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Unpublished Paper
Diagnosing and Responding to Violations in the Positivity Assumption
U.C. Berkeley Division of Biostatistics Working Paper Series
  • Maya L. Petersen, University of California - Berkeley
  • Kristin Porter, University of California, Berkeley
  • Susan Gruber, University of California, Berkeley
  • Yue Wang, Department of Clinical Information Services, Novartis Pharmaceuticals Corporation
  • Mark J. van der Laan, University of California - Berkeley
Date of this Version

The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative pro jection function to define the target parameter within a non-parametric marginal structural model, restriction of the sample, and modification of the target intervention. All of these approaches can be understood as trading off proximity to the initial target of inference for identifiability; we advocate approaching this tradeoff systematically.

Citation Information
Maya L. Petersen, Kristin Porter, Susan Gruber, Yue Wang, et al.. "Diagnosing and Responding to Violations in the Positivity Assumption" (2010)
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