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.     

Bioequivalence trials with the incomplete 3 x 3 crossover design

In bioequivalence trials, one often considers two or more generic products with the original one. The 3 x 3 crossover design can be adopted to evaluate the two generic candidates with a brand name drug, rather than conducting two separate 2 x 2 crossover trials. Dropouts, however, are more likely to occur due to various administrative reasons when we consider a higher order crossover design. A modified method, which was originally given by Chow and Shao (1997), is extended to compare two generic products with a reference in the incomplete 3 x 3 crossover design. A simulation study and discussion are also presented.     

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 Alternative Approach for the Assessment of Bioequivalence Between Two Formulations of a Drug

The problem of the assessment of bioequivalence between a test formulation (T) and a reference formulation (R) of a drug using a two-way crossover experiment is considered. To claim bioequivalence between two formulations, it is required by the United States Food and Drug Administration (FDA) to demonstrate that the true ratio of means μT/μR of pharmacokinetic parameters of concern falls within some reasonable limits (e.g., (80%, 120%)) with certain assurance. A commonly used approach is to construct an approximate 90% confidence interval for μT/μR and compare it with (80%, 120%). In this paper, an exact approach according to the FDA's criteria is proposed. The proposed procedure is derived by constructing an exact confidence region (an ellipse) for (μR, μT) and comparing it with the region bounded by μT = 0.8 μR and μT = 1.2 μR. Bioequivalence is concluded if the ellipse is within the critical region.     

A Problem of Equivalence in Clinical Trials

Several methods exist for testing the bioequivalence in bioavailability trials. In this article we propose a method for testing the equivalence of two drugs in clinical trials when the response variable is assumed to have a normal distribution. The null and alternative hypotheses are formulated in a nonconventional manner. Computing aspects for the power and sample size are discussed.     

Operability region equivalence: simultaneous confidence bands for the equivalence of two regression models over restricted regions

In many scientific problems the purpose of comparing two linear regression models is to demonstrate that they have only negligible differences and so can be regarded as being practically equivalent. The frequently used statistical approach of testing the homogeneity null hypothesis of the two models by using a partial F test is not appropriate for this purpose. In this paper, a simultaneous confidence band is proposed which provides an upper bound on the largest possible difference between the two models, in units of the standard error of the observations, over a given region of the covariates. This is demonstrated to be a more practical method for assessing the equivalence of the two regression models.     

Confidence intervals for the similarity between algal communities

While researchers commonly use similarity measures to compare algal communities, very few researchers have considered the variability of these estimated measures. This paper discusses a recent method for estimating the variance of and confidence intervals for similarity measures proposed by Johnson & Millie (1982, Hydrobiologia 89: 3–8). Applications of this method to data have produced confidence intervals that are too narrow. Two alternative methods, the jackknife method and the bootstrap, are shown to provide superior estimates of the variability.     

Assessing distributions of estimated drug shelf lives in stability analysis

A stability study is usually conducted to ensure that a drug product can meet the approved specifications prior to its expiration dating period (shelf life). Several approaches for determination of drug shelf life assuming random batches have been proposed. In this paper, we examine sampling distributions of the estimated shelf lives proposed by Shao and Chow (1994, Biometrics 50, 753-763). An application to some stability data from the pharmaceutical industry is presented.     

An Improvement of the Westlake Symmetric Confidence Interval

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST -LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one-sided t-tests. An (1-α)-confidence interval consistent with the two one-sided t-tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)-confidence interval of the t-test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one-sided confidence intervals.     

Normal approximation diagnostics for the Cox model

We discuss two diagnostic methods for assessing the accuracy of the normal approximated confidence region to the likelihood-based confidence region for the Cox proportional hazards model with censored data. The proposed diagnostic methods are extensions of the contour measures of Hodges (1987, Journal of the American Statistical Association 82, 149-154) and Cook and Tsai (1990, Journal of the American Statistical Association 85, 770-777) and the curvature measures of Jennings (1986, Journal of the American Statistical Association 81, 471-476) and Cook and Tsai (1990). These methods are also illustrated in a study of hepatocyte growth factor in patients with lung cancer and a Mayo Clinic randomized study of participants with primary biliary cirrhosis.     

