# Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems

arXiv: https://arxiv.org/abs/2602.24131 · HTML: https://mlsanity.com/paper/2602.24131/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Causal inference for social network data](https://mlsanity.com/paper/1705.08527/) (2017)
- [Longitudinal Targeted Minimum Loss-based Estimation with Temporal-Difference Heterogeneous Transformer](https://mlsanity.com/paper/2404.04399/) (2024)
- [Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes](https://mlsanity.com/paper/2105.02088/) (2021)
- [Adaptive debiased machine learning using data-driven model selection techniques](https://mlsanity.com/paper/2307.12544/) (2023)
- [Adaptive-TMLE for the Average Treatment Effect based on Randomized Controlled Trial Augmented with Real-World Data](https://mlsanity.com/paper/2405.07186/) (2024)
- [Tutorial: Deriving The Efficient Influence Curve for Large Models](https://mlsanity.com/paper/1903.01706/) (2019)
- [Optimal sampling for design-based estimators of regression models](https://mlsanity.com/paper/2106.08530/) (2021)
- [Assessing treatment effects in observational data with missing confounders: A comparative study of practical doubly-robust and traditional missing data methods](https://mlsanity.com/paper/2412.15012/) (2024)
- [Efficient Estimation of Causal Effects Under Two-Phase Sampling with Error-Prone Outcome and Treatment Measurements](https://mlsanity.com/paper/2506.21777/) (2025)

## Built on by (most cited first, 1 of 1)

- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)

## Abstract (arXiv)

In a typical two-phase design, a random sample is drawn from the target population in phase 1, during which only a subset of variables is collected. In phase 2, a subsample of the phase-1 cohort is selected, and additional variables are measured. This setting induces a coarsened data structure on the data from the second phase. We assume coarsening at random, that is, the phase-2 sampling mechanism depends only on variables fully observed. We review existing estimators, including the generalized raking estimator and the inverse probability of censoring weighted targeted maximum likelihood estimation (IPCW-TMLE) along with its extensions that also target the phase-2 sampling mechanism to improve efficiency. We further introduce a new class of estimators constructed within the TMLE framework that are asymptotically equivalent.