Stability analysis using mixed models: A critique of tolerance interval methods and a probabilistic solution.

Recently, tolerance interval approaches to the calculation of a shelf life of a drug product have been proposed in the literature. These address the belief that shelf life should be related to control of a certain proportion of batches being out of specification. We question the appropriateness of the tolerance interval approach. Our concerns relate to the computational challenges and practical interpretations of the method. We provide an alternative Bayesian approach, which directly controls the desired proportion of batches falling out of specification assuming a controlled manufacturing process. The approach has an intuitive interpretation and posterior distributions are straightforward to compute. If prior information on the fixed and random parameters is available, a Bayesian approach can provide additional benefits both to the company and the consumer. It also avoids many of the computational challenges with the tolerance interval methodology.

Bayesian statistical approaches to drug product variability assessment and release.

The determination of the variability of critical dosage form attributes has been a challenge in establishing the quality of pharmaceutical products. During the development process knowledge is minimal. Consequently, ad hoc statistical tools such as hypothesis or significance tests, with calibrated decision error rates are often used in an effort to vet CQAs (Critical Quality Attributes) and keep their levels "between the curbs". As progress moves towards product launch, process and mechanistic understanding grows considerably and there are opportunities to leverage that knowledge for predictive modeling. Bayesian models offer a coherent strategy for integrating prior knowledge into both experimental design as well as predictive analysis for optimal risk-based decision making. This is because the Bayesian paradigm, unlike the frequentist paradigm, can assign probabilities to underlying states of nature that directly impact safety and efficacy such as the population distribution of tablet potencies or dissolution profiles in a batch. However, there are challenges and reluctance in switching to a predictive modeling quality framework once regulatory approval has been attained. This paper offers encouragement to make this switch. In this paper, we review a joint Long Island University - Purdue University (LIU-PU) FDA funded project whose purpose was to further integrate the concepts of this adaptive approach to lot release with the rationale and methods for data generation and curation and to extend the testing of this approach. We discuss the utility of the approach in product development. We consider the regulatory compliance implications, with examples, and establish a potential way forward toward implementation of this approach for both industry and regulatory stake-holders.

DISSOLUTION PROFILE SIMILARITY ANALYSES-STATISTICAL PRINCIPLES, METHODS AND CONSIDERATIONS.

The pharmaceutical industry and regulatory agencies rely on dissolution similarity testing to make critical product decisions as part of drug product life cycle management. Accordingly, the application of mathematical approaches to evaluate dissolution profile similarity is described in regulatory guidance with the emphasis given to the similarity factor f2 with little discussion of alternative methods. In an effort to highlight current practices to assess dissolution profile similarity and to strive toward global harmonization, a workshop entitled "In Vitro Dissolution Similarity Assessment in Support of Drug Product Quality: What, How, When" was held on May 21-22, 2019 at the University of Maryland, Baltimore. This manuscript provides in-depth discussion of the mathematical principles of the model-independent statistical methods for dissolution profile similarity analyses presented in the workshop. Deeper understanding of the testing objective and statistical properties of the available statistical methods is essential to identify methods which are appropriate for application in practice. A decision tree is provided to aid in the selection of an appropriate statistical method based on the underlying characteristics of the drug product. Finally, the design of dissolution profile studies is addressed regarding analytical and statistical recommendations to sufficiently power the study. This includes a detailed discussion on evaluation of dissolution profile data for which several batches per reference and/or test product are available.

In Vitro Dissolution Profiles Similarity Assessment in Support of Drug Product Quality: What, How, When-Workshop Summary Report.

The pharmaceutical industry and regulatory agencies rely on dissolution similarity testing to make critical product performance decisions as part of drug product life cycle management. Accordingly, the application of mathematical approaches to evaluate dissolution profile similarity is described in regulatory guidance. However, the requirements (e.g., which time points, number of time points, %CV) to apply the widely known similarity factor f2 and other alternative statistical approaches diverge noticeably across regulatory agencies. In an effort to highlight current practices to assess dissolution profile similarity and to strive towards global harmonization, a workshop entitled "in vitro dissolution similarity assessment in support of drug product quality: what, how, when" was held May 21-22, 2019, at the University of Maryland, Baltimore. This article summarizes key points from the podium presentations and breakout (BO) sessions focusing on (1) contrasting the advantages and disadvantages of several statistical methods; (2) the importance of experimental design for successful similarity evaluation; (3) the value of similarity evaluation in light of clinically relevant specifications; and (4) the need for creating a robust and scientifically appropriate path (e.g., non-prescriptive decision tree) for dissolution profile similarity assessment as a stepping stone for global harmonization.

