Journal of Bioequivalence & Bioavailability

Models, Optimal Sampling and Bioequivalence-A New Paradigm Case Study for a Drug with Complex Absorption Modified Release Methylphenidate

Andre J. Jackson^1*, Mutaz Jaber², Henry C. Foehl³ and Inder Chaudhary^{4 1}Department of Pharmacy, Howard University, 2300 4th street, Washingtom D.C, USA
²Department of Experimental and Clinical Pharmacology, University of Minnesota, Minneapolis, USA
³Foehl Statistics & Analytics LLC, Glenmoore, Pennsylvania, USA
⁴Rhodes Pharmaceuticals, 498 Washington St, Coventry, USA
^*Correspondence: Andre J. Jackson, Department of Pharmacy, Howard University, 2300 4th street, Washingtom D.C, USA, Email:

Received: 28-May-2024, Manuscript No. JBB-24-25878; Editor assigned: 31-May-2024, Pre QC No. JBB-24-25878 (PQ); Reviewed: 14-Jun-2024, QC No. JBB-24-25878; Revised: 21-Jun-2024, Manuscript No. JBB-24-25878 (R); Published: 28-Jun-2024, DOI: 10.35248/0975-0851.24.16.583.

Introduction

With passage of the Drug Price Competition and Patent Term Restoration Act in 1984 [1], the design of Bioequivalence (BE) studies for generic drug products vs. approved reference drug products for orally-administered drug dosage forms required standardization of study design for purpose. Study designs recommended by the FDA to address BE-specific issues depended on properties of the specific drug under test. The types of recommended study designs and their statistical analyses were instituted to address average, individual, population, and referenced-scaled average BE [2]. FDA BE guidances have recommended variously performing: A) Two- period, two-sequence, two-treatment, single-dose, crossover studies, B) parallel-design studies, and/or C) replicated-design studies [3-5] as needed to address various types of BE-related concerns. These study designs have been developed to address oral drug products that have first-order, zero-order, and/or complex absorption, as well as oral drugs with highly-variable absorption patterns. These designs have also been used to establish BE for some long-term injectable drug products. All of the designs have generally required that plasma samples be collected for approximately three terminal elimination half-lives to determine exposure [4].

There have been some published studies discussing modification of the number of samples specified for collection in the currently recommended designs. One study reference in a publication used an optimal-sampling approach for a novel adaptive sequential design which would allow for re-estimation of the second-stage sample size based upon first-stage results [6]. The author’s main emphasis was to define the intra-subject Coefficient of Variation (COV) to better define sample size. Another publication looked specifically at using optimal times for sample collection, with the main emphasis being the estimation of (AUC) using a one- compartment model. The authors of the Kong FH and Gonin R, publication concluded from simulation studies that the trapezoidal approximation for AUCs up to 24 hrs post-dose under an optimal sampling design is an improvement over the ordinary sampling time design when the number of samples was reduced from ten to six [7]. In particular, the ordinary design has a non-negligible bias while the optimal design appeared to reduce such bias. The publication by Jackson [8] employed limited sampling (based upon the drug’s pharmacokinetics) used training and test data sets with various levels of intrasubject error and concluded these procedures were useful only for formulations with test product/reference product (T/R) ratios for Fraction Absorbed (FA) within the range of 0.90- 1.10 for drugs with highly variable absorption characteristics [8].

The aim of the current study was to focus on the effects on BE determination when using optimal sampling in BE studies for oral ER MP drug products with complex absorption characteristics. This was done by determining if use of optimal sampling will result in similar BE metrics (e.g., 90% CIs for AUC: 0-3 hrs, AUC: 3-7 hrs, AUC: 7-12 hrs, AUC_0-t, and C_max) compared with ordinary sampling for Concerta^® and a generic MP product with both having complex absorption characterized by zero and first-order PK [9-10].

Materials and Methods

Pharmacokinetic model

Concerta^®: The parameters, sampling times and PK model for Concerta^® were described in prior publications [9-11]. The model has two parallel inputs with the first being a fast, zero-order immediate-release phase and the second being a slow, first-order delayed-release phase.

