The “Obesity Paradox” Explained

To the Editor: Several prospective studies have reported a J-shaped relationship between obesity and mortality, suggesting increased risk of death in the lowest and highest body mass index (BMI) groups in men and women of all ages, races, and ethnicities.1 Although obesity is associated with a higher overall mortality risk in the general population, some authors have interpreted these patterns to suggest that obesity confers a survival advantage in surviving clinical subpopulations.2 This “obesity paradox” has been reported for various disease groups including stroke, myocardial infarction, heart failure, renal disease, and diabetes.2–5 We propose that this apparent paradox is simply the result of collider stratification, a source of selection bias that is common in epidemiologic research.6 The classic manifestation of this selection bias is a result of conditioning on a variable affected by exposure and sharing common causes with the outcome (known as a collider). Conditioning on a collider distorts the association between exposure and outcome among those selected for analysis and can therefore produce a spurious protective association between obesity and mortality in disease groups. For illustrative purposes, we explore the obesity paradox in patients with heart failure (Figure). Among patients with stable heart failure, Curtis and colleagues7 reported an unadjusted hazard ratio of mortality of 0.81 (95% confidence interval [CI]: 0.74, 0.88) for overweight participants and 0.70 (95% CI: 0.62, 0.78) for obese participants. To assess whether selection bias could be responsible for this protective association, we used data from the 1999–2000 and 2000–2001 National Health and Nutrition Examination Survey (NHANES), linked to mortality data from the National Death Index up to 31 December 2006. We created three BMI categories: normal weight (18.5–24.5 kg/m2), overweight (25.0–29.9 kg/m2), and obese (>30 kg/m2). We stratified the dataset on heart failure status and then calculated sampling fractions by dividing the number of participants in each cell of the 2 × 3 table stratified by heart failure by the number of participants in the corresponding cell of the unstratified table (See eAppendix, https://links.lww.com/EDE/A668). Using a simple selection bias correction formula, we calculated crude odds ratios for being overweight or obese relative to normal weight, and adjusted the odds ratios for selection bias using sampling fractions.8 All analyses were conducted using Stata software version 11 (StataCorp).FIGURE: Directed acyclic graph of the hypothesized effects of obesity on mortality among individuals with heart failure. Potential unmeasured risk factors include a genetic factors and lifestyle behaviors.In the complete NHANES cohort (n = 11,429), 256 people of normal weight, 258 overweight, and 528 obese people died prior to 31 December 2006, whereas among those with heart failure, 29, 34, and 111 persons in the normal weight, overweight, and obese categories died. The crude odds ratio was 0.79 (95% CI: 0.70–0.88) for overweight and 0.65 (0.57–0.74) for obese—similar to the findings of Curtis and colleagues. After adjusting for selection bias, however, overweight and obesity no longer appeared protective. The corrected odds ratios were 1.88 (1.69–2.09) for overweight and 1.07 (0.94–1.22) for obese. The crude risks were biased by 58% for overweight and 39% for obese due to selection bias alone. Using sampling fractions from a population-based cohort, we were able to correct for selection bias due to conditioning on a collider. Although this deterministic bias analysis fails to account for several sources of uncertainty, it provides one simple and sufficient explanation for why the “obesity paradox” occurs. Future analyses should correct for survivor selection with probabilistic bias analysis techniques or inverse probability-of-censoring weights. The present analysis emphasizes that “paradoxes” should be met with skepticism and suggests that obesity is not protective among those with heart failure, or likely for any other disease state. It also serves as a reminder of the importance of using graphical tools, such as directed acyclic graphs, to assess sources of bias. Hailey R. Banack Department of Epidemiology, Biostatistics, and Occupational Health McGill University Montreal, Quebec, Canada [email protected] Jay S. Kaufman Department of Epidemiology, Biostatistics, and Occupational Health McGill University Montreal, Quebec, Canada

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