Diagnosing and responding to violations in the positivity assumption

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...

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Bibliographic Details
Published in:Statistical methods in medical research Vol. 21; no. 1; pp. 31 - 54
Main Authors: Petersen, Maya L, Porter, Kristin E, Gruber, Susan, Wang, Yue, van der Laan, Mark J
Format: Journal Article
Language:English
Published: London, England SAGE Publications 01.02.2012
Sage Publications Ltd
Subjects:
Anti-HIV Agents - therapeutic use
Bias
Biomedical Research - statistics & numerical data
Cohort Studies
Computer Simulation - statistics & numerical data
Confounding Factors, Epidemiologic
Data
Data Interpretation, Statistical
Drug Resistance, Viral
HIV Infections - drug therapy
HIV Infections - genetics
Humans
Inference
Lopinavir - therapeutic use
Models, Statistical
Modification
Mutation
Parameters
Positive affect
Proximity
Trading
Treatment methods
Treatment Outcome
Violations
Working models
realistic treatment rule
positivity
stabilised weights
double robust
parametric bootstrap
trimming
counterfactual
experimental treatment assignment
marginal structural model
inverse probability weight
causal inference
truncation
ISSN:0962-2802, 1477-0334, 1477-0334
Online Access:Get full text
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Summary: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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ISSN:0962-2802
1477-0334
1477-0334
DOI:10.1177/0962280210386207