Replicate experimental be fasting study for generic MP ER oral drug product vs. Concerta^®

Ethics: This study was conducted in compliance with FDA Good Clinical Practice (GCP), and all applicable regulations, including the Federal Food, Drug and Cosmetic Act., U.S. Code of Federal Regulations (Title 21), ICH Guidelines, and IRB requirements relative to clinical studies [12].

Informed consent: An Informed Consent Form (ICF) that includes all relevant elements currently required by FDA or state regulations was provided to each prospective study subject at screening and before enrollment into the study.

Study design and patients

This study was designed based on the known PK of Concerta^® ER oral tablets based upon FDA Draft Guidance [5], and generally accepted standards for the conduct of BE/BA studies under fasted conditions. The study was an open-label randomized, two-treatment, two-sequences, four-period, single-dose, four-way crossover replicate design bioequivalence and bioavailability study conducted in adult male and female healthy subjects (18-45) in a fasting state: 44 subjects completed at least wo periods of the study, one of which included the reference product. Each subject received a single 54 mg dose of the reference tablet (Concerta^®) on two occasions and a single dose of the test tablet (MP HCL ER) on two occasions with a 7-day washout period.

Analytical methods

Pre-dose samples were collected within 60 minutes before dosing. Samples were taken pre-dose (0-hour) and at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 9.0, 10.0, 11.0, 12.0, 16.0, 20.0, 24.0 and 30.0 hrs post-dose. Plasma levels of MP enantiomers were quantified using a fully-validated liquid chromatography-tandem mass spectrometry (LC-MS/MS) method. The method was linear over a concentration range of 0.105 ng/mL to 50.000 ng/mL, and the lower limit of quantitation was 0.105 ng/mL.

Optimal sampling-methods

Optimal plasma sampling times for the primary simulated BE study and for the experimental BE study were selected based on optimal experimental design using a D-optimality method [13]. Employing a priori information based on a previously-published Concerta^® Model [9], Fisher information was obtained using the Concerta^® Model’s final estimates. A minimum of five sampling time points was pre-specified (the number of total samples per individual, N-i) to produce reasonable concentration time-profiles for the estimation of the BE parameters. For the given simulated population-replicated PK model, the BE parameter estimates and the effects of between-subject variation and within-subject variation on the 90% CIs for pAUC: 0-3 hrs, pAUC: 3-7 hrs, pAUC: 7-12 hrs, C_max and AUC_0-t were investigated.

Primary simulation study-design and statistics

Simulated BE studies were performed using NONMEM version 7.5.0 (ICON Development Solutions, Dublin, Ireland) with GNU Fortran (GNU Compiler Collection version 4.7.2; Free Software Foundation, Boston, MA).

The studies were conducted using a “replicated” design—a two- formulation, two-sequence, four-period, replicated, crossover design as represented in (Table 1).

Table 1: Two sequence four period, and two formulation replicated design used for the simulations.

The between-subject-variability and within-subject variability was set at 15% for all simulations. These values were chosen based upon preliminary simulations to keep the least square means values below 30% (i.e., the threshold for highly variable drugs) and σD (i.e., subject-by-formulation standard deviation) less than 0.17, the upper-level value cited in the FDA guidance [5]. Ordinary sampling times were: Pre-dose (0 hr), and 0.25 hrs, 0.5 hrs, 1 hr, 1.5 hrs, 2 hrs, 3 hrs, 4 hrs, 5 hrs, 6 hrs, 6.5 hrs, 7 hrs, 7.5 hrs, 8 hrs, 10 hrs, 12 hrs, 16 hrs, and 24 hrs post-dose. Optimal sampling times were pre- dose (0 hr), and 0.1 hrs, 1.5 hrs, 3 hrs, 7 hrs, 12 hrs, and 24 hrs post- dose. The standard BE statistical analysis recommended by FDA [5] was performed on the resulting simulated data. The individual BE parameters pAUC: 0-3 hrs, pAUC: 3-7 hrs, pAUC: 7-12 hrs, AUC: 0-24 hrs (i.e., AUC_0-t), and C_max were log-transformed and analyzed. AUC_0-∞ was not analyzed since the T/R ratio and 90% CIs were similar to those for AUC_0-t due to the drug’s very short half-life of 3.5 hr [9]. A single 40-subject study (generic test product vs. Concerta^®) was simulated 1000 times. A linear mixed-effects model was used for the study analysis. The mixed model generalizes the standard linear model as:

Y= X β + Zγ + ε

Where γ is an unknown vector of random effects parameters with known design matrix Z and is an unknown random error vector whose elements may not be independent and homogeneous. It is also assumed that γ and ε are Gaussian random variables that are uncorrelated and have expectations 0 and variances G and R, respectively.

