Replicate Designs and Average, Individual, and Population BioEquivalence: II. Simulation Assessment of Performance of Novel Procedures and the Proposed FDA Methods for Bioequivalence Assessment
Scott D Patterson and Byron Jones
Abstract. Since the early 1990’s, 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 1980’s. Guidance has been proposed by the FDA for the implementation of these techniques in the pioneer and generic pharmaceutical industries. As of the year 2002, 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 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 summarised, and the application of these techniques in the assessment of ABE, IBE, and PBE are considered based on a database of 51 replicate design studies and using simulation.
The constrained REML procedure recommended by FDA Guidance (2001) using Satterthwaite (1941-1946) or Kenward-Roger (1997) degrees of freedom for ABE testing in replicate designs results in biased estimates for variance components on occasion; however, it uniformly constrains the rate of Type I error (of more immediate concern to regulators and consumers) to be less than 5% in ABE testing.
It is concluded that the Cornish-Fisher expansion (Hyslop et al., 2000) will adequately serve for IBE and PBE testing except in the presence of missing data where method-of-moments estimates become biased. In situations where missing data and the resulting bias in estimates are of great concern, an asymptotic testing procedure using REML (though conservative) may be used to assess inference. While valid statistical tests for PBE have been developed under the proposed FDA standards, this procedure quite easily allows for market access with very large changes in mean exposure for highly variable drug products. The potential for threats to public health generated by generic-to-generic switching should not be underestimated if IBE is used to allow market access. We recommend that the FDA reconsider the use of the IBE and PBE procedures for market access and not allow their use without major modification
to ensure patient safety and efficacy.
Pharmacokinetic Bridging and ICH-E5: Retrospective and Simulation Assessment of Proposals for Pharmacokinetic Equivalence Assessment between Independent Populations
Scott D Patterson and Byron Jones
Abstract: A topic associated with bioequivalence is considered; that of comparing rate and extent of exposure between differing ethnic groups as described in ICH-E5 (1998). The properties of the population bioequivalence metric and an alternative metric will be characterised in small and large samples from parallel group studies. Inference will be illustrated using data from a recent submission and simulation studies. The emphasis of this report is on the practical statistical design and use of pharmacokinetic data for ICH-E5 (1998) bridging assessment and for enhancing the understanding of the role of this data in enabling informed clinical development.
The Construction of Universally Optimal Uniform Cross-over Designs
Simon Bate and Byron Jones
ABSTRACT. In this report we derive the conditions that a uniform cross-over
design must satisfy to be optimal for estimating treatment and first-order carryover effects. In particular we use the notion of universal optimality introduced by Kiefer (1975). Existing appropriate methods are reviewed and new methods of construction are described. The constructed designs fall into four families, which include the balanced and strongly balanced designs as special cases: the remaining designs we refer to as nearly strongly balanced, a term first introduced by Kunert (1983). The nearly strongly balanced designs form an important family of cross-over designs which provide designs where balanced or strongly balanced designs do not exist. These designs impose no limits on the number of periods and subjects, other than that these must be a multiple of the number of treatments. Some illustrative examples are included.
The Design and Analysis of Multicentre Trials in the Random Effects Setting
Valerii Fedorov, Byron Jones and Frank Rockhold
ABSTRACT. Dragalin, et al. (2001) defined a combined response to treatment (CRT) in a multicentre trial and showed how it could be estimated using fixed effects models which are appropriate in the ”testground” setting. Here we extend the previous work to the situation where centres can be viewed as a sample from a population and the treatment and centre effects may be assumed random. We give iterative formulae for obtaining the maximum likelihood estimators of the treatment mean vector and its variance-covariance matrix, including the case with unknown components of variance and the case where the variance is different for the compared treatments or varies randomly over the centres. While most of these formulae have appeared in various forms in the statistical literature, we have attempted to unify and simplify them both in the general setting and in the simplest case of two treatments with no covariates. Most formulae allow singular centres where some centres have data from only one of the treatments. We show that the CRT estimators generated within the random effect model approach and the estimators for various fixed effect models can be described by the same formula if additional control parameters describing the variability between centres are introduced. That unified presentation allows us, for different settings, to derive the optimal number of centres and numbers of patients per centre to recruit, subject to (i) a total cost constraint and (ii) a maximum variance constraint. The effect on the variance of the CRT caused by random enrollment is illustrated using two simulated examples. The recruitment waiting time distribution is discussed under Poisson sampling assumptions and the implications of alternative recruitment strategies are considered. Finally, we give an illustrative example
using data based on a real multicentre trial for two treatments.
An important conclusion of the results presented in this report is that the total sample size of a multicentre trial needs to take into account inflationary effects due to a number of sources: treatment effects varying over centres, centre sizes deviating from those in a balanced design due to random recruitment and varying rates of recruitment over the centres.
Replicate Designs and Average, Individual, and Population Bioequivalence
Scott D Patterson and Byron Jones
Abstract. Since the early 1990’s, average bioequivalence (ABE) studies have served as the international regulatory standard for demonstrating that two formulations of drug product will provide the same therapeutic benefit and safety profile when used in the marketplace. Population (PBE) and Individual (IBE) bioequivalence have been the subject of intense international debate since methods for their assessment were proposed in the late 1980’s and since their use was proposed in United States Food and Drug Administration guidance in 1997. Guidance has since been proposed and finalised by the Food and Drug Administration for the implementation of such techniques in the pioneer and generic pharmaceutical industries.
The current guidance calls for the use of replicate design, cross-over studies (cross-overs with sequences TRTR, RTRT where T is the Test and R is the Reference formulation) for selected drug products and proposes restricted maximum likelihood and Method-of-Moments techniques for parameter estimation. In general, marketplace access will be granted if the products demonstrate ABE based on a restricted maximum likelihood model. Study sponsors have the option of using PBE or IBE if the use of these criteria can be justified to the regulatory authority.
Novel and previously proposed SAS c -based approaches to the modelling of pharmacokinetic data from replicate design studies will be summarised. Restricted maximum likelihood and Method-of-Moments modelling results are compared and contrasted based on the analysis of data available from previously performed replicate design studies, and practical issues involved in the application of replicate designs to demonstrate ABE are characterised. Following review of previous research, properties of the restricted maximum likelihood and Method-of-Moments estimates of the IBE and PBE metrics will be explored. Inferential procedures in IBE and PBE will be described and assessed, and retrospective analysis of data is used to assess performance of the metrics.
It is concluded that IBE and (particularly) PBE are less stringent than ABE and will allow easier market access for new products having large differences in average exposure (and failing ABE), and we recommend that the PBE approach be discarded or modified significantly to protect public health. Estimates for the FDA’s IBE and PBE metric are asymptotically unbiased but positively biased (against sponsors) in small samples; however, the positive bias in small samples is not of practical significance when assessing IBE and PBE under proposed procedures for highly variable drugs. REML modelling may be used to assess ABE, IBE, and PBE, but statisticians should exercise caution when choosing the structure of the variance-covariance matrix. Last asymptotic and nonparametric percentile bootstrap based IBE and PBE inference appears similar to that of the Cornish-Fisher expansion recommended by FDA and provide practical alternatives to the FDA procedure when missing data and/or imbalance are present in the data.
