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(Circulation. 2000;101:e99.)
© 2000 American Heart Association, Inc.

Circulation Electronic Pages

Qualification of the Concepts of Unqualified Success and Unmitigated Failure

Darrel P. Francis

British Heart Foundation Research Fellow

L. Ceri Davies

Robert Luff Foundation Research Fellow

Andrew J. S. Coats

Professor of Cardiology Royal Brompton Hospital, London, UK

	Introduction

 
Mancini and Schulzer¹ have developed advanced methods for calculation of the benefit accruing from treatment, with new formulas for the "chance of unqualified success" of a treatment. The primary formula is (p1-p2)[1-(q1-q2)], where the primary end-point rates in the control and treatment groups are p1 and p2, respectively, and the adverse event rates q2 and q1, respectively. We suggest this formula cannot represent a probability calculation. Consider a hypothetical situation in which treatment reduces end points from 0.9 to 0.1 while reducing the rate of the adverse events from 0.6 to 0.2. The "chance of unqualified success" is 0.8x1.4=1.12, exceeding 1. Other legitimate p and q probabilities between 0 and 1 produce results ranging from -2 to +2. This contrasts with the allowable range of 0 to 1 for orthodox measures of probability. The formula can therefore be doubted, even when it returns values between 0 and 1.

Perhaps the formula the authors seek is [(1-p1)(1-q2)]- [(1-p2)(1-q1)]. This is still not truly a probability (since it ranges from -1 to +1), but it does represent the change (attributable to treatment) in absolute risk of the combined end point of primary end point and/or adverse effect. The reciprocal of its absolute value gives the number needed to treat to change the number of combined end points by 1.

The authors appear to believe that the difference of 2 probabilities should itself be a probability. We argue that this is only true in general when the events of 1 probability . . . [Full Text of this Article]

Michael Schulzer, MD, PhD

Professor of Medicine and Statistics University of British Columbia, Vancouver, BC, Canada

G. B. John Mancini, MD, FRCP(C)

Professor and Head, Department of Medicine University of British Columbia, Vancouver, BC, Canada