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J Thorac Cardiovasc Surg 2008;135:460-462
© 2008 The American Association for Thoracic Surgery
Letter to the Editor |
a Medical Data Research Center, Providence Health System, Portland, Ore
b Department of Cardio-Thoracic Surgery, Erasmus University Medical Center, Rotterdam, The Netherlands
c St Paul’s Hospital–Heart Centre, University of British Columbia, Vancouver, British Columbia, Canada
d Department of Cardiothoracic Surgery, Stanford University Medical School, Stanford, Calif
To the Editor:
The life of a bioprosthetic heart valve usually ends as a result of structural valve deterioration (SVD) or death of the patient. In this competing risks situation, the probability of SVD is estimated by the cumulative incidence function, sometimes referred to as "actual" analysis.
The editorial by Bodnar and Blackstone published in the January 2006 issue of the Journal
1
criticized this method and recommended its prohibition. Specifically, Bodnar and Blackstone object to: (1) terminology: using the name "actual" instead of "cumulative incidence"; (2) presentation: plotting its complement and calling it "actual freedom"; and (3) comparison: using this statistic instead of the Kaplan–Meier (KM) method to compare valve performance. We disagree with Bodnar and Blackstone on all 3 points.
Regarding the first point, terminology, Bodnar and Blackstone state: "We should stop using the term ‘actual freedom.’ ... There is no reason to abandon the expression ‘cumulative incidence.’" Statisticians use several names for this method, including "cumulative incidence," "crude probability," "crude incidence," "cause-specific failure probability," "absolute cause-specific risk," and "subdistribution function." "Actual" is just a shortcut name, like saying "Ross"—not a medical term—instead of "pulmonary autograft" or "linearized rate"—not a statistical term—instead of "the constant hazard rate of an exponential distribution."
Bodnar and Blackstone also state: "Synonyms of ‘actual’ are current, eventual, and real, and the implication of its use is that it is more real than the actuarial estimate." That is exactly the point; the term "actual" is appropriate because it is "more real" than the KM actuarial estimate for the individual patient’s perspective because it estimates the percentage of patients who will "actually" experience an event. If one has a strong emotional aversion to the use of the term "actual," then the statistical terms "subdistribution function" instead of "actual failure" and "subsurvival function" instead of "actual freedom"2 can be substituted.
Regarding the second point, presentation, Bodnar and Blackstone state: "Other authors ... displayed graphically the complement of cumulative incidence, which normally rises from zero to a certain positive value, so that the new curve declined from 100% to a certain value." Although the probability of having an event is the more direct concept, its complement—the probability of being event-free—contains the same information and is usually preferred in survival analysis and complication-free analysis.
In reference to the third point, comparison, Bodnar and Blackstone state: "Cumulative incidence ... must not be used to define or compare valve performance. This should be done using actuarial [KM] methods." The first two issues are really a matter of taste, but this one is a matter of substance and statistical correctness. The subdistribution and subsurvival functions estimate the probability of having, or not having, respectively, SVD in the presence of the competing risk of death. As such, it would not be fair to use them to compare, say, valve A from a series with a high death rate to valve B from a series with a low death rate. If the death rates in 2 series were similar, however, then the comparison of SVD subdistribution or subsurvival functions would be appropriate.3 But this same caveat applies to KM actuarial estimates. Comparing high SVD rates with valve X in a younger population to low SVD rates with valve Y in an older population would not be correct, as the difference could be due to patient age and other patient-related factors alone. To make a fair comparison of KM curves, the patient groups should also be similar. But there also is a deeper, technical issue involved here. The subdistribution function gives a proper probability of experiencing SVD; the KM estimate does not.
Bodnar and Blackstone also state: "We assume that patients who die before a nonfatal event occurs were just as likely, while they were alive, as anybody else to have experienced that event, even though they didn’t. Now, that sounds more sensible, doesn’t it?" That is true, if indeed the events of death and SVD are independent. It may sound sensible, but it cannot be demonstrated using competing risks data,4 and for this reason the KM curve resulting from this assumption has dubious value. It has been widely criticized as "an incorrect use of the Kaplan–Meier method,"3 "a meaningless quantity,"5 "irrelevant,"6 and "inappropriate for estimation purposes in the presence of competing risks, while the cumulative incidence is appropriate."7 That is the statistical argument.8 Then there is the clinical issue: The KM curve gives the probability of SVD in the counterfactual (or artificial) situation where death has been eliminated. This, of course, will never happen.
Bodnar and Blackstone conclude that "the Journal will no longer publish ‘actual freedom’ results in articles reporting long-term performance of replacement valves." Although this prohibition was stated to only apply to the reporting of long-term performance of heart valves, this method has other valuable uses in cardiothoracic clinical research. Examples include the analysis of nonfatal complications such as aortic reoperation or stroke after surgical repair of aortic dissection, reintervention after thoracic aortic stent grafting, recurrent obstruction after esophagectomy, complications after lung volume reduction operations, and transplant graft disease in cardiac allograft recipients. Presumably, these other clinical applications are not affected by the proposed prohibition. In light of the above, we argue that the use of "actual freedom" for reporting heart valve complications or those following other cardiothoracic interventions should not be banned from The Journal of Thoracic and Cardiovascular Surgery.
References
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