  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/.
