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Journal of Causal Inference

Ed. by Imai, Kosuke / Pearl, Judea / Petersen, Maya Liv / Sekhon, Jasjeet / van der Laan, Mark J.

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A Simple Model Allowing Modification of the Effect of a Randomized Intervention by Post-Randomization Variables

Jennifer A. Faerber
  • Children’s Hospital of Philadelphia, 3535 Market Street, 15th floor, Philadelphia, PA 19104, USA
  • Roberts Center for Pediatric Research, 2716 South Street, Philadelphia, PA 19146, USA
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/ Marshall M. Joffe
  • Corresponding author
  • Department of Biostatistics and Epidemiology, Perlman School of Medicine, University of Pennsylvania, Blockley Hall, 6th floor 423 Guardian Drive, Philadelphia, PA 19104, USA
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/ Dylan S. Small
  • Department of Statistics, The Wharton School, University of Pennsylvania,400 Huntsman Hall, Philadelphia, PA 19104, USA
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/ Rongmei Zhang / Gregory K. Brown
  • Department of Psychiatry, Perlman School of Medicine, University of Pennsylvania; 3535 Market Street, Philadelphia, PA 19104, USA
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/ Thomas R. Ten Have
  • Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA 19104, USA
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Published Online: 2017-05-04 | DOI: https://doi.org/10.1515/jci-2015-0016


We address several questions relating to the use of standard regression and Structural Nested Mean Model (SNMM) approach (e. g., Ten Have et al. 2007) to analyze post-randomization effect modifiers of the intent-to-treat effect of a randomized intervention on a subsequent outcome, which has not been well examined. We show through simulations that the SNMM performs better with respect to bias of estimates of the intervention and interaction effects than does the corresponding standard interaction approach when the baseline intervention is randomized and the post-randomization factors are subject to confounding, and even when there is no association between the intervention and effect modifier. However, causal inference under the SNMM makes untestable assumptions that the causal contrasts do not vary across observed levels of the intervention and post-randomization factor. In addition, the precision of the SNMM-based estimators depends on the effect of the randomized intervention on the post-randomization factor varying across baseline covariate combinations. These issues and methods are illustrated with the application of the standard and causal methods to a randomized cognitive therapy (CT) trial, for which there is a conceptual model of negative cognitive styles or distortions impacted by CT but then in turn modifying the effect of CT on subsequent suicide ideation and social problem solving outcomes.

Keywords: cognitive therapy; depression; interaction; stratification


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About the article

Published Online: 2017-05-04

This research was supported in part by grants from the National Institute of Health including R01MH078016 Causal Methods for Mediation and Interaction and T32MH065218 “Mental Health Biostatistics training grant.”

Citation Information: Journal of Causal Inference, Volume 5, Issue 2, 20150016, ISSN (Online) 2193-3685, DOI: https://doi.org/10.1515/jci-2015-0016.

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