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To the Editor: Dr Shishehbor and colleagues¹ showed that much of the mortality risk associated with SES may be explained by functional capacity and heart rate recovery. To quantify the contribution of these variables to the observed association between SES and mortality using hazard ratios (HR), they used the following formula:

Proportion of excess risk explained = [HR_U–HR_A]/[HR_U–1], where HR_U is the hazard ratio for mortality conferred by low SES but unadjusted for functional capacity and heart rate recovery, and HR_A is the adjusted hazard ratio after accounting for functional capacity and heart rate recovery. This formula was taken from an article examining the contribution of surgeon volume to the relationship between hospital volume and surgical mortality.²

However, this equation is mathematically unstable and should be avoided because HRs are odds, not proportions, and calculations involving odds are multiplicative, not additive. For example, suppose that being male is a . . . [Full Text of this Article]

Daniel J. Brotman, MD
brotman@jhmi.edu
Johns Hopkins Hospital
Baltimore, Md

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"Proportion Explained": A Causal Interpretation for Standard Measures of Indirect Effect?
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ABSTRACT | FULL TEXT