Checking distributional assumptions for pharmacokinetic summary statistics based on simulations with compartmental models

Impact of model misspecification on model-based tests in PK studies with parallel design: real case and simulation studies

This article evaluates the performance of pharmacokinetic (PK) equivalence testing between two formulations of a drug through the Two-One Sided Tests (TOST) by a model-based approach (MB-TOST), as an alternative to the classical non-compartmental approach (NCA-TOST), for a sparse design with a few time points per subject. We focused on the impact of model misspecification and the relevance of model selection for the reference data. We first analysed PK data from phase I studies of gantenerumab, a monoclonal antibody for the treatment of Alzheimer’s disease. Using the original rich sample data, we compared MB-TOST to NCA-TOST for validation. Then, the analysis was repeated on a sparse subset of the original data with MB-TOST. This analysis inspired a simulation study with rich and sparse designs. With rich designs, we compared NCA-TOST and MB-TOST in terms of type I error and study power. With both designs, we explored the impact of misspecifying the model on the performance of MB-TOST and adding a model selection step. Using the observed data, the results of both approaches were in general concordance. MB-TOST results were robust with sparse designs when the underlying PK structural model was correctly specified. Using the simulated data with a rich design, the type I error of NCA-TOST was close to the nominal level. When using the simulated model, the type I error of MB-TOST was controlled on rich and sparse designs, but using a misspecified model led to inflated type I errors. Adding a model selection step on the reference data reduced the inflation. MB-TOST appears as a robust alternative to NCA-TOST, provided that the PK model is correctly specified and the test drug has the same PK structural model as the reference drug.

Comparing a Bayesian Approach (BEST) with the Two One-Sided t-Tests (TOSTs) for Bioequivalence Studies

The two one-sided t-tests (TOST) procedure has been used to evaluate average bioequivalence (BE). As a regulatory standard, it is crucial that TOST distinguish BE from not-BE (NBE) when BE data are not lognormal. TOST was compared with a Bayesian procedure (BEST by Kruschke) in simulated datasets of test/reference ratios (T/R) which were BE and NBE, wherein (1) log(T/R) or T-R were normally distributed, (2) sample sizes ranged 10–50, and (3) extreme log(T/R) or T-R values were randomly included in datasets. The 90% “credible interval” (CrI) from BEST is a Bayesian alternative of the 90% confidence interval (CI) of TOST and it can be derived from a posterior distribution that is more reflective of the observed mean log(T/R) distribution that often deviates from normality. In the absence of extreme T/R values, both methods agreed BE when observed T/R were lognormal. BEST more accurately concluded BE or NBE, while requiring fewer subjects, when observed log(T/R) or T-R were normal in the presence of extreme values. Overall, TOST and BEST perform comparably on lognormal T/R, while BEST is more accurate, requiring fewer subjects when datasets are normal for T-R or contain extreme values. Of note, the normally distributed datasets only rarely contain extreme values. Our results imply that when BEST and TOST yield different BE assessment results from bioequivalent products, TOST may disadvantage applicants when T/R are not lognormal and/or include extreme T/R values. Application of BEST can address the situation when T/R are not lognormal or include extreme data values. Application of BEST to BE data can be considered a useful alternative to TOST for evaluation of BE and for efficient development of BE formulations.

Establishing the Pharmacokinetics of Genetic Vaccines is Essential for Maximising their Safety and Efficacy

In a typical course of drug development, thorough pharmacokinetic (PK) studies are essential for the determination of drug biodistribution, dosage and efficacy without toxicity. For vaccines, however, unless a new formulation component is used, most regulatory agencies rule out the need for studying the biodistribution of the vaccine antigenic material per se, and only dose-immunogenicity studies are performed. This is because traditional vaccines are meant to directly induce immunogenicity by locally recruiting immunocytes that will carry on with the pursuing immunogenic processes. Thus, the clinical outcome from traditional vaccines is determined mainly by an immunological response phase. Yet, the case is significantly different for the emergent genetic vaccines (vectorised DNA or mRNA vaccines), where the clinical outcome is dependent on a combination of two major response phases: a pharmacological phase that involves biodistribution, assimilation, gene translation and epitope(s) presentation, followed by an immunological phase, which is similar to that of traditional vaccines. From a mathematical perspective, processes involved in drug administration are typically subject to inter- and intra-patient statistical distributions like most physiological processes. Therefore, the clinical outcome after administering genetic vaccines obeys a statistical probability distribution combined of the sum of two major response probability distributions, pharmacological and immunological. This implies that the variance coefficient of the summed response probability distributions has a larger value than the variance of each underlying distribution. In other words, due to the multi-phased mode of action of genetic vaccines, their clinical outcome has more variability than that of traditional vaccines. This observation points toward the necessity for regulating genetic vaccines in a similar manner to bio-therapeutics to ensure better efficacy and safety. A structural PK model is provided to predict the sources of variability, biodistribution and dose optimisation.