Sample size determination for studies designed to estimate covariate-dependent reference quantile curves

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 pth quantile at a given covariate value by the probability with which this estimate lies between the p1 th and p2 th quantile, where p1 < p < p2 . 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.