Collider Bias Is Only a Partial Explanation for the Obesity Paradox

Abstract

Background: "Obesity paradox" refers to an association between obesity and reduced mortality (contrary to an expected increased mortality). A common explanation is collider stratification bias: unmeasured confounding induced by selection bias. Here, we test this supposition through a realistic generative model.

Methods: We quantify the collider stratification bias in a selected population using counterfactual causal analysis. We illustrate the bias for a range of scenarios, describing associations between exposure (obesity), outcome (mortality), mediator (in this example, diabetes) and an unmeasured confounder.

Results: Collider stratification leads to biased estimation of the causal effect of exposure on outcome. However, the bias is small relative to the causal relationships between the variables.

Conclusions: Collider bias can be a partial explanation of the obesity paradox, but unlikely to be the main explanation for a reverse direction of an association to a true causal relationship. Alternative explanations of the obesity paradox should be explored. See Video Abstract at http://links.lww.com/EDE/B51.

FIGURE 1.

Illustration of collider stratification bias.

FIGURE 2.

Association (OR) between A and Y in the null case for varying values of α_A,α_U, β_U, and α_AU. In each panel, along the x axis, one of these variables is varied from −3 to 3 (left panel: α_A, mid-left panel: α_U, mid-right panel: β_U, right panel: α_AU), and the other parameters are set to default values.

FIGURE 3.

Association (OR) between A and Y in the null case for varying values of α_A,α_U, and β_U, without interaction (α_AU = 0, solid line) and with interaction (α_AU = 1, dotted line). Each column (row) in the lattice corresponds to the given value of β_U (α_A). Within each subgraph, along the x axis, α_U is varied from −3 to 3.

FIGURE 4.

Association (OR) between A and Y (solid line) versus causal effect (log odds) of A on Y (dashed line) for a range of values of α_A,α_U, β_U, and α_AU. In each panel, along the x axis, one of these variables is varied from −3 to 3 (left panel: α_A, mid-left panel: α_U, mid-right panel: β_U, right panel: α_AU), and the other parameters are set to default values.

FIGURE 5.

Association (OR) between A and Y versus causal effect (log odds) of A on Y for varying values of α_A,α_U, and β_U, with β_B = 1. Each column (row) in the lattice corresponds to the given of β_U (α_A). Within each subgraph, along the x axis, α_U is varied from −3 to 3. Association without interaction (α_AU = 0): solid line; association with interaction (α_AU = 1): dotted line; causal effect: dashed line.