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Editor's Correspondence |

Controlling for Patient Risk in Volume-Outcome Studies—Reply

Brahmajee K. Nallamothu, MD, MPH; Timothy P. Hofer, MD, MSc; Steven J. Bernstein, MD
Arch Intern Med. 2005;165(14):1664. doi:10.1001/archinte.165.14.1664-b.
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We used the California CABG Mortality Reporting Program (CCMRP) risk prediction model to estimate expected surgical risk, primarily because it was an independently derived and previously reported tool for estimating in-hospital death following coronary artery bypass grafting.1 The concern by Ho is that the absence of hospital volume within this risk prediction model may have influenced our results owing to omitted variable bias. This is a valid and potentially important concern, and we evaluated for its presence in 2 ways. First, we used a generalized version of the Hausman specification test to compare coefficients in the original CCMRP risk prediction model with coefficients estimated from a similar model that included categories of hospital volume.2,3 (We performed these analyses on the subset of 27 355 patients in our study owing to a lack of publicly available data on the full study population originally used by CCMRP.) The omnibus comparison for this test suggested that estimated coefficients between the 2 models were not significantly different overall (P = .74); however, some coefficients appeared to have varied during individual comparisons (eg, an individual test for similarity between coefficients for age between the 2 models resulted in a P value of .04). We therefore re-estimated the CCMRP risk prediction model but now added hospital volume as a continuous covariate. From this model, expected surgical risk was calculated for each patient using their individual covariates but assuming an “average” (ie, mean) hospital volume. We then repeated our earlier analyses examining the association between expected surgical risk and in-hospital death across tertiles of coronary artery bypass grafting volume. Our main results were largely unchanged. As before, we noted that adjusted in-hospital mortality rates between low- and high-volume centers rose as the expected risk of in-hospital death increased: 0.9% vs 0.4% at the 20th risk percentile (P <.001) vs 3.6% vs 2.6% at the 80th risk percentile (P <.001).4

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