All parameters were fixed to the reference published values except for K0fast (test) and KAslow (test). Simulations were done by observing changes in one absorption rate constant while the other was fixed at the published reference value. Each individual K0fast (test) and KAslow (test) value was increased or decreased from the published reference value to give the desired individual K0fast (test)/K0fast (reference) and KAslow (test)/KAslow (reference) ratio. Subsequent changes in the T/R ratios for K0fast (test) and KAslow (test) were done to determine how close were the 90% Cis for BE parameter values between simulations using ordinary sampling times vs. those using optimal sampling times with the above referenced changes in the absorption rate constants made for both sampling schemes.

The Fa was fixed to 1.00 for all simulations except those that investigated Fa at T/R levels of 0.8. 0.90, 0.95, and 1.00. The simulations for Fa were done under the assumption that the BA was more likely to decrease rather than increase, other than for dose dumping.

Power and type 1 error

Power and type 1 error were determined as in a prior published study [11], except the comparisons were for results using ordinary sampling times vs. simulated optimal sampling times for generic product vs. Concerta^®.

Additional studies 1 and 2-experimental be data and simulations

Two additional studies were done as described below to add further proof of applicability of an optimal sampling design to that of an ordinary sampling design for use in BE studies (proof of concept).

Study 1 was done by comparing results from the experimental replicated BE study of the generic drug product vs. Concerta^® performed using ordinary sampling with results that would have been obtained from the clinical study if optimal sampling had been used instead.

Study 2 was a separate simulated study done to challenge the validity of the Primary Simulated Study results by conducting additional BE study simulations comparing BE results obtained using lower and higher PK model parameter T/R ratio values for test MP of (0.95 Fa, 0.85 KAfast, 0.85 KAslow) and (0.95 Fa, 1.15 KAfast, 1.15 KAslow).

Results

Primary simulation study

( Figure 1), (upper plot) shows the generic test product vs. Concerta^® reference product mean plasma levels for sequence 1- (period 1 (T) vs. period 2 (R) and period 3 (T) vs. period 4 (R)). Figure 1 (lower plot) shows T vs. R mean plasma levels for sequence 2- (period 1 (R) vs. period 2 (T) and period 3 (R) vs. period 4 (T)). The graphs clearly show the overlap of the test and reference product mean plasma levels.

Figure 1: Mean graphs for the sequences and periods for the generic methylphenidate vs. Concerta^®. Concerta.

(Figure 2) shows the impact of changes in KAfast T/R ratios at values of 0.8, 1, 1.10, and 1.25 on the BE metrics of pAUC: 0-3 hrs, pAUC: 3-7 hrs, pAUC: 7-12 hrs, and AUC: 0-24 hrs for ordinary vs. optimal sampling. All studied KA ratios resulted in pAUC parameters within the 0.8-1.25 acceptable 90% CI limits except for pAUC: 0-3 hrs at the 0.8 KA ratio. At the 0.8 ratio, the lower limit value for ordinary sampling was 0.78 while that for optimal sampling was 0.79, both outside the acceptable BE criteria. The other occasion when the CIs exceeded the limit was at the 1.25 KAfast T/R ratio for pAUC: 0-3 hrs which resulted in upper 90% CI values of 1.25 for ordinary sampling and 1.24 for optimal sampling. In both cases the CIs did not exceed the BE upper limit of 1.25. Other CIs that showed a notable difference between ordinary and optimal sampling were those for pAUC: 7-12 hrs. Although neither the ordinary or optimal sampling 90% CI values were near the upper or lower BE limits for failure, ordinary sampling resulted in a wider CI range compared with optimal sampling as the KAfast T/R ratios moved closer to 0.8. In contrast, optimal sampling had a narrower range for the 90% CIs than did original sampling and was more responsive to increases in the T/R ratio at 1.25. This may be related to the increase in intersubject variability from 10% in a prior published simulation to 15% in the current simulations [11].

