Model-based inference on average causal effect in observational clustered data

  • Meng Wu
  • Recai M. YucelEmail author


We study causal inference using the framework of potential outcomes in clustered data settings where observational units are clustered in naturally occurring groups (e.g. patients within hospitals). To incorporate the correlated nature of the data, we employ mixed-effects models and a sandwich estimator to make inferences on the average causal effect (ACE). Our methods apply the concept of potential outcomes from the Rubin Causal Model (Holland in J Am Stat Assoc 81(396):945–960, 1986), and extend Schafer and Kang’s methods of estimating the variance of the ACE (Schafer and Kang in Psychol Methods 13(4):279–313, 2008). Particularly, we develop two model-based approaches to estimate the ACE and its variance under a dual-modeling strategy which adjusts for the confounding effect through inverse probability weighting. These two approaches use linear mixed-effects models for the estimation of potential outcomes, but differ in how clustering is handled in the treatment assignment model. We present a summary of our comprehensive simulation study assessing the repetitive sampling properties of the two approaches in a pseudo-random simulation environment. Finally, we report our findings from an application to study the ACE of inadequate prenatal care on birth weight among low-income women in New York State.


ACE Causal inference Clustered data Dual-modeling Linear mixed-effects model Potential outcomes Sandwich estimator 



The authors are grateful to the referees and Associate Editor whose reviews improved the manuscript significantly. The code used in the computations is available upon request from the authors.

Compliance with ethical standards

Human and animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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Authors and Affiliations

  1. 1.Department of Epidemiology and BiostatisticsUniversity at Albany, SUNYAlbanyUSA
  2. 2.Office of Quality and Patient SafetyNew York State Department of HealthAlbanyUSA
  3. 3.School of Public HealthState University of New York at AlbanyRensselaerUSA

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