Diagnosing and responding to violations in the positivity assumption

By M. Petersen, Kristin E. Porter, Susan Gruber, Yue Wang, M. J. van der Laan. Statistical Methods in Medical Research, 2010

603 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/988b394472b7f3a7ce55f6d534f4ed38df61325e

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Citations in the corpus

Overlap in observational studies with high-dimensional covariates (2017, background): “This motivates the common practice of trimming, where the investigator drops observations in regions without overlap (Rosenbaum & Rubin, 1983; Petersen et al., 2012).”
Causal machine learning for predicting treatment outcomes (2024, neutral): “The propensity score is the probability of receiving the treatment given the observed specific patient characteristics.”
Comparison of Approaches to Weight Truncation for Marginal Structural Cox Models (2013, methodology): “Petersen et al. (2012) systematically reviewed alternative approaches to deal with the positivity violation and pointed out that most of these approaches represent some trade-off between unbiasedness and proximity to the initial target of inference.”
Using Big Data to Emulate a Target Trial When a Randomized Trial Is Not Available. (2016, background): “The specification of the protocol of the target trial will typically be an iterative process during which wewill learn which particular target trials may be reasonably supported by the observational data (55).”
Precision Medicine. (2019, background): “These assumptions are standard (Kidwell 2016) though they are not as general as possible (Robins et al 2000; Petersen et al 2012).”
Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores (2018, methodology): “Petersen et al. (2012) used a projection function to define the target parameter within a marginal structural working model.”
Semiparametric theory and empirical processes in causal inference (2015, background): “Condition (C3) is called “positivity” and means treatment i s not assigned deterministically [33].”
A Survey on Causal Inference (2020, methodology): “Based on the above implication, methods that eliminate the information about the treatment assignment while still hold the unconfounderness assumption are recommended, such as trimming [36, 110, 122] that drops the records in the region without overlap, and instrumental variable adjustment methods [”