Quick Takeaways
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Selecting covariates solely based on prediction models can lead to biased effect estimates because true confounders may appear unimportant if they don’t strongly predict outcomes, risking under-adjustment.
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The Bayesian Adjustment for Confounding (BAC) approach recommends jointly modeling exposure and outcome to identify confounders, helping avoid the pitfalls of traditional selection methods that may omit key variables like weak but critical confounders or mistakenly include instruments.
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Adjusting for variables that predict exposure but have no direct effect on the outcome (instruments) can amplify bias through bias amplification—a critical caution highlighted by simulations showing it worsening estimates.
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To improve causal inference, prioritize modeling exposure alongside outcome, recognize that over- or under-adjustment carries different risks, and treat adjustment uncertainty as a genuine source of statistical uncertainty rather than relying solely on predictive-fit criteria.
The Challenge of Choosing the Right Variables
Estimation of treatment effects sounds simple, but it’s quite tricky. The goal is to understand how an exposure impacts an outcome, like air pollution on hospital visits. Usually, researchers use observational data with many variables. Some are confounders, meaning they influence both exposure and outcome; others are noise. The key question is: which variables should go into the model? Many rely on common methods like stepwise routines or cross-validation. However, these tools focus on predicting the outcome well. Just because a model predicts outcomes accurately doesn’t mean it correctly estimates treatment effects. It’s easy to run into the problem where the best predictor gives misleading results about the true effect.
Why Prediction Doesn’t Guarantee Correct Effect Estimates
Predictive models often highly weight variables that explain outcome variability. But these might not be the true confounders. For example, a variable one model ignores may strongly influence exposure but only weakly relate to the outcome. Such a variable could be wrongly excluded because it doesn’t help predict the outcome directly. However, this exclusion shifts the effect estimate, contaminating it. When the model drops a true confounder, it biases the results. For instance, a confounder linked strongly to exposure but weakly to outcome can be mistakenly labeled as irrelevant. This leads to under-adjustment, resulting in biased conclusions that appear statistically significant. Notably, traditional methods might prefer simpler models that omit these confounders, mistakenly giving us the wrong treatment effect.
Tools, Risks, and the Way Forward
Traditional model selection methods—like Bayesian model averaging—also face the same problem. They weigh models based on predictive fit, which can favor under-adjusted models that bias estimates. One effective approach is to consider the exposure model and the outcome model together. By linking variables—i.e., including only variables that predict both exposure and outcome—we better identify true confounders. This method, often called a confounder-aware approach, helps avoid bias amplification. For example, including a variable that predicts only the exposure, called an instrument, may worsen bias. Such variables can distort the effect estimate because they do not serve as confounders. To make sound decisions, researchers must weigh their causal assumptions carefully. Adjusting based solely on predictive performance risks misestimating the effect. Fitting both the exposure and outcome models, then combining their insights, offers a clearer picture. This balanced approach helps ensure that the treatment effect estimates are more accurate and trustworthy.
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