@article {doi:10.1093/ije/dyy275,
	title = {Educational Note: Paradoxical collider effect in the analysis of non-communicable disease epidemiological data: a reproducible illustration and web application},
	journal = {International Journal of Epidemiology},
	year = {2019},
	pages = {dyy275},
	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 {\textrightarrow} C {\textleftarrow} 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/].},
	doi = {10.1093/ije/dyy275},
	url = {http://dx.doi.org/10.1093/ije/dyy275},
	author = {Luque-Fernandez, Miguel Angel and Schomaker, Michael and Redondo-Sanchez, Daniel and Perez, Maria Jose Sanchez and Vaidya, Anand and Schnitzer, Mireille E}
}