Risk-Based Approach to Lot Release.

In this work, a novel risk-based methodology for lot release is proposed. Its objective is to assess the risk that a lot declared to have passed truly meets product specifications. The methodology consists of 3 parts: adaptive sample size determination, estimation of the probability that the product was within specifications, and the lot-release decision. The methodology provides a probabilistic statement about the true quality of the batch. Having a probability estimate is the essential condition of risk-based decision-making. We demonstrate the proposed methodology on experimental data generated from 17 immediate-release solid oral drug products from a number of different manufacturers with 5 to 10 lots per manufacturer.

Simple Approach to Calculate Random Effects Model Tolerance Intervals to Set Release and Shelf-Life Specification Limits of Pharmaceutical Products.

Tolerance intervals are used to statistically derive the acceptance limits to which drugs must conform upon manufacture (release) and throughout shelf-life. The single measurement per lot in release data and repeated measurements per lot longitudinally for stability data have to be considered in the calculation. Methods for the one-way random effects model by Hoffman and Kringle (HK) for two-sided intervals and Hoffman (H) for one-sided limits are extended to a random-intercept, fixed-slope model in this paper. The performance of HK and H was evaluated via simulation by varying the following factors: (a) magnitude of stability trend over time, (b) sample size, (c) percentage of lot-to-lot contribution to total variation, (d) targeted proportion, and (e) data inclusion. The performance metrics are average width (for two-sided) or average limit (for one-sided) and attained confidence level. HK and H maintained nominal confidence levels as originally developed, but H is too conservative (i.e., achieved confidence level exceeds the nominal level) in some situations. The HK method adapted for an attribute that changes over time performed comparably to the more computationally intensive generalized pivotal quantity and Bayesian posterior predictive methods. Mathematical formulas and example calculations as implemented using R statistical software functions are provided to assist practitioners in implementing the methods. The calculations for the proposed approach can also be easily performed in a spreadsheet given basic regression output from a statistical software package. Microsoft Excel spreadsheets are available from the authors upon request.LAY ABSTRACT: Tolerance intervals (a measure of what can be expected from the manufacturing process) calculated from attribute measurements of drug product lots are one of the factors considered when establishing acceptance limits to ensure drug product quality. The methods often used to calculate tolerance intervals when there are multiple measurements per lot and the attribute changes over time are either lacking in statistical rigor or statistically rigorous but computationally intensive to implement. The latter type requires simulations that have to be programmed using specialized statistical software, because closed-form mathematical formulas are not available. As a consequence, some quality practitioners and applied statisticians involved in setting acceptance limits may be hindered in using such computationally intensive methods. This paper aims to address this need by proposing an approach that is statistically rigorous yet simple enough to implement using spreadsheets. The approach builds upon previously published works developed for attributes that do not change over time and adapts the cited works for attributes that change over time. The proposed approach is demonstrated to have good statistical properties and compares favorably against the more computationally intensive alternative methods. The paper provides closed-form mathematical formulas, example data, and illustrative calculations as implemented in programmed R functions to facilitate implementation by practitioners. Alternatively, the calculations can be performed without requiring complex programming/simulation using Microsoft Excel spreadsheets that can be requested from the authors.

Evaluating Current Practices in Shelf Life Estimation.

The current International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH) methods for determining the supported shelf life of a drug product, described in ICH guidance documents Q1A and Q1E, are evaluated in this paper. To support this evaluation, an industry data set is used which is comprised of 26 individual stability batches of a common drug product where most batches are measured over a 24 month storage period. Using randomly sampled sets of 3 or 6 batches from the industry data set, the current ICH methods are assessed from three perspectives. First, the distributional properties of the supported shelf lives are summarized and compared to the distributional properties of the true shelf lives associated with the industry data set, assuming the industry data set represents a finite population of drug product batches for discussion purposes. Second, the results of the ICH "poolability" tests for model selection are summarized and the separate shelf life distributions from the possible alternative models are compared. Finally, the ICH methods are evaluated in terms of their ability to manage risk. Shelf life estimates that are too long result in an unacceptable percentage of nonconforming batches at expiry while those that are too short put the manufacturer at risk of possibly having to prematurely discard safe and efficacious drug product. Based on the analysis of the industry data set, the ICH-recommended approach did not produce supported shelf lives that effectively managed risk. Alternative approaches are required.