Figure 2: 90% confidence intervals for Concerta^® simulations where KAslow and Fa were held constant at the reference values (0.40 and 0.32 respectively) while the KAfast (test) values were increased from a Test/Reference ratio of 0.8 to 1.25. The confidence intervals are for the bioequivalence parameters pAUC: 03 hrs, pAUC: 37 hrs, pAUC: 712 hrs, and AUC: 024 hrs. The blue graph represents ordinary sampling while the red graph is for optimal sampling.

(Figure 3) is the plot for KAslow at the same T/R ratios as for KAfast in Figure 2. There were similar 90% CI ranges for ordinary vs. optimal sampling; none were above or below the BE CI limits of 0.80-1.25. The only CI range that showed major differences between the sampling schemes was for pAUC: 7-12 hrs with the range for ordinary sampling always wider; however, both were still well within the acceptable CI BE range at all studied T/R ratios.

Figure 3: 90% confidence intervals for Concerta^® simulations where KAfast and Fa were held constant at the reference values (1.11 and 0.32 respectively) while the KAslow (test) values were increased from a Test/Reference ratio of 0.8 to 1.25. The confidence interval designations are the same as for Figure 3.

(Figure 4) shows pAUC results for Fa T/R ratios of 0.80, 0.90, 0.95, and 1.00 for ordinary vs. optimal sampling. The T/R ratios of 0.80 and 0.90 resulted in all pAUC BE metric CI ranges being at or below the acceptable lower BE limit of 0.80. CI ranges were similar for all BE metrics except for pAUC: 7-12 hrs where ordinary sampling had a noticeably wider range than did optimal sampling. A result of the increased range for the pAUC: 7-12 hrs CI resulted in all T/R ratios being either at or below 0.8 except for ratio=1. The upper CI for pAUC: 7-12 hrs never exceeded the upper acceptance limit of 1.25. (Figure 5) shows what effect changes in the T/R ratios (from 0.8-1.0) for KAfast, Kaslow, and Fa have on C_max. Only when the Fa T/R ratio was 0.80 did the lower 90% CI for C_max go below the lower acceptable BE limit of 0.80.

Figure 4: 90% confidence intervals for Concerta^® simulations where Kafast and Kaslow were held constant at the reference values while the Fa(test) values were increased from a Test/Reference ratio of 0.8 to 1.0. The confidence intervals are for the bioequivalence parameters pAUC: 03 hrs, pAUC: 37 hrs, pAUC: 712 hrs, and AUC: 024 hrs. The blue graph represents ordinary sampling while the red graph is for optimal sampling.

Figure 5: 90% confidence intervals for Concerta^® for the BE parameter C_max while KAfast (Test), Kaslow (Test) to reference ratios were allowed to vary between 0.8 to 1.0 and Fa (test) being varied between 0.8 to 1.0. References values for these parameters were held constant at the reference values. The blue graphs represents ordinary sampling while the red graph is for optimal sampling.

(Figure 6) shows what effect changes in the T/R ratios (from 1.10- 1.25) for KAfast and KAslow have on C_max. All the resulting CIs for C_max were within the 90% CI acceptable BE limits. Fa was not investigated for T/R above 1.00.

Figure 6: 90% confidence intervals for Concerta^® for the BE parameter Cmax while KAfast (Test), Kaslow (Test) to reference ratios were allowed to vary between 0.8 to 1.0 and Fa (test) being varied between 0.8 to 1.0. References values for these parameters were held constant at the reference values. The blue graphs represents ordinary sampling while the red graph is for optimal sampling.

Type 1 error

The results for type 1 error determined using experimental data for ordinary sampling vs. simulated sampling for generic product vs. Concerta^® are presented in (Table 2). The results for ordinary vs. optimal sampling times were comparable in most cases and all were below the nominal 5% value.

Table 2: K0fastT/K0fastR (Test/Reference) and KaslowT/KaslowR (Test/Reference) Ratios which were changed for Concerta^® and the resulting Type 1 Error Rates at H0; 80% for the Designated BE parameters for ordinary and optimal times. N=1000 simulations.

