Application of prediction intervals to the interpretation of analytical methods robustness studies

Since the emergence of the Analytical Quality by Design concept and the announcement of the future ICH Q14 "Analytical Procedure Development" guideline [1], a significant revival of the interest of the laboratories for the robustness study of their methods can be seen. Design of Experiments is a well-established tool used for this task, because of its ability to study the individual effect of a great number of factors in a minimal number of experiments. However, when assessing the robustness of an analytical method the analysis of the individual effect of each factor is not sufficient on its own. Indeed, the role of this study is also to verify, regardless of the very significance of the factors, that the chosen variations of the operating parameters of the method do not modify the experimental variance measured under the operating conditions for which the parameters are strictly defined. We therefore propose, in addition to the analysis of the individuals effects of the factors, an original tool which makes it possible to verify that the studied factors, when they vary together, do not lead to a significant variation in the measured responses. This tool is based on the prediction interval of the matrix experimental results, for each of the studied responses. This concept of prediction interval is already used in the context of analytical methods accuracy study. In a robustness design of experiments, it can represent the interval in which should be found, with a given probability, the response value if complementary experiments are conducted. It therefore represents the variation induced simultaneously by the different factors and can be easily compared to a maximum acceptable deviation of the considered response. We will detail this proposal and illustrate it with an example from a robustness study carried out on a liquid chromatography assay method.