The Duration of Measuring Partial AUCs for the Assessment of Bioequivalence

Purpose. To determine favourable sampling conditions for assessing bioequivalence by the comparison of partial AUCs in the early phase of concentration-time profiles. Methods. Two-period crossover trials were simulated. They assumed a wide range of the ratios of absorption rate constants of the test (T) and reference (R) formulations (k_aT/k_aR). Averages and standard deviations of the corresponding ratios of simulated partial AUCs (AUC_pT/AUC_pR) were determined together with the statistical power of assessing bioequivalence, i.e., the percentage of simulated trials in which bioequivalence was declared. Results. The power for stating bioequivalence was high when AUC_P was recorded until the earlier rather than the later of two peaks in each subject. Similarly, power was comparatively high when AUC_P was measured until the time of the reference peak instead of multiples of this time. Power was high also when AUC_p was determined until the fixed true, population mean time of the reference formulation instead of multiples of this time. The pattern for the kinetic sensitivity parallelled that found for the power, while the standard deviations changed generally in the opposite direction. Conclusions. The effectiveness (power) of evaluating bioequivalence in the early phase of concentration-time profiles by partial AUCs generally decreases when the duration for measuring the metric is extended. Among the investigated designs, determination of partial AUCs until the earlier of two peaks in each subject is the most powerful.     

An Alternative Approach for Assessment of Rate of Absorption in Bioequivalence Studies

The partial area method was investigated for evaluation of equivalency in the rate of absorption of immediate release formulations. The applicability of the method was demonstrated with four drugs with different pharmacokinetic/pharmacodynamic characteristics. The confidence interval approach currently employed for bioequivalence determinations was applied to the relevant absorption parameters, including C _max and partial AUCs. The method was found to be more discriminating than C _max and/or T _max in the evaluation of the absorption rate of drugs. The cutoff time or point for partial AUC calculation may vary with the type of drug under study, depending on its clinical use and onset of action. The method was shown to be useful in the assessment of rate of absorption in bioequivalence studies.     

An Improved Intercept Method for the Assessment of Absorption Rate in Bioequivalence Studies

Pharmaceutical Research -     

Sensitivity of Empirical Metrics of Rate of Absorption in Bioequivalence Studies

Purpose. The sensitivity and effectiveness of indirect metrics proposedfor the assessment of comparative absorption rates in bioequivalencestudies [C _max , T _max , partial AUC(AUC _p ), feathered slope (SL _f ), interceptmetric (I)] were originally tested by assuming first-order absorption.The present study re-evaluates their sensitivity performances using themore realistic inverse Gaussian (IG) model characterizing the inputprocess for oral drug administration. Methods. Simulations were performed for both the first-order orexponential model (EX) which is determined by only one parameter, themean absorption time (MAT = 1/k _a ), and the IG model, whichadditionally contains a shape parameter, the relative dispersion of absorptiontime distribution (CV ² _A ). Kinetic sensitivities (KS) of the indirectmetrics were evaluated from bioequivalence trials (error free data)generated with various ratios of the true parameters (MAT and CV ² _A ) of thetwo formulations. Results. The behavior of the metrics was similar with respect tochanges in MAT ratios with both models: KS was low with C _max ,moderate with SL _f and AUC _p , and high with I and T _max followingcorrection for apparent lag time (T _lag ). Changes of the shape parameterCV ² _A , however, were not detectable by C _max , T _max , SL _f , and AUC _p .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 <1 when a correction was first applied for the apparent lag time. Conclusions. The time profile of absorption rates is insufficientlycharacterized by only one parameter (MAT). Indirect metrics which aresensitive enough to detect changes in the scale and shape of the inputprofile could be useful for bioequivalence testing. Among the testedmeasures, I is particularly promising when a correction is appliedfor T _lag .     

The Cutoff Time Point of the Partial Area Method for Assessment of Rate of Absorption in Bioequivalence Studies

The partial area method has been suggested for the assessment of the absorption rate in bioequivalence studies. This paper provides a theoretical basis for the estimation of the optimal cutoff time point of the partial areas for drugs with one compartment model disposition. The analysis is performed by using the appropriate equations which relate the normalized (in terms of the extent of absorption) partial areas with time expressed in terms of multiples of half-life. Provided that the quality of experimental data ensures precise estimation of the parameters, the t_max of the formulation with the faster absorption characteristics is generally the most practical cutoff time point for calculation of the normalized partial areas, when a drug follows one compartment model disposition with linear absorption.     

