Bayesian Construction of an Improved Parametric Test for Probability‐Based Individual Bioequivalence

Assuming a lognormally distributed measure of bioavailability, individual bioequivalence is defined as originally proposed by Anderson and Hauck (1990) and Wellek (1990; 1993). For the posterior probability of the associated statistical hypothesis with respect to a noninformative reference prior, a numerically efficient algorithm is constructed which serves as the building block of a procedure for computing exact rejection probabilities of the Bayesian test under arbitrary parameter constellations. By means of this tool, the Bayesian test can be shown to maintain the significance level without being over‐conservative and to yield gains in power of up to 30% as compared to the distribution‐free procedure which gained some popularity under the name TIER. Moreover, it is shown that the Bayesian construction also allows scaling of the probability‐based criterion with respect to the proportion of subjects exhibiting bioequivalent responses to repeated administrations of the reference formulation of the drug under study.     

Mini-computer programs for bioequivalence testing of pharmaceutical drug formulations in two-way cross-over studies. Including a survey of current parametric evaluation techniques

For bioequivalence testing of pharmaceutical formulations of the same drug entity, it is not sufficient to carry out an analysis of variance on the characteristic to be evaluated (e.g., area under the plasma level vs time curve, half-life of elimination, time to plasma-peak level, plasma peak level) and to establish 'classical' 95% confidence intervals for the difference or the ratio of the characteristic concerned. In the past 10 years, several approaches have been proposed as an aid in decision-making: Westlake's 95% intervals, Rodda and Davis' probabilities, Fluehler's posterior probability histograms and the evaluation of the residual variation coefficient. A survey of these approaches is given, together with a discussion of their merits, their differences and their similarities. It is recommended that the final evaluation should be supported by probability density plots, which facilitate easy understanding of the differences and similarities between the various approaches. A bioequivalence study with two types of oral tablets containing bepridil, a new anti-anginal drug, is used as an example. Computer programs are presented, which enable the user to easily apply the various approaches in order to meet requirements of regulatory agencies.     

长半衰期药物无清洗期时的生物等效性研究

目的：探讨长半衰期药物（t1／2〉24h）在无清洗期时生物等效性研究中的AUC和Cmax的计算,通过无清洗期的实验数据推算出正常清洗期的数据。方法：利用SPSS软件,建立二室模型口服药物在无清洗期时的半衰期为100小时的生物等效性模型,通过优化AUC和Cmax的计算方法,降低药物残留对第二周期药物浓度的影响,进而增加AUC和Cmax的计算的精确性,最后用较精确的方法推算出正常清洗期的AUC和Cmax,利用精确的数据进行生物等效性的进一步验证。结果：在无清洗期的状态下,取样时间在大于0．8个半衰期时,平均值法计算的Auc和Cmax的结果误差小于5％,变异系数小于25％,较为精确,生物等效性研究进一步验证了这一观点。结论：在无清洗期的情况下,生物等效性研究最小的采样时间为0．8个半衰期。     

On Assessment of Bioequivalence for Drugs with Negligible Plasma Levels

In bioavailability studies, bioequivalence between drug products is usually determined based on some pharmacokinetic responses such as area under the blood or plasma concentration-time curve and maximum concentration. For some drug products, however, we may have negligible plasma levels because their intended routes of administration. In this case, assessment of bioequivalence between drug products of this kind may be established using clinical endpoints such as therapeutic response and time to the onset of a therapeutic response. In this paper, we propose two procedures which modify the method of generalized estimating equations (Liang and Zeger, 1986) and the proportional hazard models for paired failure times to assess bioequivalence between two drug products under the structure of a standard two-sequence, two-period crossover design. An example concerning a bioequivalence trial for albuterol metered dose inhaler indicated for acute bronchospasm (Herson, 1991) is used to illustrate the proposed procedures.     

