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On model selection and model misspecification in causal inference

Standard variable selection procedures, primarily developed for the construction of outcome prediction models, are routinely applied when assessing exposure effects in observational studies. We argue that this tradition is sub-optimal and prone to yield bias in exposure effect estimators as well as their corresponding uncertainty estimators. We weigh the pros and cons of confounder-selection procedures and propose a procedure directly targeting the quality of the exposure effect estimator. We further demonstrate that certain strategies for inferring causal effects have the desirable features (a) of producing (approximately) valid confidence intervals, even when the confounder-selection process is ignored, and (b) of being robust against certain forms of misspecification of the association of confounders with both exposure and outcome.