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Ann Thorac Surg 2001;72:677-678
© 2001 The Society of Thoracic Surgeons

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Statistician’s page

Actual versus actuarial event-free percentages

^a Providence Health System, Portland, Oregon, USA

Address reprint requests to Dr Grunkemeier, 9155 SW Barnes, 33, Portland, OR 97225
e-mail: ggrunkemeier{at}providence.org

	Introduction

Top Introduction Terminology Censored patients Survival SVD Conclusion References

 
The article by Banbury and colleagues [1] in this issue of The Annals of Thoracic Surgery has two curves for freedom from explant for structural valve dysfunction or deterioration (SVD), labeled Actual and Actuarial, in their Figure 1E. These curves are quite different, producing event-free percentages at 15 years of about 88% and 76%, respectively. What is the difference between these curves and which is correct?

	Terminology

Top Introduction Terminology Censored patients Survival SVD Conclusion References

 
First, the words themselves. Actuarial originally referred to the life table method, and its use is often extended (as here) to include the Kaplan-Meier method, which is a refinement of the life-table method. Actual is a new term used in cardiac surgery literature to refer to a technique with several designations in the statistical literature, including cumulative incidence and crude, unadjusted, absolute, or observable probability. We will use a simple example to demonstrate the fundamental difference between Kaplan-Meier and actual SVD-free curves.

	Censored patients

Top Introduction Terminology Censored patients Survival SVD Conclusion References

 
In evaluating a postoperative event (eg, death, SVD) for an ongoing series, many or most patients have not yet had the event at the time of the analysis. To use all the patients to construct an event-free curve, event-free patients are "censored" in the Kaplan-Meier analysis. The term censored sounds as if the patient is dropped from future consideration. But the opposite is actually true: such patients are added back into the calculations, as future events distributed over future time.

	Survival

Top Introduction Terminology Censored patients Survival SVD Conclusion References

 
The Kaplan-Meier method estimates a survival curve by making the reasonable assumption that the patients who are still alive (censored for death) will eventually die, and that the distribution of their life times will be the same as those who have already died. Figure 1 contains a simple example. For a survival curve, the Kaplan-Meier and actual methods give identical results.

View larger version (13K): [in this window] [in a new window]   Fig 1. Kaplan-Meier (KM) (actuarial) analysis of death. This figure shows survival time lines (solid horizontal lines) for 4 patients, labeled A–D. A and B have died, as shown by the black circles at years 3 and 4, and C and D are still alive, as shown by the white circles at 1 and 2 years. These circles represent the observed data. Patients C and D are censored in the analysis. Because there are two subsequent death times (3 and 4 years), with one death at each, C and D have their future deaths distributed as 0.5 death at each of these times. Thus, the number of (anticipated) deaths at years 3 and 4 becomes 1 + 0.5 + 0.5 = 2. And the Kaplan-Meier curve estimating survival accordingly drops to 2/4 = 50% at year 3 and 0/4 = 0% at year 4.

	SVD

Top Introduction Terminology Censored patients Survival SVD Conclusion References

View larger version (15K): [in this window] [in a new window]   Fig 2. Kaplan-Meier (KM) (actuarial) analysis of structural valve dysfunction (SVD). This figure shows the SVD time lines (solid horizontal lines) for four other patients, labeled E–H. Patients E and F have had SVD (gray circles at 3 and 4 years), and G and H have died without SVD (black circles at 1 and 2 years). Censoring implies that patients G and H each contribute 0.5 SVD to the two subsequent SVD times (3 and 4 years). Thus, the number of SVD at years 3 and 4 becomes 1 + 0.5 + 0.5 = 2. The resulting Kaplan-Meier SVD-free curve drops to 2/4 = 50% at year 3 and 0/4 = 0% at year 4.

View larger version (12K): [in this window] [in a new window]   Fig 3. Actual analysis of structural valve dysfunction (SVD). This is the same data as in Fig 2. Here the analysis is actually simpler (hence the adjectives denoting simplicity in the alternative names given above, under Terminology). This series is complete as far as the structural valve dysfunction is concerned. The number of structural valve dysfunction at 3 and 4 years are one each, therefore the actual structural valve dysfunction-free curve drops to 0.25 = 75% at year 3 and 2/4 = 50% at year 4.

	Conclusion

Top Introduction Terminology Censored patients Survival SVD Conclusion References

	References

Top Introduction Terminology Censored patients Survival SVD Conclusion References

 

1. Banbury M.K., Cosgrove D.M., White J.A., Blackstone E.H., Frater R.W., Okies J.E. Age and valve size effect on the long-term durability of the Carpentier-Edwards aortic pericardial bioprosthesis. Ann Thorac Surg 2001;72:753-757.[Abstract/Free Full Text]

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This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Add to Personal Folders Download to citation manager Author home page(s): Gary L. Grunkemeier Permission Requests Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Grunkemeier, G. L. Articles by Wu, Y. Search for Related Content PubMed PubMed Citation Articles by Grunkemeier, G. L. Articles by Wu, Y. Related Collections Valve disease