Over the period from 1998 to 2007 in Taiwan, we find there is a relationship between surgeon and hospital volumes and the duration to patient mortality. Higher volume quartile surgeons and hospitals have a reduced probability of a patient experiencing mortality at 1, 3, 6, and 12 months. Using a duration modeling approach based on Butler, Anderson, and Burkhauser (1989)
, which is based upon Heckman and Singer (1984)
, to deal with unobserved heterogeneity reveals that indeed unobserved heterogeneity is likely a concern, as suspected previously.
Overall, the results of both our GEE and hazard modeling suggest the marginal effect of having CABG performed by a higher volume surgeon are larger in the short term. While the impact of surgeon volume remains statistically significant in the long run, the impact relative to the mean mortality is rather small, suggesting less of a clinical significance than at the earlier time points. The estimated impact of hospital volume is similar to surgeon volume at 1 month in our GEE model, though the advantage is not monotonically increasing as volume increases, suggesting some potential nonlinearity to the hospital volume–outcome relationship or potentially some unobserved heterogeneity. Indeed, the later appears to be the case once we turn to our hazard modeling strategy, which adjusts for this unobserved heterogeneity.
After adjusting for unobserved heterogeneity in our hazard model, the impact on 1-month mortality of having surgery performed by a higher volume surgeon becomes quite large. With respect to the impact of hospital volume, this model suggests that there is only a mortality advantage if a patient undergoes his/her procedure in the highest quartile of volume. In both the case of surgeon and hospital volume, it appears that the hazard to mortality and unobserved heterogeneity may be an important consideration in the modeling of short-term outcomes.
Focusing on the hazard model results that adjust for unobserved heterogeneity (), one can see that the effect of surgeon and hospital volume wanes as we transition to longer term outcomes. The surgeon volume effects calculated from our model controlling for unobserved heterogeneity are still statistically significant at the time periods we considered, though one could argue that the impact is much less significant clinically by the 6- and 12-month mark, where the relative reduction in mortality compared with the mean of the reference group is at most 12.4 percent at 6 months and 2.4 percent at 12 months. With respect to the impact of having CABG performed at a higher volume hospital on the impacts on 3-, 6-, and 12-month mortality, the results are qualitatively similar to the hospital impact on 1-month mortality, that is, the mortality advantage is concentrated in the highest quartile of volume hospitals. In both the case of surgeon and hospital volume, the transition to examining longer term outcomes reveals that outcome differences at those points are still observable in Taiwan. Unsurprisingly, unobserved heterogeneity is a concern with regard to the exact magnitudes of the volume impacts at those later time points.
While there is a mortality advantage concentrated at the highest of volume hospitals, the clinical significance of this advantage is smaller than simply avoiding having CABG performed by the lowest volume surgeons. This last point suggests that surgeon volume is at least as important as hospital volume as a measure of quality in Taiwan. Similar approaches to this question using data from the United States, Canada, and Europe, from where most of the current evidence in the literature is derived, might further the understanding of the volume–outcome relationship across all systems.
More generally, our results suggest using methods that examine the hazard to a particular outcome may be an important consideration when estimating the impact of volumes on mortality. From a methodological standpoint it appears that the GEE models with binary endpoints potentially understate the impacts of surgeon volume on mortality while overstating the impacts of hospital volume on mortality. In addition, our hazard model estimates suggest that unobserved heterogeneity is present in this relationship as estimated. Unfortunately, our methodology does not allow us to specifically identify the source(s) of the unobserved heterogeneity. However, the implication of our results is that surgeon volume has a more clinically significant impact on the hazard to mortality in Taiwan.
With regard to examining longer term outcomes, one could argue that mortality outcomes further into the future are based on other factors and not attributable to the quality of the procedure or postoperative care. To a large extent we agree there are other factors that impact longer term outcomes that are beyond the control of the provider and therefore not attributable to quality differences but may be due to unobserved factors. Our hazard to mortality estimates support this assertion to a large extent, though controlling for unobserved heterogeneity in these models does not completely mitigate the long-term differences in mortality attributable to volume level.
If measures of provider quality such as volume have absolutely no impact, the estimate of the volume impact on the longer term outcomes should not be statistically different from zero. If the estimated impact of volume and other quality indicators on longer term outcomes or time to these outcomes are not zero, then there are some potential explanations. These quality indicators, such as volume, do in fact impact these other longer term measures of outcome. For example, patient behavior after discharge may have large impacts on mortality differences, and one might argue that experienced surgeons may give more effective counsel on the behavior changes a patient needs to make, which improves their patients' outcomes. Alternatively, patients who are going to change their health behaviors and preferences ex post are also differentially sorting to providers by quality indicators such as volume ex ante. A priori both explanations seem implausible, but these are empirical questions to be addressed by future research.
Our study does have limitations. The most important is that our data are drawn from Taiwan, where rates of CABG are much lower than in the United States, Canada, and Europe, even though in Taiwan there are still high-volume providers by U.S. standards. Specific estimates of the impact of provider volume by quartile may differ in other systems. Similar research using the methods suggested here on data from the United States, Canada, or Europe would be needed before drawing any definitive conclusions or making policy recommendations in these systems. Lastly, because we do not know the clinical cause of death for those who die, we are limited to using disenrollment. This has been shown to be a valid imputation in the data from Taiwan; however, the ability to focus on related causes of death might improve the evidence base. Of course, accurate data on cause of death are not easy to obtain in any nation, so this is more of a measurement limitation than a limitation specific to our data.