Diagnosing and responding to violations in the positivity assumption

Area of Science:

• Causal inference
• Epidemiology
• Biostatistics

Background:

• The positivity assumption, also known as experimental treatment assignment, is fundamental for estimating causal effects.
• Violations occur when specific subgroups rarely or never receive certain treatments, leading to data sparsity.

Purpose of the Study:

• To discuss the positivity assumption and its impact on model and parameter identifiability in causal effect assessment.
• To explore the utility of the parametric bootstrap as a diagnostic tool for positivity violations.
• To review strategies for enhancing parameter identifiability when positivity is violated.

Main Methods:

• Discussed the implications of positivity violations on bias and variance in causal effect estimation.
• Utilized simulated and real-world data to evaluate the parametric bootstrap for diagnosing data sparsity.
• Reviewed methods to improve parameter identifiability, including covariate adjustment set restriction and target parameter modification.

Main Results:

• Positivity violations can significantly threaten the validity of causal inference by increasing bias.
• The parametric bootstrap serves as a useful diagnostic tool to assess the severity of positivity violations.
• Several strategies exist to improve identifiability, each involving a systematic trade-off between inference proximity and identifiability.

Conclusions:

• Addressing positivity violations is critical for robust causal effect estimation.
• The parametric bootstrap offers a practical approach to identify and quantify the impact of these violations.
• Systematic evaluation of trade-offs is recommended when implementing strategies to enhance identifiability in sparse data settings.