Nonparametric Limits of Agreement in Method Comparison Studies: A Simulation Study on Extreme Quantile Estimation

Area of Science:

• Biostatistics
• Statistical Methods

Background:

• Bland-Altman analysis is standard for quantitative method comparison studies.
• Assumptions include normally distributed differences, constant bias, and homogeneous variance.
• Nonparametric quantile estimation is needed when assumptions are violated.

Purpose of the Study:

• To evaluate the coverage probability variability of nonparametric quantile estimators.
• To compare the performance of Sample Quantile (SQ), Harrell-Davis (HD), and Sfakianakis-Verginis (SV) estimators.

Main Methods:

• Simulation study investigating nonparametric quantile estimators.
• Sample sizes ranged from 50 to 1000.
• Evaluated coverage probability and estimator performance.

Main Results:

• The SQ estimator outperformed HD and SV for sample sizes of 50 and 100.
• SQ, HD, and SV estimators performed comparably for sample sizes of 150 and above.
• SQ estimator showed consistent performance across distributions and sample sizes.

Conclusions:

• The Sample Quantile estimator is a robust choice for nonparametric quantile estimation in method comparison studies.
• Performance of SQ, HD, and SV estimators converges with increasing sample size.
• Nonparametric methods provide reliable alternatives when Bland-Altman assumptions are not met.