Exposure-response analysis reveals that clinically important toxicity difference can exist between bioequivalent carbamazepine tablets

Abstract

Aims: To assess whether, using the current regulatory criteria, therapeutically important differences can exist between bioequivalent carbamazepine (CBZ) tablets. A secondary goal was to demonstrate quantitatively the relationship between the risk of neurological adverse effects to orally ingested CBZ and the rate of absorption.

Methods: Results of a bioequivalence study by Olling et al. (Biopharm Drug Dispos 1999; 20: 19-28) were reanalysed. Following an exploratory data analysis step, a mixed-effect pharmacokinetic-pharmacodynamic (PK-PD) model was built to describe the dependence of adverse events on the CBZ concentration.

Results: Rapid development of tolerance was demonstrated for most neurological adverse effects, with a characteristic half-life of 02.29 h and an initial EC50 of 2.33 mg l(-1). The resulting tolerance PK-PD model was characterized further using the tools and terminology of sensitivity analysis. It was demonstrated that the maximum concentration (C(max)) exhibits poor PK and PD sensitivities, and that clinically significant differences can exist between formulations which otherwise comply with the bioequivalence requirements. In contrast, another PK metric, the partial AUC, was a much better marker of the early neurological adverse events observable during the absorption phase of the drug.

Conclusions: In clinical and regulatory considerations, the development of acute tolerance for adverse effects of CBZ must be taken into account. Partial AUC reflects more sensitively the risk of adverse events than C(max). Instead of the current trend of tightening of the bioequivalence criteria for narrow therapeutic index drugs, the use of alternative, more sensitive PK metrics is proposed.

Figure 1

(A) Observed average carbamazepine concentrations of four formulations. (B) The pharmacokinetics (PK) of the four formulations was described with a single population PK model which assumed different absorption rate constants and biovailabilities, but the same clearance. The panel shows the observed concentrations (dots) and the predicted mean concentrations of the four formulations. Drug A, (•); Drug B, (▿); Drug C, (▪); Drug D, (◊). (C) As a diagnostic check of the assumed population model, the concentrations predicted by the model are plotted against the measured values

Figure 2

Time courses of concentrations and adverse events. In each panel, the measured carbamazepine concentration is plotted (small dots). When, at the same time, a volunteer reported an adverse effect, then instead of a small dot a black filled circle is shown

Figure 3

Estimated probabilities of having a particular adverse event as a function of time and carbamazepine plasma concentration. DIZ, Dizziness; DIP, diplopia; DRO, drowsiness; FAT, fatigue; HEA, headache; ABH, all adverse events but headache

Figure 4

Frequency of an adverse event as a function of the mean carbamazepine concentration. Hysteresis loops are shown which demonstrate that the time courses of concentrations and of effects are not completely superimposed. The observed frequencies of the adverse effects are connected in chronological order in the direction of the arrows. The plot shows ‘clockwise’ hysteresis, meaning that the effect decreases faster than the plasma concentration. This reveals tolerance to carbamazepine either by the development of a counter-regulatory mechanism or by the desensitization of receptors. (A) Dizziness. (B) Drowsiness. (C) All adverse events but headache

Figure 5

Comparison of the observed (dots) and predicted risk of adverse events. A tolerance PK–PD model (Equation 6) was fitted to the observed prevalences using mixed logistic regression. (A) Dizziness. (B) Drowsiness. (C) All adverse effects but headache. The dashed lines in (C) are the 90% confidence limits of the predicted risk. The term ‘all adverse events but headache’ means that at least one adverse event, not including headache, was recorded at the given time

Figure 6

(A) Concentration profiles of four hypothetical carbamazepine tablets (A′, (•); B′, (); C′, (▾); D′, (□)). The concentration profiles were simulated by assuming common distribution (V_d/F) and elimination (CL) parameters, but different absorption rate constants (k_a). The actual numerical parameters can be found in Table 1: CL and V_d/F, product D; k_a values, products A, B, C and D, respectively. (B) Predicted probabilities of observing adverse events with the hypothetical A′ (•); B′ (); C′ (▾); and the reference D′ (□) formulations. (C) Ratios of C_max, AUCP and Rmax relative to the reference formulation. A′, (▪); B′, (); C′, (); D′, ()

Figure 7

Relationships between logarithmic ratios of absorption rate constants, risks of adverse events, and bioequivalence metrics. The absorption rate constant was changed relative to the reference formulation and the corresponding AUCP, C_max and Rmax ratios were recorded. (A) Dependence of PK and PD metric ratios on the k_a ratio. (B) The relationship between PK and PD metric ratios. Ratios of PK metrics are plotted against the Rmax ratio