Additional studies 1 and 2 (proof of concept)

The results from Study 1 compared the use of (experimental study data) for ordinary sampling vs. simulated data for optimal sampling for the replicated BE study are given in (Table 3). The results indicate that the 90% CIs and T/R ratios were indistinguishable between experimental ordinary sampling and simulated optimal sampling.

Table 3: Replicated fasting study BE study results for a fasting bioequivalence study between a Concerta^® generic drug X and Concerta^® with ordinary sampling vs. optimal sampling.

The results from Study 2, a simulated BE study comparing a generic drug product vs. Concerta^® using ordinary vs. optimal sampling are given in (Table 4).

Table 4: 90% confidence intervals for proof of concept simulations at selected lower model parameter values (0.95 Fa, 0.85 Kafast, 0.85 Kaslow) and at selected upper model parameter values (0.95 Fa, 1.15 Kafast, 1.15 Kaslow) for Concerta^®.

In Study 2, the T/R ratios for K0fast, KAslow, and Fa were raised and lowered to investigate what effect, if any, this would have on BE findings for ordinary vs. optimal sampling. The results indicated that the BE results for ordinary vs. optimal sampling were essentially the same despite the changes in the PK plasma sampling times

Discussion

Based upon the results of this and other investigations [11], it becomes apparent either through observation or use of correlations that specific pAUC BE metrics are influenced more by one PK parameter than by others. In the case of Concerta^®, KAfast mainly impacts pAUC: 0-3 hrs whereas KAslow influences all other pAUC and C_max values. It is also apparent that Fa impacts all pAUC values. The overall effect may be related to inter and intra-subject variability.

The objective of this study was to take a closer look at the possible impact of optimal sampling on pAUC values since prior studies had shown the impact on AUC. The study by Kong FH and Gonin R [7], had concluded that, “the optimization approach for calculating optimal time designs for one-compartment models works well, but is sufficiently general for other compartmental models. It was concluded that the optimal design improves the accuracy of AUC estimation.”

Our results not only support this conclusion but expand their findings to also include drugs with complex absorption (i.e., Concerta^®) analyzed with a replicated-design BE study. This lends further support to the contention that optimal sampling should also be applied to BE studies for drugs having a wider range of compartmental models since the current research clearly supports its application to drugs with complex absorption.

Our study results have also shown that the point estimates and 90% CI for the BE metrics studied gave similar results for original sampling vs. optimal sampling. In the case of the comparison of simulated optimal sampling data to actual experimental data for ordinary sampling (e.g., the generic MP ER oral tablet drug product vs. Concerta^® BE study described earlier) the 90% CI results were essentially the same.

A possible point of concern for utilization of optimal sampling would be that the T/R ratios for Fa should be within a specified range, perhaps 5% to 10% of the reference but that may prove to be drug and model dependent and would likely require extensive simulation study results to support the final desired T/R ratio resulting from the firm’s pilot study when one wants to use optimal sampling.

The FDA Office of Generic Drugs had a meeting to discuss their Model Master File (MMF) in May 2024 [14], and the potential regulatory applications of a MMF.

Based upon the results of the current study, optimal sampling for use with specific PK models should be a part of the planned MMF.

On a practical level the findings presented here should influence BE study design and cost. Using ordinary sampling, the experimental generic vs. Concerta^® MP study had 24 post-dose samples taken. The Primary Simulation Study had 18 ordinary samples and only 7 optimal samples.

Conclusion

The use of optimal sampling would result in fewer samples taken for analysis thus reducing study cost and improving the safety profile for subject volunteers. These factors would benefit not only the firm sponsoring the study and the study subjects, but the entire domain of generic drug development, including regulatory agencies and the public at large. The current study looked at a drug with complex absorption but that is not highly variable. Additional studies need to be conducted to determine the utility of optimal sampling for the highly variable class of drugs.

Conflict of Interest

There are no conflicts of interest associated with this manuscript.

Funding Statement

This study received no funding.

Acknowledgment

The authors would like to thank Mr. Larry Ouderkirk for his help in editing this manuscript.

Author Contributions

1) Andre J. Jackson-Wrote the paper and prepared Figures, 2) Mutaz Jaber-Performed the optimal Sampling, 3) Henry C. Foehl-Did the statistical analysis, 4) Inder Chaudhary-Supplied the Human Data and helped edit the paper.

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