Without Extrapolation,Cmax/AUC is an Effective Metric in Investigations of Bioequivalence

Pharmaceutical Research -     

Bioequivalent or Nonbioequivalent?

The current tests for bioequivalence are based on assumptions that are not valid in general; this paper shows why it is necessary to use a method that does not depend upon assumptions that cannot, and need not, be proved in general.     

高效液相色谱法测定人血浆中文拉法辛的质量浓度及生物等效性研究

目的建立高效液相色谱（HPLC）法用于测定文拉法辛在人体血浆中的质量浓度和计算药代动力学参数。方法 18名健康志愿者单剂量口服盐酸文拉法辛胶囊6粒,肘静脉取血并分取血浆,血样经液-液萃取,采用Diamonsil（钻石）ODS色谱柱（250 mm×4.6 mm,5μm）,以乙腈-pH=6.8的磷酸盐缓冲液（32∶68）为流动相,检测波长229 nm,流速1.0 mL/min,检测器灵敏度0.01 AUFS,进样量20μL。结果受试制剂和参比制剂中文拉法辛的主要药动学参数,达峰时间为（2.11±0.21）h和（2.08±0.19）h,达峰时药物浓度为（130.78±27.78）ng/mL和（133.52±32.05）ng/mL,消除相半衰期为（5.11±1.84）h和（5.44±2.12）h,药时曲线下面积AUC0-24为（438.67±70.70）ng/（mL.h）和（449.78±79.96）ng/（mL.h）,药时曲线下面积AUC0-∞为（530.34±87.91）ng/（mL.h）和（528.12±81.77）（ng/mL.h）。结论经统计学分析,两种盐酸文拉法辛胶囊具有生物等效性。     

Optimizing Metrics for the Assessment of Bioequivalence Between Topical Drug Products

PURPOSE: Stratum corneum tape stripping post-application of a drug product followed by analysis of the active agent in this tissue layer is an approach being seriously considered for the comparative assessment of topical bioavailability. Key issues revolve around how best to perform this experiment and interpret the data. METHODS: Using previously published results from a comparative study of three 0.025% tretinoin gel products, alternative data analysis approaches are presented that may render the technique more accessible to the evaluation of new and generic topical dosage forms. RESULTS: For the tretinoin gel study, the conclusions for bioequivalence from measurements of drug levels at only one uptake and one clearance time were the same as those from the original study, which required measurements at eight different treatment times. Furthermore, comparisons of drug levels at one uptake and one clearance time discriminated differences in bioequivalence for clearance and uptake, which had previously been missed. Half-life estimates, derived from time course data of drug clearance, can be related to lag time for drug penetration through the SC. CONCLUSIONS: This new data analysis demonstrates that comparative bioequivalence might be assessed more easily.     

Why Rate of Absorption Inferences in Single Dose Bioequivalence Studies are Often Inappropriate

Purpose. Peak drug concentration (C_max) measures the extremity of drug exposure and is a secondary indicator of the extent of absorption after area under the concentration time curve (AUC). C_max serves as the indicator of absorption rate in bioequivalence (BE) studies in the US (1). The use of C_max, not the time to Cmax(Tmax), as the metric to assess absorption rate causes erratic inferences in BE studies, and incorrect conclusions for some. We can improve BE efficiency (i.e., get the answer right the first time), by properly analyzing the time to C_max(T_max) instead of C_max. Methods. We have previously redirected attention to T_max as the unconfounded absorption rate variable, instead of Cmax, and have called for equally spaced sampling times during the suspected absorption phase to improve the performance of the rate metric (2). Equal spacing converts T_max easily into a count variable and we illustrated an appropriate statistical analysis for counts. This paper provides some measurement theory concepts to help judge which is the more appropriate analysis, and also provides parametric confidence limits for T_max treatment differences. Three separate BE studies are then analyzed by both methods. Results. By focusing on the differences in conclusions, or inferences, this paper identifies three major issues with the current FDA "recommended analysis of BE studies. First, C_max, a continuous variable peak-height or extent measure has usurped T_max's function and performs erratically as a substitute measure for the rate of absorption. Second, T_max, should be analyzed as a discrete attribute, not as a continuous variable. Third, since several extent measures (AUC, C_max), not one, are actually being analyzed, an adjustment for multiple testing is mandatory if we are to maintain the size of the test at the desired level (13), and not inadvertently use a narrower bioequivalence window than is intended. These actions all can have serious unintended consequences on inferences, including making inappropriate ones.     

