# Two-Stage TMLE to Reduce Bias and Improve Efficiency in Cluster Randomized Trials

arXiv: https://arxiv.org/abs/2106.15737 · HTML: https://mlsanity.com/paper/2106.15737/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 79 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 4 of 4)

- [A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure](https://mlsanity.com/paper/1706.02675/) (2017)
- [Accounting for interactions and complex inter-subject dependency in estimating treatment effect in cluster randomized trials with missing outcomes](https://mlsanity.com/paper/1507.01822/) (2015)
- [Missing continuous outcomes under covariate dependent missingness in cluster randomised trials](https://mlsanity.com/paper/1603.04176/) (2016)
- [Missing binary outcomes under covariate dependent missingness in cluster randomised trials](https://mlsanity.com/paper/1608.05289/) (2016)

## Built on by (most cited first, 4 of 4)

- [Automated Efficient Estimation using Monte Carlo Efficient Influence Functions](https://mlsanity.com/paper/2403.00158/) (2024)
- [Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review](https://mlsanity.com/paper/2303.07329/) (2023)
- [Adaptive Selection of the Optimal Strategy to Improve Precision and Power in Randomized Trials](https://mlsanity.com/paper/2210.17453/) (2022)
- [Machine learning to optimize precision in the analysis of randomized trials: A journey in pre-specified, yet data-adaptive learning](https://mlsanity.com/paper/2512.13610/) (2025)

## Abstract (arXiv)

Cluster randomized trials (CRTs) randomly assign an intervention to groups of individuals (e.g., clinics or communities) and measure outcomes on individuals in those groups. While offering many advantages, this experimental design introduces challenges that are only partially addressed by existing analytic approaches. First, outcomes are often missing for some individuals within clusters. Failing to appropriately adjust for differential outcome measurement can result in biased estimates and inference. Second, CRTs often randomize limited numbers of clusters, resulting in chance imbalances on baseline outcome predictors between arms. Failing to adaptively adjust for these imbalances and other predictive covariates can result in efficiency losses. To address these methodological gaps, we propose and evaluate a novel two-stage targeted minimum loss-based estimator (TMLE) to adjust for baseline covariates in a manner that optimizes precision, after controlling for baseline and post-baseline causes of missing outcomes. Finite sample simulations illustrate that our approach can nearly eliminate bias due to differential outcome measurement, while existing CRT estimators yield misleading results and inferences. Application to real data from the SEARCH community randomized trial demonstrates the gains in efficiency afforded through adaptive adjustment for baseline covariates, after controlling for missingness on individual-level outcomes.