Basing the Analysis of Comparative Bioavailability Trials on an Individualized Statistical Definition of Equivalence

The conventional definition of bioequivalence in terms of population means only, is criticized for lacking relevance to the individual subject. Both approaches to bioequivalence assessment proposed here for avoiding this shortcoming, focus on the probability of an event induced by the response of a randomly selected subject to two formulations of a given active agent. The first approach leads to converting the basic idea underlying the well-known 75-rule into an exact statistical procedure. The second approach is of a parametric nature. It reduces bioequivalence assessment to testing against the alternative hypothesis that the standardized expected value of a Gaussian distribution is contained in a short interval around zero. For this problem, an exact optimal solution is provided as well.     

A simple numerical approach towards improving the two one-sided test for average bioequivalence

For testing average bioequivalence, a simple test that improves upon the two-one sided test (TOST) is derived. The new test uses a critical value that is a non-increasing continuous function of the sample standard deviation, and the function is numerically obtained. Simulation results show that the resulting test performs well in terms of type I error probability; in particular, the test avoids the conservatism of the TOST. Consequently, the test provides better power compared to the TOST, especially when the variance becomes large. Numerical results also show that our test results in power that is very similar to the other improved tests available in the literature. An advantage of our improved test is that it is just as easy to carry out as the TOST. An example is used to illustrate the new test.     

Determining the Polymer Threshold Amount for Achieving Robust Drug Release from HPMC and HPC Matrix Tablets Containing a High-Dose BCS Class I Model Drug: In Vitro and In Vivo Studies

It is challenging to achieve mechanically robust drug-release profiles from hydrophilic matrices containing a high dose of a drug with good solubility. However, a mechanically robust drug release over prolonged period of time can be achieved, especially if the viscosity and amount of the polymer is sufficiently high, above the “threshold values.” The goal of this research was to determine the hydroxypropyl cellulose (HPC) and hydroxypropyl methylcellulose (HPMC) polymer threshold amount that would enable robust drug release from matrix tablets containing a high dose of levetiracetam as a class I model drug according to the Biopharmaceutical Classification System (BCS). For this purpose, formulations containing HPC or HPMC of similar viscosity range, but in different amounts, were prepared. Based on the dissolution results, two final formulations were selected for additional in vitro and in vivo evaluation to confirm the robustness and to show bioequivalence. Tablets were exposed to various stress conditions in vitro with the use of different mechanically stress-inducing dissolution methods. The in vitro results were compared with in vivo results obtained from fasted and fed bioequivalence studies. Under both conditions, the formulations were bioequivalent and food had a negligible influence on the pharmacokinetic parameters C_max and area under the curve (AUC). It was concluded that the drug release from both selected formulations is mechanically robust and that HPC and HPMC polymers with intrinsic viscosities above 9 dL/g and in quantities above 30% enable good mechanical resistance, which ensures bioequivalence. In addition, HPC matrices were found to be more mechanically robust compared to HPMC.KEY WORDS: HPC, HPMC, matrix tablets, mechanically robust dissolution, threshold amount     

An iterative method to protect the type I error rate in bioequivalence studies under two‐stage adaptive 2×2 crossover designs

Bioequivalence studies are the pivotal clinical trials submitted to regulatory agencies to support the marketing applications of generic drug products. Average bioequivalence (ABE) is used to determine whether the mean values for the pharmacokinetic measures determined after administration of the test and reference products are comparable. Two‐stage 2×2 crossover adaptive designs (TSDs) are becoming increasingly popular because they allow making assumptions on the clinically meaningful treatment effect and a reliable guess for the unknown within‐subject variability. At an interim look, if ABE is not declared with an initial sample size, they allow to increase it depending on the estimated variability and to enroll additional subjects at a second stage, or to stop for futility in case of poor likelihood of bioequivalence. This is crucial because both parameters must clearly be prespecified in protocols, and the strategy agreed with regulatory agencies in advance with emphasis on controlling the overall type I error. We present an iterative method to adjust the significance levels at each stage which preserves the overall type I error for a wide set of scenarios which should include the true unknown variability value. Simulations showed adjusted significance levels higher than 0.0300 in most cases with type I error always below 5%, and with a power of at least 80%. TSDs work particularly well for coefficients of variation below 0.3 which are especially useful due to the balance between the power and the percentage of studies proceeding to stage 2. Our approach might support discussions with regulatory agencies.     

