Diagnosing and responding to violations in the positivity assumption

Statistical Methods in Medical Research - Tập 21 Số 1 - Trang 31-54 - 2012
Maya Petersen1, Kristin E. Porter1, Susan Gruber1, Yue Wang2, Mark J. van der Laan1
1Division of Biostatistics, University of California, Berkeley, CA 94110-7358, USA.
2Department of Clinical Information Services, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA.

Tóm tắt

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.

Từ khóa


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Thông tin xuất bản

Statistical Methods in Medical Research

Tập 21 Số 1

31-54

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