Principal stratification for quantile causal effects under partial compliance.

Area of Science:

• Causal Inference
• Statistical Modeling

Background:

• Principal stratification framework typically assumes binary compliance.
• Partial compliance presents identifiability challenges in causal effect estimation.
• Research often requires understanding causal effects on quantiles, not just means.

Purpose of the Study:

• To develop an approach for estimating quantile causal effects under partial compliance within principal stratification.
• To address the challenge of non-identifiability in modeling partial compliance.
• To estimate the principal quantile treatment effect surface at high quantiles.

Main Methods:

• Utilized a conditional copula approach to impute missing potential compliance.
• Defined principal strata by the bivariate vector of partial compliance to a binary intervention.
• Employed a bootstrap procedure to estimate parameters and account for imputation inflation.
• Allowed the copula association parameter to vary with covariates.

Main Results:

• Developed a method to estimate principal quantile treatment effects with partial compliance.
• Demonstrated the approach's ability to handle high quantiles.
• Investigated finite sample behavior via simulation studies.
• Applied the method to analyze COVID-19 transmission risk and stay-at-home orders.

Conclusions:

• The proposed conditional copula approach effectively estimates quantile causal effects in the presence of partial compliance.
• This method extends causal inference capabilities to scenarios with complex compliance patterns and quantile-based research questions.
• The study provides a robust framework for analyzing real-world interventions with non-binary compliance, such as public health policies.