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Hospital Volume versus Outcome: An Unusual Example of Bivariate Association

Summary The Leapfrog Group, a consortium of more than 100 large employers, purchasing coalitions, and states that collectively provide health insurance to more than 33 million people, convened in 2000 with the goal of using market forces to improve the quality of healthcare. The resulting Leapfrog initiative suggested selective referral of complex procedures to high‐volume hospitals and set volume thresholds for five procedures. This was based on the hypothesis that low‐volume hospitals have higher mortality, which can be viewed in simplified statistical terms as the hypothesis that the binomial p is a decreasing function of n. The analysis of the correlation between hospitals' standardized mortality ratios (SMR, i.e., the ratio of observed to expected deaths) and hospitals' procedural volumes is revealing about the volume/mortality hypothesis. This presents an unusual pedagogic example in which the detection of correlation in the presence of nonlinear dependence is of primary interest, and thus the Pearson correlation is ideally suited. The frequently preferred nonparametric measures of bivariate association are inappropriate as they are unable to discriminate between correlation and dependence.