Testing assay linearity over a pre-specified range.

Validation of linearity is a regulatory requirement. Although many methods are proposed, they suffer from several deficiencies including difficulties of setting fit-for-purpose acceptable limits, dependency on concentration levels used in linearity experiment, and challenges in implementation for statistically lay users. In this article, a statistical procedure for testing linearity is proposed. The method uses a two one-sided test (TOST) of equivalence to evaluate the bias that can result from approximating a higher-order polynomial response with a linear function. By using orthogonal polynomials and generalized pivotal quantity analysis, the method provides a closed-form solution, thus making linearity testing easy to implement.

Increased serum clearance of oligomannose species present on a human IgG1 molecule.

The role of Fc glycans on clearance of IgG molecule has been examined by various groups in experiments where specific glycans have been enriched or the entire spectrum of glycans was studied after administration in pre-clinical or clinical pharmacokinetic (PK) studies. The overall conclusions from these studies are inconsistent, which may result from differences in antibody structure or experimental design. In the present study a well-characterized recombinant monoclonal IgG1 molecule (mAb-1) was analyzed from serum samples obtained from a human PK study. mAb-1 was recovered from serum using its ligand cross-linked to Sepharose beads. The overall purity and recovery of all isoforms were carefully evaluated using a variety of methods. Glycans were then enzymatically cleaved, labeled using 2-aminobenzamide and analyzed by normal phase high performance liquid chromatography. The assays for recovering mAb-1 from serum and subsequent glycan analysis were rigorously qualified at a lower limit of quantitation of 15 µg/mL, thus permitting analysis to day 14 of the clinical PK study. Eight glycans were monitored and classified into two groups: (1) the oligomannose type structures (M5, M6 and M7) and (2) fucosylated biantennary oligosaccharides (FBO) structures (NGA2F, NA1F, NA2F, NA1F-GlcNAc and NGA2F-GlcNAc). We observed that the oligomannose species were cleared at a much faster rate (40%) than FBOs and conclude that high mannose species should be carefully monitored and controlled as they may affect PK of the therapeutic; they should thus be considered an important quality attribute. These observations were only possible through the application of rigorous analytical methods that we believe will need to be employed when comparing innovator and biosimilar molecules.

Estimating efficacy and drug ED50's using von Frey thresholds: impact of weber's law and log transformation.

UNLABELLED: The use of von Frey filaments, originally developed by Maximilian von Frey, has become the cornerstone for assaying mechanical sensitivity in animal models and is widely used for human assessment. While there are certain limitations associated with their use that make comparisons between studies not straightforward at times, such as stimulus duration and testing frequency, von Frey filaments provide a good measurement of mechanosensation. Here we describe the application of von Frey filaments to testing in animal models, specifically with respect to determining changes in sensory thresholds in a pain state using the Dixon up-down method. In a literature survey, we found that up to 75% of reports using this method analyze the data with parametric statistical analysis and of those that used nonparametric analysis, none took into account that mechanical sensation is perceived on a logarithmic scale (Weber's Law) when calculating efficacy. Here we outline a more rigorous analysis for calculating efficacy and ED(50)'s from von Frey data that incorporates Weber's Law. We show that this analysis makes statistical and biological sense and provide a specific example of how this change affects data analysis that brings results from animal models more in line with clinical observations. PERSPECTIVE: This focus article argues that analyzing von Frey paw withdrawal threshold data obtained by using the Dixon up-down method without considering Weber's Law is inappropriate. An analysis method that incorporates how mechanical sensation is perceived and how its application brings results from animal models more in line with clinical data is presented.

The Relationship between Different Assays for Detection and Quantification of Amyloid Beta 42 in Human Cerebrospinal Fluid.

