Recognize When Selection Can Create an Association

Look beyond the regression formula

Conditioning occurs when an analysis adjusts for a variable, restricts eligibility, stratifies a table or includes only people whose records are observed. Any of these operations can select on a common effect of two variables. Review the route by which participants entered the dataset before focusing on the final model.

Hernán, Hernández-Díaz and Robins’ structural account of selection bias explains why causal structure matters when evaluating selection. A collider is defined by arrows pointing into a variable on a particular path; it is not identified merely by a correlation table or a strong predictive association.

Draw the inclusion mechanism

Create a timeline and diagram for referral, testing, admission, participation and complete-case inclusion. Ask which factors influence each step. Consider whether the exposure and a cause of the outcome both affect the chance of being selected. Review adjusted variables using the same reasoning, including variables described informally as severity or healthcare use.

Do not assume that adding more covariates necessarily reduces bias. Record the scientific reason for conditioning on each variable and distinguish a baseline measurement from the process that made the measurement available. A baseline variable can still be a collider in the relevant graph.

Enumerate a hypothetical selection rule

Imagine two independent binary characteristics A and U, each present in half a fictional population. The four combinations 00, 01, 10 and 11 are equally common. Suppose a record is selected whenever A or U is present, so combination 00 is excluded.

Among selected records with A = 0, U must equal 1. Among selected records with A = 1, U equals 1 in half the cases. Selection has therefore created a negative association between originally independent characteristics. If U also affects an outcome, comparing A groups within the selected dataset can inherit that distortion.

Decide what the data can support

The example is a diagnostic illustration, not a correction formula for every selected sample. In a real study, assess whether the target population is intentionally the selected group and whether the causal question remains identifiable there. A restriction can change both the target and the bias structure.

Preserve a record of alternative inclusion definitions and explain any sensitivity analyses. If selection probabilities or necessary variables are unavailable, acknowledge the resulting limitation instead of claiming that ordinary covariate adjustment has solved it. Report the recruitment and observation process clearly enough for readers to judge how selection may relate to the exposure and outcome.

Source verification: 6 November 2026. Examples are hypothetical.