1. Australian Centre for Pharmacometrics
Comparison of non-compartmental analysis
and non-linear mixed effects ability to
determine bioequivalence in drugs with
two-compartment kinetics
Jim H Hughes1, Richard N Upton1, David J R Foster1
Australian Centre for Pharmacometrics
Australian Centre for Pharmacometrics, School of Pharmacy and Medical Sciences, Sansom Institute for Health Research, University of South Australia
Introduction and Aims
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Bioequivalence testing is employed by regulatory agencies to ensure generic drug products are the equivalent to their branded counterparts
This is commonly done using non-compartmental analysis (NCA)
NCA does not account for random unexplained variability (RUV) in measured concentrations and discards values below the limit of quantification (below LOQ)
Non-linear mixed effects modelling (NLMEM) can account for this but has been found to be no better in drugs with one-compartment kinetics
Drugs with two-compartment kinetics are more likely to be affected by NCA’s limitations due to the added complexity of the terminal phase
The aim was to determine if NLMEM has a greater ability to determine bioequivalence than NCA in drugs with two-compartment kinetics
Methods
A comparison tool was developed with R and NONMEM® able to simulate 500 bioequivalence studies for a hypothetical (or real) drug
Each bioequivalence study contained 24 participants
The hypothetical drug had two-compartment kinetics and was simulated with 30% coefficient of variation (CV) on parameters split between subject variability (BSV) and between occasion variability (BOV)
Simulations were made in R with very intense sampling to find the percentage of truly bioequivalent studies using the individual relative bioavailability parameters that were used for the simulation
This was then truncated for use with NCA and NLMEM
Truncated sampling schedule times were:
0.25, 0.5, 1, 2, 4, 6, 8, 12, 16, 24, 36, 48, 72 and 96 hours
NCA was undertaken in R using the same method as WinNonlin® NLMEM was performed using NONMEM® fitting the original model to the data for each study and provide MAP Bayes parameter estimates
The M1 and M3 methods were employed to compare the simple removal of below LOQ values with a maximum likelihood estimation method
Relative bioavailability (Frel) was determined in two ways:
'F estimate' – individual estimate of generic drug’s bioavailability
'Post-Hoc' – ratio of AUCs as determined by individual estimates of both clearance and bioavailability
Bioequivalence was determined using 90% confidence intervals calculating using a one-way ANOVA with acceptance limits of %
Multiple sets of 500 studies were tested with varying additive RUV, LLOQ and relative bioavailability of the generic formulation.
Eighteen sets were tested, half with the original sampling schedule, while the other half had a reduced sampling schedule
Figure 1: Relative bioavailability confidence intervals for 500 simulated studies
Each study contributes two dots representing the upper and lower 90% confidence intervals. If both dots are within the limits of % (represented by the dashed lines) then the study is bioequivalent. Dots within the limits are coloured blue while those outside are coloured red. Each plot represents a different method, with the 'Simulation' plot representing the analysis of individual relative bioavailability parameters used to simulate the intensely sampled data and 'Frel' plots representing the 'F estimate' method.
Figure 2: Accuracy of bioequivalence methods for differing additive RUV
Each plot shows the change in each methods accuracy as the percent of below LOQ values increases, split up by the amount of additive RUV that was used for simulation. 'Frel' – 'F estimate' method, 'PH' – 'Post-Hoc' method
Results
The tool allowed for simulation and analysis of 18 sets of 500 simulated studies testing differing simulated Frel, RUV, LOQ and sampling schedule
Use of M1 and M3 with NLMEM showed little difference with the chosen drug, while the 'F estimate' method was superior to the 'Post-Hoc' method (Figure 1) due to additional error introduced by using the individual estimate both clearance
NLMEM showed a 10-20% higher accuracy (Figure 2) and sensitivity in correctly identifying bioequivalent drugs when compared to NCA
However NLMEM exhibited a 1-20% lower specificity (Figure 3) compared to NCA when determining bioequivalence
Conclusion
Due to its higher accuracy and sensitivity non-linear mixed effect modelling is less likely to reject bioequivalent drugs
Given the higher specificity of non-compartmental analysis it is less likely to accept non-bioequivalent drugs
Figure 3: Specificity of bioequivalence methods for differing additive RUV
Each plot shows the change in each methods specificity as the percent of below LOQ values increases, split up by the amount of additive RUV that was used for simulation. 'Frel' – 'F estimate' method, 'PH' – 'Post-Hoc' method