Educational Note: Paradoxical collider effect in the analysis of non-communicable disease epidemiological data: a reproducible illustration and web application
Bibliographic record
Abstract
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 1000 observations, and run Monte-Carlo simulations to estimate the effect of 24-h dietary sodium intake on systolic blood pressure, controlling for age, which acts as a confounder, and 24-h 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/].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.099 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.004 | 0.004 |
| Insufficient payload (model declined to judge) | 0.198 | 0.072 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".