Instruments and bounds for causal effects under the monotonic selection assumption.

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Causal Inference

Background:

• Noncompliance with assigned treatment is a significant challenge in randomized clinical trials.
• Existing methods like structural mean models (SMM) and principal stratification (PS) address different causal estimands.

Purpose of the Study:

• To clarify the relationship between SMM and PS under monotonic selection.
• To propose a new, potentially more plausible assumption for bounding the average treatment effect among the treated (ATT).
• To extend these findings to the average treatment effect for the entire population.

Main Methods:

• Translating the no effect modification (NEM) assumption of SMM into the PS framework.
• Developing a new bound for ATT based on a refined assumption within the PS approach.
• Applying the proposed methods to real clinical trial data.

Main Results:

• The study establishes a clear relationship between SMM and PS under monotonic selection.
• A new bound for ATT is proposed, offering potentially tighter estimates than previous methods.
• The proposed bounds demonstrate improved precision when applied to a real clinical trial dataset.

Conclusions:

• The proposed approach provides a valuable refinement for causal inference in the presence of treatment noncompliance.
• The new bounds offer a practical tool for estimating treatment effects more accurately in clinical trials.
• Further research could explore empirical verification of the proposed assumptions.