Sample size for confidence intervals for percentiles and application to cut-point determination

Area of Science:

• Statistics
• Biostatistics

Background:

• Percentiles are crucial statistical parameters.
• Accurate confidence intervals for percentiles require appropriate sample size determination.
• Existing methods for sample size calculation lack focus on over-coverage probability.

Purpose of the Study:

• To propose a new sample size determination approach for percentile confidence intervals.
• To derive sample size formulas for parametric and nonparametric methods.
• To apply the method to bioassay cut-point estimation.

Main Methods:

• Derivation of sample size formulas for two confidence interval methods under normal distribution.
• Proposal of an approximation method for nonparametric percentile estimation.
• Demonstration using a bioassay cut-point estimation application.

Main Results:

• Developed sample size formulas for percentile confidence intervals.
• The proposed method effectively determines sample size based on over-coverage probability.
• The approach is applicable to both parametric and nonparametric estimation.

Conclusions:

• The proposed sample size determination method enhances the precision of percentile confidence intervals.
• This approach is valuable for statistical applications, particularly in bioassay.
• Controlling over-coverage probability is key for reliable interval estimation.