Bootstrap-based tolerance intervals for application to method validation

Recently a new validation procedure was developed using a graphical statistical tool – the so-called accuracy profile – that makes interpretation of results easy and straightforward. Accuracy profiles are estimated by tolerance intervals. Most existing methods for constructing tolerance limits are confined to the restrictive case of normally distributed data. The present study is focused on a nonparametric approach based on bootstrap — in order to get out of this constraint. The Mathematical section recalls some definitions and presents the derivation of the new nonparametric bootstrap approach for setting two-sided mean coverage and guaranteed coverage tolerance limits for a balanced one-way random effects model. The section concludes with a simulation study assessing the performance of the bootstrap methods in comparison to classical methods. Finally, the applicability of the proposed intervals is demonstrated by application to the problem of quantitative analytical method validation based on the accuracy profile. This approach is illustrated by an example consisting in the HPLC determination of the vitamers of vitamin B3 (nicotinamide and nicotinic acid) in milk. The efficiency of the new tolerance intervals is demonstrated as well as the applicability of accuracy profiles in the delicate situation where a correction factor must be applied because there is not a full recovery of the analyte. The comparison of the various tolerance intervals also gives some indication on their interpretation.