How to reduce the total number of samples in a bioequivalence study without impacting statistical power
Daniel Kaschek (1), Sabine Pestel (2), Oliver Ghobrial (3)
(1) IntiQuan GmbH, Basel, Switzerland (2) CSL Behring Innovation GmbH, Marburg, Germany, (3) CSL Behring LLC, KoP, USA
Introduction/Objectives:
Bioequivalence (BE) or biosimilarity studies are typically conducted to compare two drugs or formulations and show their similarity [1, 2]. For BE studies focusing on the pharmacokinetics (PK) of the drug, exposure metrics such as the area under the concentration-time profile (AUC) and the peak concentration (Cmax) are typically determined via non-compartmental analysis (NCA) of individual concentration-time profiles [3] for comparison between the treatments. Assuming the drugs/formulations are similar, the required sample size (number of subjects) to show BE is mainly driven by the total variability of AUC and Cmax. Therefore, to properly characterize AUC and Cmax, the FDA provides some general advice on the sampling time points for the individual profiles [2], e.g., to observe around Cmax, to cover at least 3 half-lives of elimination of the drug, or to collect 12-18 samples.
In the presented analysis, we focused on the question of how many samples per individual concentration-time profile were sufficient to appropriately characterize AUC and Cmax without inflating the variability of AUC and Cmax and thereby reducing the statistical power of the BE study.
Methods:
We used a simulation-estimation approach to assess how the number of samples per profile impacted the mean and the variability of AUC and Cmax. In the simulation step, individual concentration-time profiles were simulated based on a population PK model. The profile was evaluated at nobs time points which were optimally selected by the OTTER algorithm [4] to determine AUC by NCA. Furthermore, random residual variability was added to the profile concentrations at the observed time points. In the estimation step, Cmax and AUC were determined from the simulated profiles prior to and after adding residual variability (RV). AUC and Cmax were summarized across simulated profiles using the geometric mean and geometric CV% as summary statistics.
The simulation-estimation approach was repeated for different nobs between 8 and 15 per profile. Furthermore, the approach was tested with two different population PK models: one for a subcutaneously (SC) administered drug where inter-individual variability (IIV) and RV each were at ~20% CV. Another model represented an intravenously (IV) administered drug with IIV of 20% CV and RV of 5% CV, much smaller than the IIV.
Results:
Based on the simulated concentration-time profiles for SC administration without RV, the geometric mean AUC and Cmax did not show a trend with the number of observed time points. Also, the CV% of AUC and Cmax were constant over the different nobs tested (8-15). After addition of RV, the geometric mean AUC was still constant over nobs whereas the geometric mean Cmax increased with increasing nobs. The CV% of both AUC and Cmax increased from 16% to 18% and from 17% to 20%, respectively, when nobs was reduced.
Based on the simulated concentration-time profiles for IV administration without RV, the geometric mean AUC and Cmax did not show a trend with the number of observed time points. Also, the CV% of AUC and Cmax were constant over the different values of nobs tested. After addition of RV, the geometric mean AUC and Cmax as well as their CV% did not notably change for the tested nobs between 8 and 15.
Conclusions:
For low or negligible residual variability, both geometric mean AUC and Cmax and their CV% were reliably estimated for SC and IV administration, independent of the number of observed time points per profile between 8 and 15. That indicated that given the optimal selection of time points based on the simulated profiles, AUC and Cmax estimates from profiles with 15 time points were not superior to estimates from profiles with 8 time points.
When residual variability and IIV were in a similar range (SC administration example), the geometric mean Cmax increased with a higher nobs. Furthermore, we observed a slight inflation of variability of AUC and Cmax. That indicated that residual variability was a main driver of the inflation of CV% of AUC and Cmax when reducing nobs.
Overall, the results suggested that a limitation of the number of samples per profile from 15 to 8 appears feasible if the time points are chosen optimally and residual variability is low compared to IIV.
References:
[1] US Department of Health and Human Services. FDA Guidance for Industry, Statistical Approaches to Establishing Bioequivalence. http://www. fda.gov/cder/guidance/index.htm. 2001.
[2] US Food and Drug Administration. Bioavailability and Bioequivalence Studies Submitted in NDAs or INDs - General Considerations, 2014.
[3] US Food and Drug Administration. Analyses and Displays Associated to Non-Compartmental Pharmacokinetics – With a Focus on Clinical Trials (Version 1.0). 2014.
[4] Hughes Jim H., Upton Richard N., Reuter Stephanie E., Phelps Mitch A., Foster David J.R.. Optimising time samples for determining area under the curve of pharmacokinetic data using non-compartmental analysis, Journal of Pharmacy and Pharmacology 71(11):1635-1644, 2019.