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Sample size determination for studies designed to estimate covariate‐dependent reference quantile curves
Author(s) -
JennenSteinmetz Christine
Publication year - 2013
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6024
Subject(s) - covariate , quantile , quantile regression , statistics , mathematics , sample size determination , parametric statistics , range (aeronautics) , coverage probability , nonparametric statistics , econometrics , sample (material) , confidence interval , materials science , chemistry , chromatography , composite material
Accuracy and sample size issues concerning the estimation of covariate‐dependent quantile curves are considered. It is proposed to measure the precision of an estimate of the p th quantile at a given covariate value by the probability with which this estimate lies between the p 1 th and p 2 th quantile, where p 1 < p < p 2 . Requiring that this probability exceeds a given confidence bound for all covariate values in a specified range leads to a sample size criterion. Approximate formulae for the precision and sample size are derived for the normal parametric regression approach and for the semiparametric quantile regression method. A simulation study is performed to evaluate the accuracy of the approximations. Numerical evaluations show that rather large numbers of subjects are needed to construct quantile curves with a reasonable amount of accuracy, especially if the quantile regression method is applied. Copyright © 2013 John Wiley & Sons, Ltd.