Pharmaceutical Research, Vol. 17, No. 5, 2000 Research Paper rate of absorption (1–8). However, in contrast to the extent of Sensitivity of Empirical Metrics of absorption, the profile of absorption rate often cannot be Rate of Absorption in described by only one parameter. Tozer et al. (5) proposed the bioequivalence of two drug Bioequivalence Studies products could be evaluated by comparing three measures of drug exposure. One of these would be an index of early exposure and would characterize the early phase of the concentration- Arne Ring, 1 Laszlo Tothfalusi, 2 Laszlo Endrenyi, 3 time curves. The idea was incorporated into a recently published and Michael Weiss 1,4 draft guidance of the FDA (9). Thus, two questions arise. First, do the results obtained for the kinetic sensitivity of indirect metrics on the basis of the Received January 1, 2000; accepted February 8, 2000 most simple absorption model apply also under other conditions Purpose. The sensitivity and effectiveness of indirect metrics proposed of absorption, e.g., to extended-release dosage forms? (The for the assessment of comparative absorption rates in bioequivalence first-order absorption model implies exponentially distributed studies [C max , T max , partial AUC (AUC p ), feathered slope (SL f ), intercept absorption times and is abbreviated as the EX model.) Second, metric (I )] were originally tested by assuming first-order absorption. do the indirect metrics also account for other changes in the The present study re-evaluates their sensitivity performances using the absorption process (i.e., in the resulting oral concentration time more realistic inverse Gaussian (IG) model characterizing the input profile) than those described by k a ? process for oral drug administration. It is the purpose of this paper to study the kinetic sensitivi- Methods. Simulations were performed for both the first-order or expo- ties of previously proposed indirect metrics by using a more nential model (EX) which is determined by only one parameter, the flexible absorption model which has been successfully applied mean absorption time (MAT = 1/k a ), and the IG model, which addition- ally contains a shape parameter, the relative dispersion of absorption to sustained release formulations (10,11); the model was also time distribution (CV 2 A ). Kinetic sensitivities (KS) of the indirect met- capable to fit literature data (12) of three oral chlorprothixene rics were evaluated from bioequivalence trials (error free data) gener- formulations (solution, suspension, and tablet) (unpublished ated with various ratios of the true parameters (MAT and CV 2 A ) of the results). This input model assumes an inverse Gaussian distribu- two formulations. tion of the absorption times (IG model). It contains two parame- Results. The behavior of the metrics was similar with respect to ters, the mean absorption time (MAT ) which corresponds to k a changes in MAT ratios with both models: KS was low with C max , of the first-order model (MAT = 1/k a ) and acts as a scale moderate with SL f and AUC p , and high with I and T max following parameter of the input function, and the relative dispersion of correction for apparent lag time (T lag ). Changes of the shape parameter the absorption times (CV 2 A ) which is a shape parameter of the CV 2 A , however, were not detectable by C max , T max , SL f , and AUC p . absorption rate vs. time profile of the IG model. Interestingly, Changes in both MAT and CV 2 A were well reflected by I with CV 2 A - ratio  1. I exhibited approximately full KS also with CV 2 A -ratio  the latter also accounts for the problem of an apparent lag 1 when a correction was first applied for the apparent lag time. time in the concentration-time profiles of drugs following oral Conclusions. The time profile of absorption rates is insufficiently char- administration which is conventionally treated as a separate case acterized by only one parameter (MAT ). Indirect metrics which are of the EX model, the first-order absorption with lag time (13). sensitive enough to detect changes in the scale and shape of the input profile could be useful for bioequivalence testing. Among the tested measures, I is particularly promising when a correction is applied METHODS for T lag . Exponential and Inverse Gaussian Models KEY WORDS: bioequivalence; absorption rate; extended-release; mean absorption time; relative dispersion. The parameters bioavailability (F ) and mean absorption time (MAT ) completely determine the exponential density (EX) INTRODUCTION characterizing first-order absorption (MAT = 1/k a ). In the pres- ence of a lag time (T lag ) for absorption, the absorption density The role of secondary metrics for the assessment of bioe- with the EX model becomes: quivalence, which accounts for the influence of the rate of absorption, or more generally the shape of the concentration- f A (t) =  0 t  T lag F MAT -1 e -(t-Tlag)/MAT t  T lag (1) time profile in the early phase, has been of interest in recent years. The sensitivity of indirect metrics to changes in the shape of the early concentration profile was tested in simulation The use of the inverse Gaussian density as a model for the studies assuming first-order absorption and taking the absorp- assessment of drug absorption has been described in detail tion rate constant k a as a “gold standard” for defining the initial elsewhere (10). The inverse Gaussian (IG) density f A (t) = F  MAT 2CV 2 A t 3 exp  - (t - MAT ) 2 2CV 2 A MAT t  (2) 1 Section of Pharmacokinetics, Department of Pharmacology, Martin Luther University Halle-Wittenberg, 06097 Halle, Germany. contains an additional parameter, the relative dispersion 2 Department of Pharmacodynamics, Semmelweis Medical University, (CV 2 A ) in the distribution of absorption times. CV 2 A describes Budapest, Hungary. the shape of the absorption rate vs. time profile: equation 2 3 Department of Pharmacology, University of Toronto, Canada. attains its maximum at the time T A, max , and the ratio T A, max /MAT 4 To whom correspondence should be addressed. (e-mail: michael. weiss@medizin.uni-halle.de) is completely determined by CV 2 A (10). While for the EX model, 583 0724-8741/00/0500-0583$18.00/0  2000 Plenum Publishing Corporation