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Ann Thorac Surg 2007;83:1240-1244
© 2007 The Society of Thoracic Surgeons

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The Statistician's Page

What Are the Odds?

Providence Health System Cardiovascular Study Group, Providence Health & Services, Portland, Oregon

^_* Address correspondence to Dr Wu, 9205 SW Barnes Rd. Suite 33, Portland, OR 97225 (Email: yingxing.wu@providence.org).

The first 300 words of the full text of this article appear below.

	Introduction

 
This article coincides with the publication of two reports from The Society of Thoracic Surgeons (STS) Quality Measurement Task Force concerning the quality measurement in adult cardiac surgery [1, 2]. As described in their Technical Appendix [2], the authors’ analyses incorporate, appropriately, odds instead of probabilities. Here we compare the familiar concepts of probability and risk ratio with the less familiar concepts of odds and odds ratio (OR). In the process, we argue that the risk-adjusted OR is a technically better measure for comparing providers, such as hospitals and physicians, than the more commonly used observed-to-expected (O/E) risk ratio. Moreover, unlike the O/E ratio, the computation of the OR and its confidence interval is available in most statistical software programs. Before discussing their ratios, we introduce the measures themselves.

	Measuring Risk: Odds Versus Probability

 
The procedure-related risks that we will be considering are binary events such as death, in which each patient has either 1 or 0 events. Repeated events or composite events can be converted to this data type by the all or none scoring approach to data reduction [2]. Probabilities are widely used to describe such risks (eg, operative mortality). The probability of death is estimated as the number of deaths divided by the total number of patients. For example, if 1 of 5 patients dies, the probability of dying is 1/5 = .20, which is usually converted to a percentage, 20%. The odds is the number of deaths divided by the number of survivors. In the above example, the odds of dying is 1/4 = .25, sometimes written as 1:4 and spoken as "1 to 4".

The solid line in Figure 1 displays the relationship between probability and odds. The odds is always larger, since its denominator (number of survivors) is smaller than the . . . [Full Text of this Article]

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