We read with great interest the letter by Banack and Kaufman1 recently published in EPIDEMIOLOGY. The authors cited research by Curtis et al2 who found that, among persons with heart disease, those who were overweight or obese had a lower risk of death than those with a normal weight. Banack and Kaufman1 proposed that such an “obesity paradox” was the result of collider stratification bias, and they demonstrated a method to correct for such bias. We posit that, even after correction for bias, this paradoxical phenomenon may persist in observational studies of the effect of obesity on mortality among patients with heart failure.
Numerous studies conducted in the general population have shown that obesity is associated with an increased risk of mortality.3,4 We have depicted these studies using a causal diagram in Figure A. To simplify our discussion, we assume that obesity increases the risk of death through two causal pathways: one mediated through heart failure (ie, obesity → heart failure → death [indirect effect]) and the other through a mechanism that does not include heart failure (ie, obesity → death [direct effect]). The total effect of obesity on the risk of death is the net causal effect through both pathways after proper adjustment for potential confounders (CF1). Thus, the primary aim of these studies was to evaluate the total effect of obesity on the risk of death in the general population.
Many studies have also evaluated whether the effect of obesity observed in the general population persists among high-risk populations, such as those with heart failure. These studies are depicted in Figure B, where restricting the study population to patients with heart failure is indicated by a box around “heart failure.” In these studies, obesity status (a known cause of heart failure) has often been assessed before or at the time of heart failure onset. Such a study design (restricting to patients with heart failure) could not only introduce collider stratification bias by creating a spurious association pathway between obesity and death (ie, obesity → heart failure ← CF2 → death) but also change the interpretation of the effect estimates of obesity on the risk of death. By restricting the study population to patients with heart failure, one can assess only the direct effect of obesity on the risk of death because the indirect effect of obesity on the risk of death through heart failure has been blocked (by restriction). Correction of collider stratification bias would result in an unbiased estimate of the direct effect of obesity but would not generate an estimate of the total effect of obesity on the risk of death among patients with heart failure, which is the intended aim of these studies.
Assuming that both the direct and the indirect effects of obesity on the risk of death are in the same direction, one would expect the total effect of obesity to be larger than its direct effect. In an extreme scenario, if the effect of obesity on the risk of death is completely mediated through heart failure, one should expect a null direct effect of obesity on the risk of death among patients with heart failure. Nevertheless, because the direct effect of obesity on the risk of death is different from its total effect, this would not constitute a true obesity paradox.
In practice, it is challenging to assess the total effect of obesity on the risk of death among patients with heart failure. One approach would be to conduct a randomized clinical trial of a weight loss intervention (eg, exercise, weight loss diet, medication, or surgical intervention) among obese patients with heart failure to determine whether weight loss is associated with reduced risk of death. However, to obtain an unbiased estimate of the total effect of weight loss on the risk of death, the weight loss intervention itself should have no direct effect on risk of death, or such an effect should be appropriately controlled, if present. Alternatively, in observational study settings, if there were sufficient changes in obesity status after heart failure, one would be able to assess the total effect of obesity on mortality, assuming appropriate adjustment for all potential confounders. If the total effect of obesity on the risk of death among patients with heart failure was different from the total effect in the general population, one could claim that an obesity paradox does exist.
We agree with Banack and Kaufman1 that “paradoxes” should be met with skepticism. We postulate that the obesity paradox could have resulted from confusion between the direct (estimated) and total (intended) effect. Incorrect interpretations of the results, and the ensuing debate about the paradoxical phenomena from studies restricted to people with a condition that is an intermediate in the causal pathway, can undermine scientific knowledge and evidence-based clinical recommendations. To avoid these issues, the investigators should carefully specify the research question of interest; clarify the time sequence of exposure, mediators, and outcome variables; use appropriate design and analysis; and exercise proper inference. Failure in any of these steps could potentially lead to incorrect causal inference.
We thank M. Maria Glymour and Tyler J. VanderWeele for their helpful comments.
1. Banack HR, Kaufman JS. The “obesity paradox” explained. Epidemiology. 2013;24:461–462
2. Curtis JP, Selter JG, Wang Y, et al. The Obesity Paradox: body mass index and outcomes in patients with heart failure. Arch Intern Med. 2005;165:55–61
3. Allison DB, Fontaine KR, Manson JE, et al. Annual deaths attributable to obesity in the United States. JAMA. 1999;282:1530
4. Adams KF, Schatzkin A, Harris TB, et al. Overweight, obesity, and mortality in a large prospective cohort of persons 50 to 71 years old. N Engl J Med. 2006;355:763–778