Randomization inference for treatment effects on a binary outcome.

Area of Science:

• Biostatistics
• Statistical Inference
• Causal Inference

Background:

• Standard confidence intervals for treatment effects often rely on asymptotic properties or population sampling assumptions.
• Existing methods may lack exactness or have unbounded width, limiting their reliability.

Purpose of the Study:

• To develop novel, exact, and nonparametric randomization-based confidence sets for the average treatment effect on a binary outcome.
• To compare the performance of these new methods against existing confidence intervals.

Main Methods:

• Developed two distinct nonparametric methods: one using Bonferroni-adjusted prediction sets and another by inverting a permutation test.
• Both methods construct confidence sets with guaranteed coverage probability of at least 1 - α and maximum width of one.

Main Results:

• The permutation test-based confidence set demonstrated the narrowest average width among methods maintaining nominal coverage for small to moderate sample sizes.
• The proposed randomization-based confidence sets are exact, unlike previously proposed asymptotic intervals which may not guarantee coverage or have excessive width.

Conclusions:

• Randomization-based confidence sets offer exact inference for treatment effects without requiring population sampling assumptions.
• The permutation-based method is recommended for its superior width performance while ensuring accurate coverage.