Estimation of the shelf-life of drugs with mixed effects models

A Modern Approach to Stability Studies via Bayesian Linear Mixed Models Incorporating Auxiliary Effects

In preparation to the launch of a pharmaceutical product, an estimate of its shelf life via stability testing is required by regulatory agencies. The ICH-Q1E guidance has been the worldwide reference to reach this objective, but in recent years several authors have criticized many of its aspects. To that end we discuss a complete Bayesian transcript of the ICH-Q1E, treating all the apparent shortcomings, while also addressing the presence of multiple batches using a linear mixed model (LMM) for proper shelf life prediction by explicitly modelling the batch-to-batch variability. This comprises a redefinition of the linear models proposed in the ICH-Q1E by suitable LMM counterparts, and a Bayesian analogue for model selection, which is more intuitive and remedies detrimental features of the ICH approach. In that context, a proper mathematical foundation of shelf life is provided that we use to investigate and mathematically compare the two available approaches to shelf life determination via shelf life distribution and batch distribution. The discussed method is then tested and evaluated using real data in comparison with the ICH-Q1E approach demonstrating their approximate equivalency for 6 batches. As a major objective, we extended the LMM with auxiliary fixed effects, here the concentration, which interconnect data sets allowing a prediction of shelf lives for concentrations lacking a sufficient number of batches. This establishes a novel approach to accelerate the speed to submission while retaining the patients' safety. Both case studies underline the inherent superiority of LMMs within a Bayesian framework regarding predictability and interpretability, and we hope that the relevant authorities will accept this approach in the future.

The effect of long-term spaceflight on drug potency and the risk of medication failure

Pharmaceuticals selected for exploration space missions must remain stable and effective throughout mission timeframes. Although there have been six spaceflight drug stability studies, there has not been a comprehensive analytical analysis of these data. We sought to use these studies to quantify the rate of spaceflight drug degradation and the time-dependent probability of drug failure resulting from the loss of active pharmaceutical ingredient (API). Additionally, existing spaceflight drug stability studies were reviewed to identify research gaps to be addressed prior to exploration missions. Data were extracted from the six spaceflight studies to quantify API loss for 36 drug products with long-duration exposure to spaceflight. Medications stored for up to 2.4 years in low Earth orbit (LEO) exhibit a small increase in the rate of API loss with a corresponding increase in risk of product failure. Overall, the potency for all spaceflight-exposed medications remains within 10% of terrestrial lot-matched control with a ~1.5 increase in degradation rate. All existing studies of spaceflight drug stability have focused primarily on repackaged solid oral medications, which is important because non-protective repackaging is a well-established factor contributing to loss of drug potency. The factor most detrimental to drug stability appears to be nonprotective drug repackaging, based on premature failure of drug products in the terrestrial control group. The result of this study supports a critical need to evaluate the effects of current repackaging processes on drug shelf life, and to develop and validate suitable protective repackaging strategies that help assure the stability of medications throughout the full duration of exploration space missions.

Determination of acceptance criteria and sample sizes for accelerated stability comparability studies for biologics

Changes of manufacturing processes are common. It is required by the regulatory agencies that manufacturers establish adequate and appropriate comparability between pre-change and post-change products. The goals of comparability assessments are to demonstrate the comparability and consistency of product quality before and after change and to demonstrate that the changes do not have an adverse effect on safety and efficacy of the drug products. Accelerated or stressed stability studies may shed light on drug quality under stressed environmental conditions and on product differences in the degradation pathways. Comparability of accelerated stability data may provide further evidence on the impact of process change. Equivalence test has been recommended to demonstrate the comparability of stability profiles for accelerated stability studies. Selection of appropriate acceptance criteria for determining comparability is one of the most challenging steps in the comparability studies. Because of the inherent heterogeneity of biologics, the stability profiles may vary considerably from batch to batch. It is more challenging to set the acceptance criteria for comparing the accelerated stability data for biologics. In this article, we present an approach for determining the acceptance criteria and necessary sample sizes for accelerated comparability studies for biologics.

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.

Shelf life determination based on equivalence assessment

In a regular analysis of covariance (ANCOVA) approach to stability analysis, the decision for pooling data from different batches plays a key role in the determination of the shelf life of the drug product. Conventionally, the decision to pool data for the estimate of slope and intercept of common or individual regression lines is made by "no evidence to reject the null hypothesis of no difference." With typically limited observations, a significance level of much higher than 0.05 was recommended for the pooling tests in order to avoid inflation of type-I error rate of the shelf life testing. This logic of the pooling test decision making discouraged the use of replicates to improve power of testing and precision of estimation. The concept of pooling by equivalence test was originally proposed by Ruberg and Hsu in their 1990 article "Multiple comparison procedures for pooling batches in stability studies" Such a concept has evolved to pooling batches based on the shelf life equivalence test by Yoshioka et al. in their 1996 article "Power of analysis of variance for assessing batch-variation of stability data of pharmaceuticals." In this article, an approximation test of shelf life equivalence and a test of chemical value equivalence for the data pooling decision are proposed as an alternative to the conventional ANCOVA approach.

Rank regression in stability analysis

Stability data are often collected to determine the shelf life of certain characteristics of a pharmaceutical product, for example, a drug's potency over time. Statistical approaches such as the linear regression models are considered as appropriate to analyze the stability data. However, most of these regression models in both theory and practice rely heavily on their underlying parametric assumptions, such as normality of the continuous characteristics or their transformations. In this article, we propose and study some rank-based regression procedures for the stability data when the linear regression models are semiparametric with unspecified error structure. Numerical studies including Monte Carlo simulations and practical example are demonstrated with the proposed procedures as well.

Follow-up in the micronucleus frequencies and its subsets in human population with chronic low-dose gamma-irradiation exposure

Forty-eight individuals, who received protracted low-dose rate gamma-irradiation from radioactive environments for 2-10 years, have been evaluated repetitively for cytogenetic damage by the cytochalasin-B micronuclei assay (CBMN) after they relocated from radioactive buildings. These subjects were shown to have a significant decrease in the CBMN frequencies during 26.2+/-8.4 months of follow-up. By the mixed effect multiple linear regression analysis, the CBMN frequencies in these 48 subjects during repetitive measurements were significantly associated with the relocation duration since leaving the radioactive environments (relocation time or RT in months; estimate -0.47, standard error 0. 0016, p value 0.0074). The alteration rate in the proportions of binucleates carrying a single micronucleus and those with multiple micronuclei was further compared among 26 of these exposed individuals. The proportions of binucleates with multi-micronuclei were shown to decline significantly faster than those with a mono-micronucleus between these two repetitive assays (proportional Z-test, p value 0.003). Moreover, some of the exposed subjects were shown to have a persistent increase in the total micronuclei frequencies or carrying multi-micronuclei in the binuclei even 3-4 years post-cessation of exposure. This suggests potential genomic instability in stem cells of the exposed individuals and the phenomenon deserves further closer monitoring. Understanding the dynamics of micronucleus expression in lymphocytes in subjects with previous mutagenic exposure would be of significant importance for human population monitoring.