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Identification and Estimation of Long-Term Treatment Effects with Monotone Missing

Qinwei Yang, Ruocheng Guo, Shasha Han, Peng Wu

TL;DR

This work tackles long-term treatment effect estimation under multi-stage monotone missing by proposing a sequential missing mechanism that enables identifiability of $\tau$ and $\tau(x)$. It introduces three estimation strategies—IPW, SeqRI, and SeqMSM—to leverage the sequential missing data, and complements them with BalanceNet, a balancing-enhanced network that stabilizes SeqMSM under data sparsity. Empirical results on IHDP and JOBS show that SeqMSM and BalanceNet achieve superior accuracy and stability, with SeqRI hindered by extrapolation and IPW by underutilizing missing-data information. Together, these methods advance causal inference for MNAR monotone-missing settings and provide practical tools for evaluating long-term treatment effects.

Abstract

Estimating long-term treatment effects has a wide range of applications in various domains. A key feature in this context is that collecting long-term outcomes typically involves a multi-stage process and is subject to monotone missing, where individuals missing at an earlier stage remain missing at subsequent stages. Despite its prevalence, monotone missing has been rarely explored in previous studies on estimating long-term treatment effects. In this paper, we address this gap by introducing the sequential missingness assumption for identification. We propose three novel estimation methods, including inverse probability weighting, sequential regression imputation, and sequential marginal structural model (SeqMSM). Considering that the SeqMSM method may suffer from high variance due to severe data sparsity caused by monotone missing, we further propose a novel balancing-enhanced approach, BalanceNet, to improve the stability and accuracy of the estimation methods. Extensive experiments on two widely used benchmark datasets demonstrate the effectiveness of our proposed methods.

Identification and Estimation of Long-Term Treatment Effects with Monotone Missing

TL;DR

This work tackles long-term treatment effect estimation under multi-stage monotone missing by proposing a sequential missing mechanism that enables identifiability of and . It introduces three estimation strategies—IPW, SeqRI, and SeqMSM—to leverage the sequential missing data, and complements them with BalanceNet, a balancing-enhanced network that stabilizes SeqMSM under data sparsity. Empirical results on IHDP and JOBS show that SeqMSM and BalanceNet achieve superior accuracy and stability, with SeqRI hindered by extrapolation and IPW by underutilizing missing-data information. Together, these methods advance causal inference for MNAR monotone-missing settings and provide practical tools for evaluating long-term treatment effects.

Abstract

Estimating long-term treatment effects has a wide range of applications in various domains. A key feature in this context is that collecting long-term outcomes typically involves a multi-stage process and is subject to monotone missing, where individuals missing at an earlier stage remain missing at subsequent stages. Despite its prevalence, monotone missing has been rarely explored in previous studies on estimating long-term treatment effects. In this paper, we address this gap by introducing the sequential missingness assumption for identification. We propose three novel estimation methods, including inverse probability weighting, sequential regression imputation, and sequential marginal structural model (SeqMSM). Considering that the SeqMSM method may suffer from high variance due to severe data sparsity caused by monotone missing, we further propose a novel balancing-enhanced approach, BalanceNet, to improve the stability and accuracy of the estimation methods. Extensive experiments on two widely used benchmark datasets demonstrate the effectiveness of our proposed methods.
Paper Structure (34 sections, 2 theorems, 16 equations, 3 figures, 11 tables, 2 algorithms)

This paper contains 34 sections, 2 theorems, 16 equations, 3 figures, 11 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation and Setup
  4. Problem Formulation
  5. Challenges and Classical Method
  6. Challenges
  7. Classical Method: Missing At Random
  8. Proposed IPW, SeqRI, and SeqMSM Methods
  9. Identifiability
  10. Inverse Probability Weighting
  11. Sequential Regression Imputation
  12. Sequential Marginal Structural Model
  13. Limitations of IPW and SeqRI Methods
  14. Sequential MSM Method
  15. Proposed Balancing-Enhanced Network
  16. ...and 19 more sections

Key Result

Theorem 5

Under Assumptions assum:2-1, assum:2-2, and assum:4-1, $\tau$ and $\tau(x)$ are identifiable.

Figures (3)

  • Figure 1: Architecture of BalanceNet.
  • Figure A2: Effects of different scaling constant on $\epsilon_{CATE}$ with missing ration $\gamma=0.15$.
  • Figure A3: Effects of different scaling constant on $\epsilon_{ATE}$ with missing ration $\gamma=0.15$.

Theorems & Definitions (3)

  • Theorem 5: Identifiability
  • Proposition 6
  • Definition 1: MSM, Hernan-Robins2020