## INTRODUCTION

This JAMA Guide to Statistics and Methods describes collider bias, illustrates examples in directed acyclic graphs, and explains how it can threaten the internal validity of a study and the accurate estimation of causal relationships in randomized clinical trials and observational studies.

Bias is a systematic, nonrandom error in the estimation of a treatment effect or the effect of an exposure or risk factor. Bias can lead to invalid results in observational studies and randomized clinical trials (RCTs). Bias is often broadly categorized into 3 groups: confounding, information (or measurement) bias, and selection bias.1,2 Selection bias is a general term describing bias that occurs when study participants are identified in a manner such that they are no longer representative of the target population. This can occur when an exposure and outcome each influence a common third variable—the collider—and that variable has been controlled for in the statistical analysis of the study data.3 Collider bias threatens the internal validity of a study and the accurate estimation of causal relationships.

In an observational study of 4480 patients with confirmed COVID-19 published in JAMA, Fosbøl et al4 found no increase in mortality among patients using angiotensin-converting enzyme inhibitors (ACEIs) or angiotensin receptor blockers (ARBs). The possibility of collider bias should be considered in interpreting this result because the study was restricted to patients with COVID-19, and COVID-19 might represent a collider associated with drug treatment and mortality.

## WHAT IS COLLIDER BIAS?

Collider bias occurs when an exposure and outcome (or factors causing these) each influence a common third variable and that variable or collider is controlled for by design or analysis.3 In contrast, confounding occurs when an exposure and outcome have a shared common cause that is not controlled for. Methods for statistically controlling for a variable include restricting the analysis to patients with a given characteristic (ie, the patients have been selected for this analysis) or applying a statistical adjustment based on a variable (eg, the variable of interest is included as a variable in a regression model). Collider bias is often inadvertently introduced by controlling for a variable that occurs after the exposure or intervention.

Collider bias can be illustrated using directed acyclic graphs (DAGs).5 A DAG is a graphical representation of the potential causal relationships between variables, with arrows used to denote the direction of causality. Collider bias occurs when 2 arrows collide on a variable that has been controlled for (panel A in Figure 1).

###### Figure 1

Example of Directed and Nondirected Paths

The arrows represent hypothetical causal relationships. Text in the final rectangles indicates that the outcome or characteristic is controlled for by design or analysis. In panel A, the general structure leading to collider bias is illustrated, with the variable C representing the collider. In panel B, no causal relationship ...

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