Alzheimer's disease (AD), which is characterized by a degeneration of neurons and their synapses, is one of the most common forms of dementia. CSF levels of amyloid ß(42) (Aß(42)) have been recognized as a strong candidate to serve as an AD biomarker. There are a number of commercial assays that are routinely employed for measuring Aß(42); however, these assays give diverse ranges for the absolute levels of CSF Aß(42). In order to employ CSF Aß(42) as a biomarker across multiple laboratories, studies need to be performed to understand the relationship between the different platforms. We have analyzed CSF samples from both diseased and nondiseased subjects with two different widely used assay platforms. The results showed that different values for the levels of CSF Aß(42) were reported, depending on the assay used. Nonetheless, both assays clearly demonstrated statistically significant differences in the levels of Aß(42) in CSF from AD relative to age-matched controls (AMC). This paper provides essential data for establishing the relationship between these assays and provides an important step towards the validation of Aß(42) as a biomarker for AD.

Effect of human cerebrospinal fluid sampling frequency on amyloid-ß levels.

BACKGROUND: ß-amyloid peptide (Aß) is associated with neurodegeneration in Alzheimer's disease. Emerging evidence indicates that Aß levels in cerebrospinal fluid (CSF) may serve as an early clinical biomarker for evaluating pharmacological activity of new drug candidates targeting Aß production or Aß clearance. Therefore, it is critical to understand whether intrasubject levels of CSF Aß are consistent between sampling intervals to determine whether Aß can be used as a pharmacodynamic biomarker for drug candidates. Previous studies have produced seemingly conflicting observations for the intrasubject stability of CSF Aß levels; we attempt to reconcile these conflicting observations. METHODS: The current study examined the Aß levels in CSF collected with various sampling frequencies from three clinical studies conducted in healthy young or elderly subjects at the same investigative site for the purpose of designing future studies. RESULTS: The results suggest that CSF sampling frequency and/or sampling volume contributes to intrasubject variability in CSF Aß levels, and that lowering the CSF sampling frequency may help minimize this effect. CONCLUSION: These results will help guide clinical trial design for Alzheimer's disease therapy.

A QbD case study: Bayesian prediction of lyophilization cycle parameters.

As stipulated by ICH Q8 R2 (1), prediction of critical process parameters based on process modeling is a part of enhanced, quality by design approach to product development. In this work, we discuss a Bayesian model for the prediction of primary drying phase duration. The model is based on the premise that resistance to dry layer mass transfer is product specific, and is a function of nucleation temperature. The predicted duration of primary drying was experimentally verified on the lab scale lyophilizer. It is suggested that the model be used during scale-up activities in order to minimize trial and error and reduce costs associated with expensive large scale experiments. The proposed approach extends the work of Searles et al. (2) by adding a Bayesian treatment to primary drying modeling.

An enzyme-linked immunosorbent poly(ADP-ribose) polymerase biomarker assay for clinical trials of PARP inhibitors.

Many established cancer therapies involve DNA-damaging chemotherapy or radiotherapy. The DNA repair capacity of the tumor represents a common mechanism used by cancer cells to survive DNA-damaging therapy. Poly(ADP-ribose) polymerase (PARP) is a nuclear enzyme that is activated by DNA damage and has critical roles in DNA repair. Inhibition of PARP potentiates the activity of DNA-damaging agents such as temozolomide, topoisomerase inhibitors and radiation in both in vitro and in vivo preclinical models. Recently, several PARP inhibitors have entered clinical trials either as single agents or in combination with DNA-damaging chemotherapy. Because PARP inhibitors are not cytotoxic, a biomarker assay is useful to guide the selection of an optimal biological dose. We set out to develop an assay that enables us to detect 50% PAR reduction in human tumors with 80% power in a single-plate assay while assuring no more than a 10% false-positive rate. We have developed and optimized an enzyme-linked immunosorbent assay (ELISA) to measure PARP activity that meets the above-mentioned criterion. This robust assay is able to detect PAR levels of 30-2000 pg/ml in both tumor and peripheral blood monocyte samples. In a B16F10 mouse syngeneic tumor model, PARP inhibitor ABT-888 potentiates the effect of temozolomide in suppressing tumor growth, and PARP activity is greatly reduced by ABT-888 at efficacious doses. In summary, the ELISA assay described here is suitable for biomarker studies in clinical trials of PARP inhibitors.