surg 2008;86:348.[Free Full Text]
- Spiegelhalter DJ. Funnel plots for comparing institutional performance Stat Med 2005;24:1185-1202.[Medline]
- Grunkemeier GL, Wu Y. What are the odds? Ann Thorac Surg 2007;83:1240-1244.[Free Full Text]
Related Article
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In the Context of Performance Monitoring, the Caterpillar Plot Should Be Mothballed in Favor of the Funnel Plot
- Mohammed A. Mohammed and Jonathan J. Deeks
Ann. Thorac. Surg. 2008 86: 348.
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