Journal
STATISTICAL METHODS IN MEDICAL RESEARCH
Volume 21, Issue 1, Pages 31-54Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/0962280210386207
Keywords
experimental treatment assignment; positivity; marginal structural model; inverse probability weight; double robust; causal inference; counterfactual; parametric bootstrap; realistic treatment rule; trimming; stabilised weights; truncation
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Funding
- NIAID NIH HHS [R01 AI074345] Funding Source: Medline
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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 and real 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 projection function to define the target parameter within a marginal structural working 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.
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