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Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data

Matthew Pryce, Karla Diaz-Ordaz, Ruth H. Keogh, Stijn Vansteelandt

TL;DR

This work tackles the challenge of estimating heterogeneous treatment effects when outcomes are missing at random (MAR). It introduces two de-biased estimators, the mDR-learner and mEP-learner, which embed inverse probability of censoring weights into EIF-based DR- and EP-learner frameworks to correct for under-representation due to MAR. The authors prove oracle efficiency under reasonable conditions and demonstrate superior performance in simulations across diverse MAR scenarios, including a real-world application to the GBSG2 breast cancer trial. They provide detailed implementation guidance, discuss uncertainty quantification via half-sample bootstrap, and highlight stability considerations across cross-fitting seeds. The work offers practical methods for robust CATE estimation in real-world datasets with MAR missing outcomes and suggests avenues for extending these techniques to more complex data structures and covariate types.

Abstract

When estimating heterogeneous treatment effects, missing outcome data can complicate treatment effect estimation, causing certain subgroups of the population to be poorly represented. In this work, we discuss this commonly overlooked problem and consider the impact that missing at random (MAR) outcome data has on causal machine learning estimators for the conditional average treatment effect (CATE). We propose two de-biased machine learning estimators for the CATE, the mDR-learner and mEP-learner, which address the issue of under-representation by integrating inverse probability of censoring weights into the DR-learner and EP-learner respectively. We show that under reasonable conditions, these estimators are oracle efficient, and illustrate their favorable performance through simulated data settings, comparing them to existing CATE estimators, including comparison to estimators which use common missing data techniques. We present an example of their application using the GBSG2 trial, exploring treatment effect heterogeneity when comparing hormonal therapies to non-hormonal therapies among breast cancer patients post surgery, and offer guidance on the decisions a practitioner must make when implementing these estimators.

Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data

TL;DR

This work tackles the challenge of estimating heterogeneous treatment effects when outcomes are missing at random (MAR). It introduces two de-biased estimators, the mDR-learner and mEP-learner, which embed inverse probability of censoring weights into EIF-based DR- and EP-learner frameworks to correct for under-representation due to MAR. The authors prove oracle efficiency under reasonable conditions and demonstrate superior performance in simulations across diverse MAR scenarios, including a real-world application to the GBSG2 breast cancer trial. They provide detailed implementation guidance, discuss uncertainty quantification via half-sample bootstrap, and highlight stability considerations across cross-fitting seeds. The work offers practical methods for robust CATE estimation in real-world datasets with MAR missing outcomes and suggests avenues for extending these techniques to more complex data structures and covariate types.

Abstract

When estimating heterogeneous treatment effects, missing outcome data can complicate treatment effect estimation, causing certain subgroups of the population to be poorly represented. In this work, we discuss this commonly overlooked problem and consider the impact that missing at random (MAR) outcome data has on causal machine learning estimators for the conditional average treatment effect (CATE). We propose two de-biased machine learning estimators for the CATE, the mDR-learner and mEP-learner, which address the issue of under-representation by integrating inverse probability of censoring weights into the DR-learner and EP-learner respectively. We show that under reasonable conditions, these estimators are oracle efficient, and illustrate their favorable performance through simulated data settings, comparing them to existing CATE estimators, including comparison to estimators which use common missing data techniques. We present an example of their application using the GBSG2 trial, exploring treatment effect heterogeneity when comparing hormonal therapies to non-hormonal therapies among breast cancer patients post surgery, and offer guidance on the decisions a practitioner must make when implementing these estimators.
Paper Structure (35 sections, 81 equations, 10 figures, 6 tables, 3 algorithms)

This paper contains 35 sections, 81 equations, 10 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Setting
  4. Estimating the CATE using ML - No missing outcome data
  5. Estimating the CATE using ML - With missing outcome data
  6. DR-learner/EP-learner extensions
  7. mDR-learner
  8. mEP-learner
  9. Implementation
  10. Decisions required for obtaining CATE estimates
  11. Decisions required for assessing CATE performance
  12. Simulation study
  13. Set up
  14. Findings
  15. GBSG2 trial analysis
  16. ...and 20 more sections

Figures (10)

  • Figure 1: mDR-learner algorithm
  • Figure 2: mEP-learner algorithm
  • Figure 3: Root mean square median error (RMSME) for mDR-learner, mEP-learner, DR-learner, EP-learner and T-learner in three DGPs plotted by training sample size. Plots in the left column compare the mDR-learner and mEP-learner to the DR-learner, EP-learner and T-learner when used in combination with an outcome imputation model in DGP 1, 2 and 3 respectively. Plots in the right column compare the mDR-learner and mEP-learner to the available case versions of the DR-learner, EP-learner and T-learner in DGP 1, 2 and 3 respectively.
  • Figure 4: Median CATE estimates plotted by progesterone receptor (fmol/l).
  • Figure 5: CATE estimates from single cross-fitting seeds plotted by progesterone receptor (fmol/l).
  • ...and 5 more figures