Tmax: An Unconfounded Metric for Rate of Absorption in Single Dose Bioequivalence Studies

Purpose. While peak drug concentration (Cmax) is recognized to be contaminated by the extent of absorption, it has long served as the indicator of change in absorption rate in bioequivalence studies. This concentration measure per se is a measure of extreme drug exposure, not absorption rate. This paper redirects attention to Tmax as the absorption rate variable. Methods. We show that the time to peak measure (Tmax), if obtained from equally spaced sampling times during the suspected absorption phase, defines a count process which encapsulates the rate of absorption. Furthermore such count data appear to follow the single parameter Poisson distribution which characterizes the rate of many a discrete process, and which therefore supplies the proper theoretical basis to compare two or more formulations for differences in the rate of absorption. This paper urges limiting the use of peak height measures based on Cmax to evaluate only for dose-dumping, a legitimate safety concern with, any formulation. These principles and techniques are illustrated by a bioequivalence study in which two test suspensions are compared to a reference formulation. Results. Appropriate statistical evaluation of absorption rate via Tmax supports bioequivalence, whereas the customary analysis with Cmax leads to rejection of bioequivalence. This suggests that the inappropriate use of Cmax as a surrogate metric for absorption rate contributes to the unpredictable and uncertain outcome in bioequivalence evaluation today.     

A Note on Sample Size Determination for Bioequivalence Studies with Higher-Order Crossover Designs

Similar to Liu and Chow, approximate formulas for sample size determination are derived based on Schuirmann's two one-sided tests procedure for bioequiealence studies for the additive and the multiplicative models under various higher order crossover designs for comparing two formulations of a drug product. The higher order crossover designs under study include Balaam's design, the two-sequence dual design, and two four-period designs (with two and four sequences), which are commonly used for assessment of bioequivalence between formulations. The derived formulas are simple enough to be carried out with a pocket calculator. The number of subjects required for each of the four higher order designs are tabulated for selected powers and various parameter values.     

Comparison of Single and Multiple Dose Pharmacokinetics Using Clinical Bioequivalence Data and Monte Carlo Simulations

The purpose of this study was to evaluate the relative performance and usefulness of single dose (SD) and multiple dose (MD) regimens for bioequivalence (BE) determination. Drugs such as indomethacin, procainamide, erythromycin, quinidine, nifedipine were tested for BE under SD and MD dose regimens. Drugs characterized by low accumulation indices (AI) showed virtually no change in the 90% confidence interval (CI) of AUC and CMAX upon multiple dosing. On the other hand, drugs with higher AI appeared to have smaller CI at steady-state. For example, the CI range of AUC and CMAX of quinidine (AI of 1.54) decreased from 26 to 12 and from 22 to 12, respectively, upon multiple dosing. A Monte Carlo simulation study of SD and MD bioequivalence trials was performed. The probability of failing the bioequivalence test was evaluated for several situations defined by different levels of variability and correlation in ka constants, presence or absence of inter- and/or intra-individual variability in clearance (CL) and volume of distribution (V), and different degrees of accumulation. All the possible combinations of these factors were tested with SD and MD study designs. All simulations used 1000 data sets with 30 subjects in each data set for a total of 144 unique designs (total of 144,000 simulations of bioequivalence trials). Upon multiple dosing, narrowing of CI ranges was observed for drugs simulated to have high AI, high variability and a large difference in absorption constants (ka) between test and reference formulations. The mean AUC and CMAX CI ranges for this situation decreased from 15 to 6 and from 16 to 10, respectively, in going from SD to MD design. Thus, there was concordance between simulated and experimental data. The probability of failing the bioequivalence test is shown to dramatically decrease upon multiple dosing due to the changes (range and shift) in the confidence interval.     

