Longitudinal assessment of the impact of multiple switches between a biosimilar and its reference product on efficacy parameters

Patients, physicians, and health care providers in Europe have more than 10 years of experience with biosimilars. However, there are still debates if switching between a biosimilar and its reference product influences the efficacy of the treatment. In this paper, we address this uncertainty by developing a formal statistical test that can be used for showing that switching has no negative impact on the efficacy of biosimilars. For that, we first introduce a linear mixed‐effects model that is used for defining the null hypothesis (switching influences the efficacy) and the alternative hypothesis (switching has no influence on the efficacy). Using this as the foundation of our work, we propose several approaches for testing for changes in the efficacy of the treatment due to switching and discuss the properties of these tests in an extensive simulation study. It is shown that all these methods have advantages and disadvantages and the decision regarding which method is preferred depends on the expectation of a switching assessment. To demonstrate the applicability of the methods in practice, the approaches were applied to the data of the EGALITY study, which compares the reference product Enbrel® (Amgen) with the approved biosimilar Erelzi® (Sandoz).     

Simulation assessments of statistical aspects of bioequivalence in the pharmaceutical industry

An Erratum has been published for this article in Pharmaceutical Statistics 2004; 3(3): 232 Since the early 1990s, average bioequivalence (ABE) has served as the international standard for demonstrating that two formulations of drug product will provide the same therapeutic benefit and safety profile. Population (PBE) and individual (IBE) bioequivalence have been the subject of intense international debate since methods for their assessment were proposed in the late 1980s. Guidance has been proposed by the Food and Drug Administration (FDA) for the implementation of these techniques in the pioneer and generic pharmaceutical industries. Hitherto no consensus among regulators, academia and industry has been established on the use of the IBE and PBE metrics. The need for more stringent bioequivalence criteria has not been demonstrated, and it is known that the PBE and IBE criteria proposed by the FDA are actually less stringent under certain conditions. The statistical properties of method of moments and restricted maximum likelihood modelling in replicate designs will be summarized, and the application of these techniques in the assessment of ABE, IBE and PBE will be considered based on a database of 51 replicate design studies and using simulation. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal cross-over designs for nonlinear mixed models using a first-order expansion

We consider the construction of optimal cross-over designs for nonlinear mixed effect models based on the first-order expansion. We show that for AB/BA designs a balanced subject allocation is optimal when the parameters depend on treatments only. For multiple period, multiple sequence designs, uniform designs are optimal among dual balanced designs under the same conditions. As a by-product, the same results hold for multivariate linear mixed models with variances depending on treatments.     

Teachers and the birth rate

A theoretical model is developed in which the market for teachers is linked to the time path of fertility in the general population. The model is simple in its components but when the components are combined they form a complex long-memory dynamic system. Simulation experiments are carried out to investigate the effects of changes in fertility rates on supply/requirements imbalances in the teachers' market, the median age of teachers, and other variables. The model (and by implication, the real-world system) is found to be highly volatile in response to fertility variations.This study was supported by a grant from the Social Sciences and Humanities Research Council of Canada. The authors are grateful for the able research assistance provided by Guy Brockington and Renqun Wang and for the helpful comments of the referees.