# Educational Note: Paradoxical Collider Effect in the Analysis of Non-Communicable Disease Epidemiological Data: a reproducible illustration and web application

arXiv: https://arxiv.org/abs/1809.07111 · HTML: https://mlsanity.com/paper/1809.07111/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2018.

## Built on by (most cited first, 4 of 4)

- [Designing Reinforcement Learning Algorithms for Digital Interventions: Pre-implementation Guidelines](https://mlsanity.com/paper/2206.03944/) (2022)
- [Evaluating counterfactual explanations using Pearl's counterfactual method](https://mlsanity.com/paper/2301.02499/) (2023)
- [Integrating Fuzzy Logic with Causal Inference: Enhancing the Pearl and Neyman-Rubin Methodologies](https://mlsanity.com/paper/2406.13731/) (2024)
- [Probabilistic Easy Variational Causal Effect](https://mlsanity.com/paper/2403.07745/) (2024)

## Abstract (arXiv)

Classical epidemiology has focused on the control of confounding but it is only recently that epidemiologists have started to focus on the bias produced by colliders. A collider for a certain pair of variables (e.g., an outcome Y and an exposure A) is a third variable (C) that is caused by both. In a directed acyclic graph (DAG), a collider is the variable in the middle of an inverted fork (i.e., the variable C in A -> C <- Y). Controlling for, or conditioning an analysis on a collider (i.e., through stratification or regression) can introduce a spurious association between its causes. This potentially explains many paradoxical findings in the medical literature, where established risk factors for a particular outcome appear protective. We use an example from non-communicable disease epidemiology to contextualize and explain the effect of conditioning on a collider. We generate a dataset with 1,000 observations and run Monte-Carlo simulations to estimate the effect of 24-hour dietary sodium intake on systolic blood pressure, controlling for age, which acts as a confounder, and 24-hour urinary protein excretion, which acts as a collider. We illustrate how adding a collider to a regression model introduces bias. Thus, to prevent paradoxical associations, epidemiologists estimating causal effects should be wary of conditioning on colliders. We provide R-code in easy-to-read boxes throughout the manuscript and a GitHub repository (https://github.com/migariane/ColliderApp) for the reader to reproduce our example. We also provide an educational web application allowing real-time interaction to visualize the paradoxical effect of conditioning on a collider http://watzilei.com/shiny/collider/.