Evaluation of Different Metrics as Indirect Measures of Rate of Drug Absorption from Extended Release Dosage Forms at Steady-State

Bioequivalence assessment of extended release (ER) dosage forms is usually carried out at steady-state, using area under the curve (AUC) to evaluate extent of absorption and maximum concentration (C_max) and % peak trough fluctuation ratio (%PTF) to evaluate rate of absorption. Other metrics such as C_max/AUC and partial AUCs have recently been proposed as alternatives for assessing the absorption rate of drugs from immediate release (IR) dosage forms under single dose conditions. The performances of these metrics were assessed using the results of two sets of simulated experiments of ER dosage forms at steady-state and 2 actual pharmacokinetic studies involving ER dosage forms of a Glaxo drug. In the first set of simulations there was no difference in bioavailability between the two formulations; in the second set of simulations the test formulation had a 50% greater absorption rate-constant (ka) than the reference formulation. The following conclusions were reached: 1. For ER dosage forms at steady-state, all the metrics, with the exception of %PTF, resulted in much smaller increases than the underlying 50% increase in ka. Although, %PTF gave the largest effect it was also the most imprecisely estimated. 2. In our studies, none of the metrics tested provided reliable information about changes in the underlying rate of absorption from ER dosage forms under steady-state conditions. 3. The current practice of comparing rate of absorption from ER dosage forms using steady-state C_max is inappropriate due to lack of sensitivity. The use of %PTF may require a widening in the currently accepted 80-125% permissible range set for C_max and AUC.     

Evaluation of Bioequivalence of Highly Variable Drugs Using Monte Carlo Simulations. I. Estimation of Rate of Absorption for Single and Multiple Dose Trials Using Cmax

Purpose. A Monte Carlo simulation study was done to investigate the effects of high intrasubject variation in clearance (CL), and volume of distribution (V) on the calculation of the 90% confidence interval (CI) for Cmax for single dose and multiple dose studies. Methods. Simulations were done for both immediate release and sustained release scenarios. The simulated data were compared with clinical data from bioequivalence studies performed on indomethacin and verapamil. Results. Previous reviews and simulations have shown that the probability of failure for the Cmax for single dose studies was always greater than that for multiple dose studies. However, the results for the simulated scenarios currently investigated indicate that if intrasubject (period-to-period) variation in CL and V is high (% CV's above 25%, and 12%, respectively), multiple dose studies can exhibit a higher probability of failure for Cmax than do single dose studies. Furthermore, Cmax values from studies performed with a sustained release scenario are more sensitive to changes in Ka, CL, and V than are results of studies on immediate release products. As an example, the probability of failure for immediate release products in simulated single dose studies is about 11% and 21% when the mean difference in Ka is 10% and 20%, respectively; while, the probability of failure for multiple dose studies is about 36% regardless of the difference in Ka. The corresponding values for the probability of failure for sustained release products were 25%, 53% for single dose studies and 39% for multiple dose studies. The simulations also indicate that changes in the fraction absorbed have a greater effect on the estimation of Cmax in multiple dose regimens than in single dose studies. Conclusions. The results from these investigations indicate that multiple dose studies do not necessarily always reduce variability in Cmax.     

Sensitive and Specific Determination of the Equivalence of Absorption Rates

Purpose. To develop a new method for the direct, sensitive evaluation of the equivalence of absorption rates in linear kinetic systems. Methods. Concentrations are obtained before the earlier peak. Ratios of concentrations adjusted for the corresponding ratio of AUCs (area under the curve contrasting plasma concentration with time), or their logarithm, are extrapolated by linear regression to the time of drug administration. The intercept estimates the ratio of absorption rate constants (k_a), or its logarithm. Results. The intercept metric assesses the equivalence of absorption rates with very favourable characteristics. The metric reflects the k_a-ratio specifically (i.e., not affected by other kinetic parameters), is approximately linear to it, exhibits high kinetic sensitivity and excellent statistical properties. With many observations, the intercept metric has near-ideal features, including high power for determining bioequivalence and the ability to detect a 25% difference between k_a values. With only 3 or 4 measurements before the earlier peak, the performance of the metric depends on the preset regulatory conditions. Reasonably good power is noted if the bioequivalence limits determine a 50% difference between two metrics and, approximately, between two k_a values. The intercept metric shows very high power with a wider bioequivalence range. The power declines only moderately with increasing intraindividual variation of k_a. The equivalence of absorption rates is assessed with much higher power by the intercept metric than by C_max. Conclusions. The excellent kinetic and statistical properties of the intercept metric enable the specific and sensitive determination of the equivalence of absorption rates.     

