Accurate interval estimation for the risk difference in an incomplete correlated 2 × 2 table: Calf immunity analysis

Area of Science:

• Biostatistics
• Statistical Inference
• Correlated Data Analysis

Background:

• Accurate interval estimation for risk difference (RD) in correlated 2x2 tables with structural zero is crucial.
• Existing methods like score test-based and Bayesian tail-based confidence intervals (CIs) show limitations in coverage probability for finite and moderate sample sizes.

Purpose of the Study:

• To propose novel confidence intervals (CIs) for risk difference (RD) estimation.
• To evaluate the performance of new CIs based on fiducial, inferential model (IM), and modified IM (MIM) methods.

Main Methods:

• Development of three new CIs for RD: fiducial, IM, and MIM.
• Theoretical validation of the IM interval.
• Simulation studies to compare coverage probability and expected length of the proposed CIs against existing methods.

Main Results:

• The IM interval is theoretically proven to be valid.
• Fiducial and MIM CIs demonstrate the ability to maintain preset coverage rates, even with small sample sizes.
• The MIM interval exhibits superior performance over other methods regarding both coverage probability and expected length.

Conclusions:

• The proposed fiducial and MIM CIs offer accurate interval estimation for risk difference, particularly in challenging scenarios with small sample sizes.
• The MIM method is recommended as the optimal approach for constructing confidence intervals for risk difference due to its superior performance characteristics.