Diagnosing and responding to violations in the positivity assumption
Open accessAbstract
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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The impact of the absence of current smokers and women with no prior vaginal birth in the UP group was assessed through sensitivity analyses demonstrating robustness of results.
“was assessed for its impact through sensitivity analyses demonstrating robustness of results.53”
From Hysterectomy versus uterine preservation for pelvic organ prolapse surgery: a prospective cohort study (2025) · cites this paper as [53]
Section 5.2 (page unavailable) examines bootstrap diagnostics in an HIV resistance-mutation analysis, not an UP group. Searches for current smokers, prior vaginal birth, and sensitivity analyses found no passage assessing those absences or demonstrating robustness of the cited results. (LLM, conf=0.78)
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- Authors
- Petersen, M. L., Porter, K. E., Gruber, S., Wang, Y., & van der Laan, M. J.
- Affiliations
- University of California, Berkeley (US)
- Novartis (United States) (US)
- Division of Biostatistics, University of California, Berkeley, CA 94110-7358, USA.
- Corresponding author
- Petersen, Maya L
- Venue
- Statistical Methods in Medical Research
- Publisher
- SAGE Publications
- Published
- 2010-10-28
- Volume
- 21
- Issue
- 1
- Pages
- 31-54
- ISSN
- 0962-2802 (ISSN-L)
- 1477-0334
- PMC
- PMC4107929
- OpenAlex
- W2155169076
- Cited by
- 548
- References
- 45
- Citations by year
- 2026: 52 · 2025: 54 · 2024: 58 · 2023: 51 · 2022: 62 · 2021: 41 · 2020: 51 · 2019: 36 · 2018: 26 · 2017: 18 · 2016: 26 · 2015: 16 · 2014: 24 · 2013: 14 · 2012: 9
- FWCI
- 8.99
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Statistical Methods in Medical Research (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Collection of Biostatistics Research Archive (submittedVersion)
- Funders
- National Institute of Allergy and Infectious Diseases (R01AI074345)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- positivity assumption, positivity violation, data sparsity, parametric bootstrap, marginal structural models, projection functions, bias-variance trade-off
- MeSH terms
- Computer Simulation, Data Interpretation, Statistical, Humans, Mutation, Models, Statistical, Cohort Studies, HIV Infections, Bias, Confounding Factors, Epidemiologic, Treatment Outcome, Anti-HIV Agents, Drug Resistance, Viral, Biomedical Research, Lopinavir
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