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During drug discovery, compounds/biologics are screened against biological targets of interest to find drug candidates with the most desirable activity profile. The compounds are tested at multiple concentrations to understand the dose-response relationship, often summarized as AC50 values and used directly in ranking compounds. Differences between compound repeats are inevitable because of experimental noise and/or systematic error; however, it is often desired to detect the latter when it occurs. To address this, the β-expectation tolerance interval is proposed in this article. Besides the classical acceptance criteria on assay performance, based on control compounds (e.g., quality control samples), this metric permits us to compare new estimates against historical estimates of the same study compound. It provides a measure that detects whether observed differences are likely due to systematic error. The challenge here is that limited information is available to build such compound-specific acceptance limits. To this end, we propose the use of Bayesian β-expectation tolerance intervals to validate agreement between replicate potency estimates for individual study compounds. This approach allows the variability of the compound-testing process to be estimated from reference compounds within the assay and used as prior knowledge in the computation of compound-specific intervals as from the first repeat of the compound and then continuously updated as more information is acquired with subsequent repeats. A repeat is then flagged when it is not within limits. Unlike a fixed threshold such as 0.5log, which is often used in practice, this approach identifies unexpected deviations on each compound repeat given the observed variability of the assay.

The concept of quality by design (QbD) as published in ICH-Q8 is currently one of the most recurrent topics in the pharmaceutical literature. This guideline recommends the use of information and prior knowledge gathered during pharmaceutical development studies to provide a scientific rationale for the manufacturing process of a product and provide guarantee of future quality. This poses several challenges from a statistical standpoint and requires a shift in paradigm from traditional statistical practices. First, to provide "assurance of quality" of future lots implies the need to make predictions regarding the quality given past evidence and data. Second, the quality attributes described in the Q8 guidelines are not always a set of unique, independent measurements. In many cases, these criteria are complicated longitudinal data with successive acceptance criteria over a defined period of time. A common example is a dissolution profile for a modified or extended-release solid dosage form that must fall within acceptance limits at several time points. A Bayesian approach for longitudinal data obtained in various conditions of a design of experiment is provided to elegantly address the ICH-Q8 recommendation to provide assurance of quality and derive a scientifically sound design space.

Since the adoption of the ICH Q8 document concerning the development of pharmaceutical processes following a quality by design (QbD) approach, there have been many discussions on the opportunity for analytical procedure developments to follow a similar approach. While development and optimization of analytical procedure following QbD principles have been largely discussed and described, the place of analytical procedure validation in this framework has not been clarified. This article aims at showing that analytical procedure validation is fully integrated into the QbD paradigm and is an essential step in developing analytical procedures that are effectively fit for purpose. Adequate statistical methodologies have also their role to play: such as design of experiments, statistical modeling, and probabilistic statements. The outcome of analytical procedure validation is also an analytical procedure design space, and from it, control strategy can be set.