Comparing causal parameters with many treatments and positivity violations

Area of Science:

• Causal inference
• Statistical modeling
• Health services research

Background:

• Comparing treatment outcomes is crucial for medicine and policy.
• Standard methods often rely on the positivity assumption, which is frequently violated with multi-value treatments.
• Existing causal parameters may not accurately reflect target treatment effects when positivity fails.

Purpose of the Study:

• To establish a criterion for when causal parameters allow meaningful comparisons of treatment efficacy.
• To identify parameters that satisfy this criterion under weaker assumptions.
• To develop robust estimators for these parameters in complex treatment settings.

Main Methods:

• Proposed a comparability criterion based on the relationship between conditional treatment-specific means.
• Identified parameters satisfying this criterion under a mild positivity assumption.
• Developed doubly robust-style estimators for smooth-trimmed treatment-specific means achieving parametric rates.

Main Results:

• Demonstrated that many standard causal parameters do not satisfy the proposed comparability criterion.
• Showed that trimmed and smooth-trimmed means satisfy the criterion and are identifiable under mild positivity.
• Illustrated the methods using data from New York State dialysis providers.

Conclusions:

• The proposed comparability criterion ensures that causal parameter comparisons reflect true treatment efficacy.
• Trimmed and smooth-trimmed means offer robust and identifiable comparisons for multivalued treatments.
• The developed estimators provide efficient and reliable tools for analyzing complex treatment effects in real-world data.