Estimating Shelf Life Through Tolerance Intervals Extended to Nonlinear Response Trends

Methods for estimating pharmaceutical shelf life based on tolerance intervals are proposed by Schwenke, et al. AAPS PharmSciTech. 2020;21:290, [1] where a critical quality attribute that follows a simple linear (straight line) response trend across storage time is presented as the traditional example. A random coefficient mixed linear regression model is used to characterize the between batch and within batch variation. These methods are further discussed for various stability study scenarios, number of stability batches, and levels of assumed risk in Schwenke, et al. AAPS PharmSciTech. 2021;22:273, [4] through a simulation study, again based on a critical quality attribute assuming a simple linear response. However, in practice, not all stability response profiles conveniently follow straight line or linear trends. The purpose of this paper is to extend the proposed tolerance interval and random coefficient mixed regression methods for estimating pharmaceutical shelf life to critical quality attributes that follow more complex stability response profiles. As an example, a nonlinear response is typically characterized by either an increasing or decreasing response, starting from an initial concentration, trending with storage time towards some limiting response or asymptote. Nonlinear responses cannot be statistically analyzed with linear model methods. Practical information supported by simulation results based on a pharmaceutical stability study are discussed to allow for appropriate statistical analyses and shelf life estimates through random coefficient mixed nonlinear regression and tolerance interval methods.

A Practical Discussion on Estimating Shelf Life Through Tolerance Intervals

This paper is a companion article to the research originally presented in "Estimating Shelf Life through Tolerance Intervals" (Schwenke et al., 21:290, 2020) published in AAPS PharmSciTech where tolerance intervals are introduced as an alternative methodology for estimating pharmaceutical shelf life. An industry stability shelf life example data set was used to demonstrate the proposed methods. Although using industry data does give relevance to examples demonstrating shelf life estimation, measures of how well the proposed methods accurately and effectively estimate shelf life cannot be obtained because the true shelf life values are not known for example data sets. In this current paper, the results of a computer simulation are reported where the tolerance interval estimates of shelf life are compared to theoretically known true shelf life values. Various factors that affect a tolerance interval estimate of pharmaceutical shelf life are investigated. A critical decision factor is the choice of the proportion of the stability distribution allowed out of specification at expiry to define the pharmaceutical risk. The number of stability batches available for shelf life estimation and the storage time at which the estimate is made are also considered in this simulation study. The industry example data are again used as the basis for the simulation study to give relevance to this research.

Estimating Shelf Life Through Tolerance Intervals

This paper is a continuation of the research published by the Stability Shelf Life Working Group as chartered under the Product Quality Research Institute. The Working Group was formed in 2006 and disbanded in late 2019. Following the philosophy presented by the Working Group on how to characterize the stability shelf life paradigm (Capen et al., 2012), shelf life is estimated here in terms of defining risk as a specified proportion of the pharmaceutical stability distribution of interest being out of specification. Shelf life can be defined for the batch mean distribution for regulatory issues, as well as for the product distributions for patient interests. Estimates of shelf life are proposed corresponding to each stability distribution through the use of statistical tolerance intervals. Appropriate estimates of the between-batch and within-batch variance components are obtained through a random coefficient mixed regression model analysis based on the best fit to batch stability response data. Tolerance interval estimates are computed as part of the mixed model analysis and computed directly using the statistical definition of the stability distributions. A proposed rationale is offered on how to select an appropriate proportion allowed out of specification to define a meaningful shelf life. Examples of the proposed shelf life estimates are presented using industry stability batch data. For each example, the traditional ICH shelf life estimate is given for comparison.

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.

Evaluating the performance of the ICH guidelines for shelf life estimation

The goal of shelf life estimation is to determine the storage time during which the entire product meets specification with acceptably high probability. The estimated shelf life should be "applicable to all future batches" (ICH Q1E, International Conference on Harmonization, 2003b). There is compelling evidence of issues with the International Conference on Harmonization (ICH) guidelines for shelf life estimation. Issues include fixed batch effects, poolability tests, and confidence intervals for the mean. Two conclusions from evaluating the ICH procedure are that batch effects should be random and that focus should be on a quantile. A procedure is needed that combines random batches with the ICH objective of estimating the minimum batch shelf life.

On the distribution of batch shelf lives

Implicit in ICH Q1E (International Conference on Harmonization [ICH], 2003b ) are definitions of batch shelf life (the time the batch mean crosses the acceptance limit) and product shelf life (the minimum batch shelf life). The distribution of batch means over time projects to a distribution of batch shelf lives on the x-axis. Assuming multivariate normality, shelf life is the ratio of correlated Gaussian variables. Using Hinkley ( 1969 ), we describe the relationship between quantiles of the distributions of batch shelf lives and batch means. Exploiting this relationship, a linear mixed model is used to estimate a target quantile of batch shelf lives to address the ICH objective.

On the shelf life of pharmaceutical products

This article proposes new terminology that distinguishes between different concepts involved in the discussion of the shelf life of pharmaceutical products. Such comprehensive and common language is currently lacking from various guidelines, which confuses implementation and impedes comparisons of different methodologies. The five new terms that are necessary for a coherent discussion of shelf life are: true shelf life, estimated shelf life, supported shelf life, maximum shelf life, and labeled shelf life. These concepts are already in use, but not named as such. The article discusses various levels of "product" on which different stakeholders tend to focus (e.g., a single-dosage unit, a batch, a production process, etc.). The article also highlights a key missing element in the discussion of shelf life-a Quality Statement, which defines the quality standard for all key stakeholders. Arguments are presented that for regulatory and statistical reasons the true product shelf life should be defined in terms of a suitably small quantile (e.g., fifth) of the distribution of batch shelf lives. The choice of quantile translates to an upper bound on the probability that a randomly selected batch will be nonconforming when tested at the storage time defined by the labeled shelf life. For this strategy, a random-batch model is required. This approach, unlike a fixed-batch model, allows estimation of both within- and between-batch variability, and allows inferences to be made about the entire production process. This work was conducted by the Stability Shelf Life Working Group of the Product Quality Research Institute.

Measuring the development of executive control with the shape school

Although several neurodevelopmental and psychiatric disorders can emerge during the preschool period, there are comparatively few instruments to assess executive control. Evidence for validity of the Shape School (K. A. Espy, 1997) was examined in a sample of 219 typically developing young children. There was good evidence for validity, as Shape School performance variables were interrelated and were associated to other criterion measures considered to measure aspects of executive control. Also suggesting validity, the Shape School variables varied as a function of whether the task demands (a) were executive, (b) required inhibition of a prepotent response or context-controlled selection among relevant stimulus-response sets, and (c) included unitary or concurrent processing. The Shape School may be an effective tool by which to measure executive control in young children who have atypical developmental patterns.