Likelihood-based inference for bounds of causal parameters.

Area of Science:

• Causal inference
• Statistical modeling
• Biostatistics

Background:

• Causal inference often yields parameter bounds instead of precise estimates, even with ample data.
• This limitation affects areas like risk factor interaction and instrumental variable analysis.

Purpose of the Study:

• To develop a novel likelihood-based procedure for estimating causal parameters and confidence intervals.
• To address limitations of current methods like linear programming and bootstrapping in non-regular likelihood scenarios.

Main Methods:

• A likelihood-based procedure is proposed to derive interval estimates from flat likelihood regions.
• Theoretical framework is presented for constructing confidence intervals from non-regular likelihoods.

Main Results:

• The new method automatically yields interval estimates.
• Demonstrated application in estimating causal interaction and treatment effects under partial compliance.

Conclusions:

• The likelihood-based procedure offers an effective approach for causal inference with non-regular likelihoods.
• Provides a robust method for obtaining confidence intervals in challenging causal estimation problems.