An Investigation into the Influence of Experimental Conditions on In Vitro Drug Release from Immediate-Release Tablets of Levothyroxine Sodium and Its Relation to Oral Bioavailability

The aim of this study was to investigate the influence of experimental conditions on levothyroxine sodium release from two immediate-release tablet formulations which narrowly passed the standard requirements for bioequivalence studies. The in vivo study was conducted as randomised, single-dose, two-way cross-over pharmacokinetic study in 24 healthy subjects. The in vitro study was performed using various dissolution media, and obtained dissolution profiles were compared using the similarity factor value. Drug solubility in different media was also determined. The in vivo results showed narrowly passing bioequivalence. Considering that levothyroxine sodium is classified as Class III drug according to the Biopharmaceutics Classification System, drug bioavailability will be less sensitive to the variation in its dissolution characteristics and it can be assumed that the differences observed in vitro in some of investigated media probably do not have significant influence on the absorption process, as long as rapid and complete dissolution exists. The study results indicate that the current regulatory criteria for the value of similarity factor in comparative dissolution testing, as well as request for very rapid dissolution (more than 85% of drug dissolved in 15 min), are very restricted for immediate-release dosage forms containing highly soluble drug substance and need further investigation. The obtained results also add to the existing debate on the appropriateness of the current bioequivalence standards for levothyroxine sodium products.KEY WORDS: bioequivalence, dissolution, immediate release, levothyroxine sodium, solubility     

Overfitting,generalization, and MSE in class probability estimation with high‐dimensional data

Accurate class probability estimation is important for medical decision making but is challenging, particularly when the number of candidate features exceeds the number of cases. Special methods have been developed for nonprobabilistic classification, but relatively little attention has been given to class probability estimation with numerous candidate variables. In this paper, we investigate overfitting in the development of regularized class probability estimators. We investigate the relation between overfitting and accurate class probability estimation in terms of mean square error. Using simulation studies based on real datasets, we found that some degree of overfitting can be desirable for reducing mean square error. We also introduce a mean square error decomposition for class probability estimation that helps clarify the relationship between overfitting and prediction accuracy.     

Comparative study of azithromycin pharmacokinetics in healthy volunteers in open cross randomized procedure]

A method of quantitative determination of azithromycin in HPLC with mass spectrometric detection was developed. The detection limit is 0.5 ng/ml. The method was used in the study of pharmacokinetics and bioequivalence of Zi-Factor (capsules of 250 mg of azithromycin made by Veropharm, Russia) vs. reference-drug. The pharmacokinetic study was performed by the open cross randomized procedure in 18 volunteers. The pharmacokinetic parameters required for estimation of the drug bioequivalence were calculated. The statistical analysis of the pharmacokinetic parameters revealed bioequivalence of Zi-Factor and the reference-drug.     

A Confidence Region Approach for Assessing Equivalence in Variability of Bioavailability

The problem for assessment of equivalence in variability of bioavailability between two drug products is considered. Similar to the method for assessing bioequivalence in average bioavailability proposed by Chow and Shao (1990), an exact confidence region approach is derived when the intersubject variance is known. When the intersubject variance is unknown, a large sample approximation is considered. The proposed method for assessing equivalence of variability of bioavailability appears to be asymptotically uncorrelated with that of Chow and Shao (1990) for average bioavailability. As a result, the proposed method in conjunction with the method proposed by Chow and Shao (1990) constitutes a confidence region approach for assessing population bioequivalence. An example concerning a bioequivalence trial with 24 healthy volunteers is provided to illustrate the proposed method.     

The Total Least Squares Method in Individual Bioequivalence Evaluation

We propose a simple method for comparison of series of matched observations. While in all our examples we address “individual bioequivalence” (IBE), which is the subject of much discussion in pharmaceutical statistics, the methodology can be applied to a wide class of cross‐over experiments, including cross‐over imaging. From the statistical point of view the considered models belong to the class of the “error‐in‐variables” models. In computational statistics the corresponding optimization method is referred to as the “least squares distance” and the “total least squares” method. The derived confidence regions for both intercept and slope provide the basis for formulation of the IBE criteria and methods for its assessing. Simple simulations show that the proposed approach is very intuitive and transparent, and, at the same time, has a solid statistical and computational background.     

