Generalized Confidence Intervals for Intra- and Inter-subject Coefficients of Variation in Linear Mixed-effects Models

Linear mixed-effects models are linear models with several variance components. Models with a single random-effects factor have two variance components: the random-effects variance, i.e., the inter-subject variance, and the residual error variance, i.e., the intra-subject variance. In many applications, it is practice to report variance components as coefficients of variation. The intra- and inter-subject coefficients of variation are the square roots of the corresponding variances divided by the mean. This article proposes methods for computing confidence intervals for intra- and inter-subject coefficients of variation using generalized pivotal quantities. The methods are illustrated through two examples. In the first example, precision is assessed within and between runs in a bioanalytical method validation. In the second example, variation is estimated within and between main plots in an agricultural split-plot experiment. Coverage of generalized confidence intervals is investigated through simulation and shown to be close to the nominal value.