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Semiparametric Estimation of Treatment Effects in Observational Studies with Heterogeneous Partial Interference

Zhaonan Qu, Ruoxuan Xiong, Jizhou Liu, Guido Imbens

Abstract

In many observational studies in social science and medicine, subjects or units are connected, and one unit's treatment and attributes may affect another's treatment and outcome, violating the stable unit treatment value assumption (SUTVA) and resulting in interference. To enable feasible estimation and inference, many previous works assume exchangeability of interfering units (neighbors). However, in many applications with distinctive units, interference is heterogeneous and needs to be modeled explicitly. In this paper, we focus on the partial interference setting, and only restrict units to be exchangeable conditional on observable characteristics. Under this framework, we propose generalized augmented inverse propensity weighted (AIPW) estimators for general causal estimands that include heterogeneous direct and spillover effects. We show that they are semiparametric efficient and robust to heterogeneous interference as well as model misspecifications. We apply our methods to the Add Health dataset to study the direct effects of alcohol consumption on academic performance and the spillover effects of parental incarceration on adolescent well-being.

Semiparametric Estimation of Treatment Effects in Observational Studies with Heterogeneous Partial Interference

Abstract

In many observational studies in social science and medicine, subjects or units are connected, and one unit's treatment and attributes may affect another's treatment and outcome, violating the stable unit treatment value assumption (SUTVA) and resulting in interference. To enable feasible estimation and inference, many previous works assume exchangeability of interfering units (neighbors). However, in many applications with distinctive units, interference is heterogeneous and needs to be modeled explicitly. In this paper, we focus on the partial interference setting, and only restrict units to be exchangeable conditional on observable characteristics. Under this framework, we propose generalized augmented inverse propensity weighted (AIPW) estimators for general causal estimands that include heterogeneous direct and spillover effects. We show that they are semiparametric efficient and robust to heterogeneous interference as well as model misspecifications. We apply our methods to the Add Health dataset to study the direct effects of alcohol consumption on academic performance and the spillover effects of parental incarceration on adolescent well-being.

Paper Structure

This paper contains 31 sections, 10 theorems, 68 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Model Setup
  4. General Assumptions
  5. Conditional Exchangeability
  6. Semiparametric Treatment Effect Estimation under Conditional Exchangeability
  7. Estimands
  8. Estimators
  9. Main Asymptotic Results
  10. Simulation Studies
  11. Inference and Hypothesis Tests of Treatment Effects
  12. Robustness Properties of Our Estimators
  13. Two Applications to the Add Health Dataset
  14. Alcohol Consumption and Academic Performance
  15. Paternal Incarceration and Adolescent Well-Being
  16. ...and 16 more sections

Key Result

Theorem \oldthetheorem

Suppose Assumptions ass:network-ass:partial-prop-exchangeable hold. As $M \rightarrow \infty$, for any $z$ and $\mathbf{g}$, if either the estimated joint propensity $\hat{p}_{i,(z,\mathbf{g})}(\mathbf{X}_{c})$ or the estimated outcome $\hat{\mu}_{i,(z,\mathbf{g})}(\mathbf{X}_{c})$ is uniformly cons In particular, if at least one of $\hat{p}_{i,(z,\mathbf{g})}(\mathbf{X}_{c})$ and $\hat{\mu}_{i,(z

Figures (2)

  • Figure 1: Illustration of our setting under heterogeneous partial interference. In Figure \ref{['fig:family']}, each household consists of two exchangeable subsets (see Section \ref{['subsec:exchangeability']}): parents and children, so that interference from units within each subset is homogeneous (denoted by links with the same color). In Figure \ref{['fig:village']}, each village consists of leaders/influencers and villagers, and interference depends on the social status of a person in the village. Homogeneous interference among villagers is indicated by the blue-shaded ring. We allow for varying cluster sizes in extensions.
  • Figure A.1: Illustration of the extension with varying cluster sizes (Figure \ref{['subfig:varying-cluster-size']}, see Section \ref{['sec:varying-cluster-size']}) and the extension with arbitrary cluster structures (Figure \ref{['subfig:arbitrary']}, see Section \ref{['subsection:general-cluster-structure']}). Now each family consists of heterosexual parents and a variable number of children. For Figure \ref{['subfig:arbitrary']}, family members may not be fully connected.

Theorems & Definitions (18)

  • Remark 1: Aggregate Estimands
  • Remark 2: Alternative Estimators
  • Theorem \oldthetheorem: Consistency, ADE
  • Theorem \oldthetheorem: Asymptotic Normality and Semiparametric Efficiency, ADE
  • Remark 3: Conditional Independence
  • Remark 4: Heterogeneous Interference
  • Lemma 1
  • Proposition 1: Oracle AIPW Estimator
  • Theorem \oldthetheorem: Asymptotic Normality, General Estimand
  • Corollary 1: Asymptotic Normality, ASE
  • ...and 8 more