An Investigation into the Influence of Experimental Conditions on <Emphasis Type="Italic">In Vitro</Emphasis> Drug Release from Immediate-Release Tablets of Levothyroxine Sodium and Its Relation to Oral Bioavailability

The aim of this study was to investigate the influence of experimental conditions on levothyroxine sodium release from two immediate-release tablet formulations which narrowly passed the standard requirements for bioequivalence studies. The in vivo study was conducted as randomised, single-dose, two-way cross-over pharmacokinetic study in 24 healthy subjects. The in vitro study was performed using various dissolution media, and obtained dissolution profiles were compared using the similarity factor value. Drug solubility in different media was also determined. The in vivo results showed narrowly passing bioequivalence. Considering that levothyroxine sodium is classified as Class III drug according to the Biopharmaceutics Classification System, drug bioavailability will be less sensitive to the variation in its dissolution characteristics and it can be assumed that the differences observed in vitro in some of investigated media probably do not have significant influence on the absorption process, as long as rapid and complete dissolution exists. The study results indicate that the current regulatory criteria for the value of similarity factor in comparative dissolution testing, as well as request for very rapid dissolution (more than 85% of drug dissolved in 15 min), are very restricted for immediate-release dosage forms containing highly soluble drug substance and need further investigation. The obtained results also add to the existing debate on the appropriateness of the current bioequivalence standards for levothyroxine sodium products.     

Biopharmaceutics Classification System-Based Biowaivers for Generic Oncology Drug Products: Case Studies

Establishing bioequivalence (BE) of drugs indicated to treat cancer poses special challenges. For ethical reasons, often, the studies need to be conducted in cancer patients rather than in healthy volunteers, especially when the drug is cytotoxic. The Biopharmaceutics Classification System (BCS) introduced by Amidon (1) and adopted by the FDA, presents opportunities to avoid conducting the bioequivalence studies in humans. This paper analyzes the application of the BCS approach by the generic pharmaceutical industry and the FDA to oncology drug products. To date, the FDA has granted BCS-based biowaivers for several drug products involving at least four different drug substances, used to treat cancer. Compared to in vivo BE studies, development of data to justify BCS waivers is considered somewhat easier, faster, and more cost effective. However, the FDA experience shows that the approval times for applications containing in vitro studies to support the BCS-based biowaivers are often as long as the applications containing in vivo BE studies, primarily because of inadequate information in the submissions. This paper deliberates some common causes for the delays in the approval of applications requesting BCS-based biowaivers for oncology drug products. Scientific considerations of conducting a non-BCS-based in vivo BE study for generic oncology drug products are also discussed. It is hoped that the information provided in our study would help the applicants to improve the quality of ANDA submissions in the future.KEY WORDS: Biopharmaceutics Classification System, bioequivalence, biowaiver, cancer, oncology     

A two-stage procedure for bioequivalence studies

A two-stage experimental procedure for bioequivalence studies is proposed. The procedure is based on the idea that information from a first-stage experiment can be used to form a predictive distribution for the outcome of a second-stage experiment, thus permitting an assessment of the probability of a successful overall outcome. A systematic numerical study of a variety of possible strategies results in the identification of procedures that lead to substantial increases in efficiency compared with single-stage studies.     

