Modeling Interference Via Symmetric Treatment Decomposition

Classical causal inference assumes a treatment meant for a given unit does not have an effect on other units. When this "no interference" assumption is violated, new types of spillover causal effects arise, and causal inference becomes much more difficult. In addition, interference introduces a unique complication where outcomes may transmit treatment influences to each other, which is a relationship that has some features of a causal one, but is symmetric. In settings where detailed temporal information on outcomes is not available, addressing this complication using statistical inference methods based on Directed Acyclic Graphs (DAGs) (Ogburn & VanderWeele, 2014) leads to conceptual difficulties. In this paper, we develop a new approach to decomposing the spillover effect into direct (also known as the contagion effect) and indirect (also known as the infectiousness effect) components that extends the DAG based treatment decomposition approach to mediation found in (Robins & Richardson, 2010) to causal chain graph models (Lauritzen & Richardson, 2002). We show that when these components of the spillover effect are identified in these models, they have an identifying functional, which we call the symmetric mediation formula, that generalizes the mediation formula in DAGs (Pearl, 2011). We further show that, unlike assumptions in classical mediation analysis, an assumption permitting identification in our setting leads to restrictions on the observed data law, making the assumption empirically falsifiable. Finally, we discuss statistical inference for the components of the spillover effect in the special case of two interacting outcomes, and discuss a maximum likelihood estimator, and a doubly robust estimator.

[1]  Tyler J VanderWeele,et al.  On causal inference in the presence of interference , 2012, Statistical methods in medical research.

[2]  Judea Pearl,et al.  Identification of Conditional Interventional Distributions , 2006, UAI.

[3]  Jin Tian,et al.  On the Testable Implications of Causal Models with Hidden Variables , 2002, UAI.

[4]  Peter Spirtes,et al.  Directed Cyclic Graphical Representations of Feedback Models , 1995, UAI.

[5]  Judea Pearl,et al.  Identification of Joint Interventional Distributions in Recursive Semi-Markovian Causal Models , 2006, AAAI.

[6]  J. Robins,et al.  Alternative Graphical Causal Models and the Identification of Direct E!ects , 2010 .

[7]  Hua Yun Chen.  A semiparametric odds ratio model for measuring association. , 2007 .

[8]  M. Halloran,et al.  Causal Inference in Infectious Diseases , 1995, Epidemiology.

[9]  T. Richardson.  Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality , 2013 .

[10]  D. A. Kenny,et al.  The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. , 1986, Journal of personality and social psychology.

[11]  D. Annis.  Dyadic Data Analysis , 2007 .

[12]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[13]  J. Pearl.  The Causal Mediation Formula—A Guide to the Assessment of Pathways and Mechanisms , 2012, Prevention Science.

[14]  J. Robins.  A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[15]  P. Shrout,et al.  Causality and Psychopathology: Finding the Determinants of Disorders and their Cures , 2010 .

[16]  Michael E. Sobel,et al.  What Do Randomized Studies of Housing Mobility Demonstrate? , 2006 .

[17]  Jeffrey M. Wooldridge,et al.  Introductory Econometrics: A Modern Approach , 1999 .

[18]  J. Robins,et al.  Identifiability and Exchangeability for Direct and Indirect Effects , 1992, Epidemiology.

[19]  T. VanderWeele,et al.  Components of the indirect effect in vaccine trials: identification of contagion and infectiousness effects. , 2012, Epidemiology.

[20]  Hua Yun Chen.  A Semiparametric Odds Ratio Model for Measuring Association , 2007, Biometrics.

[21]  Judea Pearl,et al.  Direct and Indirect Effects , 2001, UAI.

[22]  Elizabeth L. Ogburn,et al.  Causal diagrams for interference , 2014, 1403.1239.