# Doubly Robust Inference for Targeted Minimum Loss Based Estimation in Randomized Trials with Missing Outcome Data

## TL;DR

This paper introduces a doubly robust estimator for treatment effect analysis in randomized trials with missing outcome data, which remains consistent and normal under data-adaptive estimation of nuisance parameters, improving bias and efficiency.

## Contribution

It develops a new doubly robust estimator that is consistent and asymptotically normal with data-adaptive nuisance parameter estimation, enhancing inference in trials with missing data.

## Key findings

- Estimator has smaller finite-sample bias.
- Improved coverage of confidence intervals.
- Enhanced efficiency in simulation studies.

## Abstract

Missing outcome data is one of the principal threats to the validity of treatment effect estimates from randomized trials. The outcome distributions of participants with missing and observed data are often different, which increases the risk of bias. Causal inference methods may aid in reducing the bias and improving efficiency by incorporating baseline variables into the analysis. In particular, doubly robust estimators incorporate estimates of two nuisance parameters: the outcome regression and the missingness mechanism, to adjust for differences in the observed and unobserved groups that can be explained by observed covariates. Such nuisance parameters are traditionally estimated using parametric models, which generally preclude consistent estimation, particularly in moderate to high dimensions. Recent research on missing data has focused on data-adaptive estimation of the nuisance parameters in order to achieve consistency, but the large sample properties of such estimators are poorly understood. In this article we discuss a doubly robust estimator that is consistent and asymptotically normal (CAN) under data-adaptive consistent estimation of the outcome regression or the missingness mechanism. We provide a formula for an asymptotically valid confidence interval under minimal assumptions. We show that our proposed estimator has smaller finite-sample bias compared to standard doubly robust estimators. We present a simulation study demonstrating the enhanced performance of our estimators in terms of bias, efficiency, and coverage of the confidence intervals. We present the results of an illustrative example: a randomized, double-blind phase II/III trial of antiretroviral therapy in HIV-infected persons, and provide R code implementing our proposed estimators.