苯酰甲硝唑分散片的血药浓度及生物等效性测定

目的:建立人血清中苯酰甲硝唑体内代谢产物--甲硝唑的反相高效液相色谱分析方法,比较苯酰甲硝唑分散片和苯酰甲硝唑胶囊生物等效性。方法:采用Eurosphex-100 C18柱,以乙腈-KH2PO4(0．01 mol·L-1)(22:78,v／v)为流动相,替硝唑作内标,紫外检测波长为318 nm,测定血清中甲硝唑的血药浓度。结果:血清中甲硝唑的浓度在0．1-20．0μg·ml-1范围内线性关系良好,r=0．999 9(n=8)。受试制剂及参比制剂的Cmax分别为(10．475±2．135)和(10．118±2．116),Tmax分别为(4．000±1．414)和(4．667±1．138)h,t1／2分别为(11．247±2．264)和(10．800±2．000)h,根据AUC0→t计算受试制剂的相对生物利用度为(100．9±20．2)％。结论:本方法操作简便、灵敏度高、重现性好,可用于血清中甲硝唑浓度的测定。苯酰甲硝唑分散片和苯酰甲硝唑胶囊具有生物等效性。     

LC-MS/MS测定人血浆中罗红霉素的浓度及其在生物等效性研究中的应用

目的建立LC-MS/MS测定人血浆中罗红霉素浓度的方法,并研究其制剂的生物等效性。方法以克拉霉素为内标,色谱柱:Alltech Alltima(2.1 mm×100 mm,3.5μm);流动相:0.1%甲酸溶液-乙腈(45∶55);流速:0.2 mL·min-1;柱温:30℃。采用三重四极杆串联质谱,电喷雾离子源,正离子模式检测,以选择反应监测(SRM)方式进行检测,罗红霉素母离子[M+H]+m/z 837.5,子离子m/z 679.2,内标克拉霉素母离子[M+H]+m/z 748.5,子离子m/z 590.2。结果罗红霉素线性范围为0.10～20.00μg·mL-1,最低检测限为0.01μg·mL-1,3种浓度的相对回收率为100.8%～103.1%,日内、日间RSD均<5.9%(n=5)。生物等效性研究表明受试制剂和参比制剂生物等效,受试制剂相对生物利用度为(100.655±9.552)%(P=0.5%)。结论该方法专属、灵敏、快速,适用于罗红霉素制剂的生物等效性研究。     

Limits for the Scaled Average Bioequivalence of Highly Variable Drugs and Drug Products

Purpose. To provide a rational procedure for establishing regulatory bioequivalence (BE) limits that can be applied in determinations of scaled average BE for highly-variable (HV) drugs and drug products. Methods. Two-period crossover BE investigations with either 24 or 36 subjects were simulated with assumptions of a coefficient of variation of 10, 20, 30, or 40%. The decline in the fraction of accepted studies was recorded as the ratio of geometric means (GMR) for the two formulations was raised from 1.00 to 1.45. Acceptance of BE was evaluated by scaled average BE, assuming various BE limits, and, for comparison, by unscaled average BE. A procedure for calculating exact confidence limits in two-period studies is presented, and an approximate method, based on the linearization of the regulatory model, is applied. Results. A mixed model is proposed for average BE. Accordingly, at low variabilities, the BE limit is constant, ±BEL_o, generally log(1.25). Beyond a logarithmic, limiting, switching variability (_o), in the region of HV drugs, the approach of scaled average BE is applied with limits of ±(BEL_o /_o). It is demonstrated that the performance of the mixed model corresponds to these expectations. The effect of _o and of the resulting BE limits is also demonstrated. Scaled average BE, with all reasonable limits for HV drugs, requires fewer subjects than an unscaled average BE. In two-period studies, the exact and approximate methods calculating confidence limits yield very comparable inferences. Conclusions. Scaled average BE can be effectively applied, with the recommended limits, for determining the BE of HV drugs and drug products. The limiting, switching variability (_o) will have to be established by regulatory authorities.