Randomization-based inference for Bernoulli trial experiments and implications for observational studies.

Area of Science:

• Statistics
• Experimental Design
• Causal Inference

Background:

• Randomization tests typically assume equal treatment probabilities within blocks.
• Existing methods often require additional modeling or asymptotic assumptions.

Purpose of the Study:

• To develop a general randomization-based inferential framework for experiments with independent treatment probabilities.
• To provide methods for point estimates, confidence intervals, and conditional inference.
• To offer a minimal-assumption approach applicable to observational studies.

Main Methods:

• Developed a randomization-based inferential framework for independent treatment probabilities.
• Introduced rejection-sampling and importance-sampling for conditional inference.
• Established the validity of the proposed randomization tests.

Main Results:

• The framework allows for valid randomization tests and precise inference.
• Rejection-sampling and importance-sampling yield powerful tests.
• The approach requires only the strongly ignorable assignment mechanism assumption.

Conclusions:

• The proposed framework extends randomization tests to a more general setting.
• It offers a robust and minimal-assumption alternative for experimental and observational studies.
• Enables precise causal inference with fewer restrictive assumptions.