Two-Sided Tolerance Intervals for Balanced and Unbalanced Random Effects Models

Abstract

A procedure for constructing two-sided beta-content, gamma-confidence tolerance intervals is proposed for general random effects models, in both balanced and unbalanced data scenarios. The proposed intervals are based on the concept of effective sample size and modified large sample methods for constructing confidence bounds on functions of variance components. The performance of the proposed intervals is evaluated via simulation techniques. The results indicate that the proposed intervals generally maintain the nominal confidence and content levels. Application of the proposed procedure is illustrated with a one-fold nested design used to evaluate the performance of a quantitative bioanalytical method.

Surgical inaccuracy of tumor resection and reconstruction within the pelvis: An experimental study

“…The 95% confidence interval (CI) of the probability was calculated using the delta method (Hoffman and Kringle 2005). The variance of the probability was computed from the variance of µ and the variance of X by using partial derivatives of the probability.…”

Pre‐study analytical method validation: comparison of four alternative approaches based on quality‐level estimation and tolerance intervals

“…This idea has already been introduced in the framework of method validation 1,3,4 . These authors propose the -expectation and the -content confidence intervals as possible solutions.…”

“…The values of k E and k C depend on the experimental design used for validation and cannot be derived exactly if the design is more complicated than a simple sampling scheme. From 3,7,11,12 it can be shown that, for the general variance-component model, k E and k C can be approximated by…”

“…The method-validation procedures presented in this paper, and already partially available in the literature 1,3,4 , aim at improving these 'classical' approaches by directly focusing on the validation principles described in Section 2.1.…”

“…These methods are not all new; some have already been introduced, for example, in 1,3,4 . However, this paper presents those methods in a common framework, generalizes former results to very general validation experimental designs and variance-components models, and compares them on a case study and through simulations.…”