Nonparametric limits of agreement in method comparison studies: A simulation study on extreme quantile estimation

Abstract

Bland–Altman limits of agreement and the underlying plot are a well-established means in method comparison studies on quantitative outcomes. Normally distributed paired differences, a constant bias, and variance homogeneity across the measurement range are implicit assumptions to this end. Whenever these assumptions are not fully met and cannot be remedied by an appropriate transformation of the data or the application of a regression approach, the 2.5% and 97.5% quantiles of the differences have to be estimated nonparametrically. Earlier, a simple Sample Quantile (SQ) estimator (a weighted average of the observations closest to the target quantile), the Harrell–Davis estimator (HD), and estimators of the Sfakianakis–Verginis type (SV) outperformed 10 other quantile estimators in terms of mean coverage for the next observation in a simulation study, based on sample sizes between 30 and 150. Here, we investigate the variability of the coverage probability of these three and another three promising nonparametric quantile estimators with n = 50(50)200, 250(250)1000. The SQ estimator outperformed the HD and SV estimators for n = 50 and was slightly better for n = 100, whereas the SQ, HD, and SV estimators performed identically well for n ≥ 150. The similarity of the boxplots for the SQ estimator across both distributions and sample sizes was striking.