Abstract
Abstract The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate. Via simulation study, we compare fractional imputation’s accuracy and precision with that of multiple imputation.
Highlights
It is commonplace in scientific research for investigators to rely on observational data to address questions of interest
We show that the fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate
Similar results were seen for the Augmented IPW (AIPW) estimates: As expected, both multiple imputation (MI) and fractional imputation (FI) do better than complete case estimation (CC) estimators in all regards
Summary
Researchers must utilize observational data and make careful corrections to address various biases. It is considerably more difficult to draw correct causal conclusions from observational data than from a randomized experiment. Researchers make unverifiable assumptions to draw causal conclusions of treatment effects, such as unconfoundedness of the treatment-outcome relationship, after adjusting for a set of confounders. Current causal inference methods, including propensity score methods [1], outcome regression methods, and doubly robust methods [2,3,4,5], have been developed to remove confounding bias, mainly in the settings where confounders are fully observed. Observational data is highly prone to missingness. It is important, and at many times critical, to handle missing data properly to avoid introducing additional bias to the data analysis
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