Bounds and sensitivity analysis when estimating average treatment effects with imputation and double robust estimators
(English)Manuscript (preprint) (Other academic)
When estimating average causal effects of treatments with observational data, scientists often rely on the assumption of unconfoundedness. We propose a sensitivity analysis for imputation estimators and doubly robust estimators, based on bounds (defining an identification interval) for the causal effect of interest, which allow for unobserved confounders. The bounds are derived from the bias of the estimators, expressed as a function of a sensitivity parameter. We describe how such bounds can take into account sampling variation, thereby yielding an uncertainty interval. We are also able to contrast the size of potential bias due to violation of the unconfoundedness assumption, to the misspecification of the models used to explain outcome with the observed covariates. While the latter bias can in principle be made arbitrarily small with increasing sample size (by increasing the flexibility of the models used), the bias due to unobserved confounding does not disappear with increasing sample size. Through numerical experiments we illustrate the relative size of the biases due to unobserved confounders and model misspecification, as well as the empirical coverage of the uncertainty interval on which the proposed sensitivity analysis is based.
Probability Theory and Statistics
Research subject Statistics
IdentifiersURN: urn:nbn:se:umu:diva-127119OAI: oai:DiVA.org:umu-127119DiVA: diva2:1043963