A confidence interval for Pr(X < Y) - Pr(X > Y) estimated from simple cluster samples

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• Accurate statistical inference is crucial for comparing independent populations.
• Existing methods may not adequately address complex sampling designs or data censoring.

Purpose of the Study:

• To develop distribution-free confidence intervals for Pr(X < Y) - Pr(X > Y) using Somers' d.
• To accommodate complex sampling designs and progressive censoring in statistical analysis.

Main Methods:

• Utilized Somers' d, a function of the Mann-Whitney U statistic.
• Developed explicit formulas for simple cluster sampling.
• Incorporated methods for simple progressive left- and right-censoring.
• Applied the tanh-1 transform to enhance interval accuracy.

Main Results:

• The proposed confidence intervals effectively handle complex sampling and censoring.
• The tanh-1 transform significantly improved the accuracy of the confidence intervals.
• A bootstrap solution was evaluated but demonstrated inferior performance compared to the proposed method.

Conclusions:

• The developed distribution-free confidence intervals offer a robust method for comparing independent populations.
• The approach is particularly valuable when dealing with complex survey data and censored observations.
• The proposed method provides a more accurate and reliable alternative to bootstrap solutions.