9-fluorenylmethyl chloroformate as a fluorescence-labeling reagent for derivatization of carboxylic acid moiety of sodium valproate using liquid chromatography/tandem mass spectrometry for binding characterization: a human pharmacokinetic study

In High Performance Liquid Chromatographic (HPLC) determination of chemicals with acidic functions, different labeling agents are used to improve sensitivity of the assay. 9-Fluorenylmethyl chloroformate (FMOC-Cl), on the other hand, is a suitable labeling agent, which reacts with both primary and secondary amines and less readily with hydroxyl groups in alkaline conditions. However, the reagent has not been applied in labeling of chemicals with acidic function yet. In this study which is the first report on application of FMOC-Cl in derivatization and analysis of a drug with acidic function, valproic acid (VPA), one of a series of fatty carboxylic acids with anticonvulsant activity, was derivatized using the reagent and quantified in serum samples by HPLC with fluorescence detection. In addition, to document the reaction between the labeling agent and carboxylic acid moiety of the drug, we developed a liquid chromatography-tandem MS/MS (LC-MS/MS) method. Following liquid-liquid extraction, derivatization of the drug and an internal standard was achieved in alkaline medium. The elute was monitored by a fluorescence detector with respective excitation and emission wavelengths of 265 and 315 nm. The present method is more sensitive comparing with other published HPLC procedures for analysis of VPA. The assay is sensitive enough to measure drug levels obtained in human single dose studies with a limit of quantification of 0.01 μg/mL. Also the method is linear over the concentrations range of 0.01-32 μg/mL of VPA in human serum using 100 μL serum sample and 5 μL injection. The coefficient variation values of both inter and intra day analysis were less than 12% and the percentage error was less than 4%. The method performance was studied and the validated procedure applied in a randomized cross-over bioequivalence study of two different VPA preparations in 24 healthy volunteers.     

A Note on Testing Hypotheses about Trimmed Means

A well known result is that skewness can cause problems when testing hypotheses about measures of location, particulary when a one-sided test is of interest. Wilcox (1994) reports both theoretical and simulation results showing that when testing hypotheses about trimmed means, control over Type I error probabilities can be substantially better than methods for means. However, at least in some situations, control over the probability of a Type I error might still be judged to be inadequate. One way of adressing this concern is to combine trimmed means with the bootsrap method advocated by Westfall and Yuong (1993). This note reports simulation results indicating that there are situations where substantial improvements over Type I error probabilities are indeed obtained.     

Interval Estimation for Ratios in Bioequivalence Trials

The problem for assessment of equivalence in variability of bioavailability between two drug products is considered. An exact confidence region for the ratio between intrasubject variabilities is derived when the intersubject variance is known. When the intersubject variance is unknown, a large sample approximation is considered. The proposed method for assessing equivalence in variability of bioavailability appears to be asymptotically uncorrelated with the sample mean ratio for average bioavailabilty. As a result, the proposed method in conjunction with the sample mean ratio method can be utilized for assessing population bioequivalence. An example concerning a bioequivalence trial with 24 healthy volunteers is presented to illustrate the proposed method.     

Application of one-step liquid chromatography–electrospray tandem MS/MS and collision-induced dissociation to quantification of ezetimibe and identification of its glucuronated metabolite in human serum: A pharmacokinetic study

A new one-step liquid chromatography–electrospray tandem MS/MS method is described to quantify ezetimibe (EZM) a novel lipid lowering drug in human serum. Also using collision-induced dissociation (CID) of the analyte, identification and chromatographic separation of its major metabolite, ezetimibe glucuronide (EZM-G) is achieved in this study. A thawed serum aliquot of 100 μL was deproteinated by addition of 500 μL methanol containing omeprazole as internal standard (I.S.). Separation of the drug, its metabolite and the I.S. were achieved using acetonitrile–water (70:30, v/v) as mobile phase at flow rate of 0.5 mL/min on a MZ PerfectSil target C18 column. Multiple reaction monitoring (MRM) mode of precursor–product ion transition (408.7 → 272.0 for EZM and 345 → 194.5 for the I.S.) was applied for detection and quantification of the drug while, EZM-G was chromatographically separated and identified using CID. The analytical method was linear over the concentration range of 1–32 ng/mL of EZM in human serum with a limit of quantification of 1 ng/mL. The coefficient variation values of both inter- and intra-day analysis were less than 8% whereas the percentage error was less than 3.7. The validated method was applied in a randomized cross-over bioequivalence study of two different EZM preparations in 24 healthy volunteers.