# Collider Bias Is an Insufficient Explanation for the Inverse Obesity Paradox in Prostate Cancer

## TL;DR

This study shows that collider bias cannot fully explain the inverse obesity paradox in prostate cancer, suggesting the link between BMI and cancer death is real.

## Contribution

The paper demonstrates that collider bias has limited impact on the BMI-prostate cancer death association compared to classical confounding.

## Key findings

- Collider bias distorted the BMI-PCa death odds ratio by no more than 4%.
- Classical confounding had a greater potential to distort the BMI-PCa death association than collider bias.
- The positive BMI-PCa death relationship is likely real, not a statistical artifact.

## Abstract

Collider bias is often considered a potential explanation when the association between obesity and disease diagnosis differs from that with disease outcome, as seen in the “obesity paradox.” For prostate cancer (PCa), in particular localized PCa, an “inverse” obesity paradox has been observed, where body mass index (BMI) is negatively associated with diagnosis (hazard ratio [HR] ~0.9 per 5‐kg/m2 increase), but positively associated with PCa‐specific death (HR ~ 1.2). However, collider bias in this context remains unexplored.

We simulated binary disease diagnosis and outcome data, including the typically unmeasured/unknown background variable (U) that could introduce collider bias. We calculated U‐unadjusted (biased) and U‐adjusted (true) marginal odds ratios (OR) from a case‐only analysis, and determined the bias percentage using ORBiased−ORTrue/ORTrue×100. Similar simulations were performed for classical confounding.

Across a broad range of plausible parameter values for the PCa context, collider bias did not distort the OR of BMI on PCa death by more than 4%, equivalent to a ± 0.04 distortion in the OR estimate for continuous BMI. In comparison, classical confounding showed a higher potential for distorting BMI and PCa death associations than collider bias.

Collider bias alone is unlikely to explain the inverse obesity paradox in (localized) PCa, reinforcing some mechanistic evidence that the observed positive relationship between BMI and PCa death is real, and not a statistical artifact. This finding emphasizes the importance of exploring alternative mechanisms beyond collider bias to better understand the underlying factors driving this paradox.