Unconditional Exact Tests for Equivalence or Noninferiority for Paired Binary Endpoints

Problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions. When the sample size is small, the asymptotic tests may not be reliable. This article proposes an unconditional exact test procedure to assess equivalence or noninferiority. Two statistics, a sample-based test statistic and a restricted maximum likelihood estimation (RMLE)-based test statistic, to define the rejection region of the exact test are considered. We show the p-value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis. Assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits. We also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics. A typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods. The p-value from the unconditional exact tests is generally larger than the p-value from the asymptotic tests. In other words, an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test.     

Empirical Bayes estimation of random effects parameters in mixed effects logistic regression models

We extend an approach for estimating random effects parameters under a random intercept and slope logistic regression model to include standard errors, thereby including confidence intervals. The procedure entails numerical integration to yield posterior empirical Bayes (EB) estimates of random effects parameters and their corresponding posterior standard errors. We incorporate an adjustment of the standard error due to Kass and Steffey (KS; 1989, Journal of the American Statistical Association 84, 717-726) to account for the variability in estimating the variance component of the random effects distribution. In assessing health care providers with respect to adult pneumonia mortality, comparisons are made with the penalized quasi-likelihood (PQL) approximation approach of Breslow and Clayton (1993, Journal of the American Statistical Association 88, 9-25) and a Bayesian approach. To make comparisons with an EB method previously reported in the literature, we apply these approaches to crossover trials data previously analyzed with the estimating equations EB approach of Waclawiw and Liang (1994, Statistics in Medicine 13, 541-551). We also perform simulations to compare the proposed KS and PQL approaches. These two approaches lead to EB estimates of random effects parameters with similar asymptotic bias. However, for many clusters with small cluster size, the proposed KS approach does better than the PQL procedures in terms of coverage of nominal 95% confidence intervals for random effects estimates. For large cluster sizes and a few clusters, the PQL approach performs better than the KS adjustment. These simulation results agree somewhat with those of the data analyses.     

Intrasubject variability in the pharmacokinetics of ethynyloestradiol

Intrasubject and intersubject variability in the metabolism of ethynyloestradiol (EE) was assessed in a cross-over randomized study of 6 women who each received 3 months treatment with 50 μg EE and 50 μg EE with 250 μg levonorgestrel (LNG). Blood samples were collected at the end of each treatment month, assayed for EE and the half-life of elimination (T_el and bioavailability (area under the serum concentration-time curve, AUC) calculated. Intrasubject variability for T_el and AUC varied markedly; the variability was random and not correlated with the formulation administered. The intrasubject variability for T_el and AUC was 31 and 17%, respectively, and intersubject variability 66 and 95%. The intersubject range of values was more than 3-fold for both T_el and AUC and the intrasubject range about 2-fold. The pharmacokinetics of EE were not influenced by LNG; mean values for T_el and AUC were 17.3 ± 5.5 h and 11.1 ± 3.8 ng/ml/h, respectively, when EE was administered alone compared with 16.4 ± 4.8 h and 12.5 ± 3.9 ng/ml/h when given with LNG. However, EE influenced the metabolism of LNG; T_el for LNG was 19.3 ± 4.2 h when administered alone and significantly higher (30.0 ± 11.2 h) when given with EE. There was no correlation between the rate of metabolism of EE and that of LNG. The intrasubject variability shown in this and other studies suggests that genetic factors are less important in intersubject variability than previously thought. Some implications of intrasubject variability are discussed.     

Bioavailability of Soil-Borne Chemicals: Method Development and Validation

Chemicals present in contaminated soils generally exhibit altered bioavailability compared to other vehicles used in studies of chemical toxicity. Methods used to assess the bioavailability of soil-borne chemicals have generally been modified versions of methods that are widely used in biomedical research. Oral and dermal bioavailability of semivolatile organic chemicals and metals in soil has been assessed by a variety of in vivo and in vitro methods. Due to variations in metabolism and excretion of different chemicals, approaches to measuring bioavailability must be selected with an understanding of disposition of the chemical being studied. Standard methods need to be modified due to constraints associated with doses relevant to environmental concentrations, the need to reflect weathering behavior in soils over time, and the need to generate data applicable to human health risk assessments. Estimates of relative bioavailability for chemicals in soil can be used directly to modify exposure estimates. Application of bioavailability data in a site-specific risk assessment requires regulatory acceptance of the data. Acceptance of the data will generally be dependent on either the use of a validated test method or a careful scientific review of the test method employed. A process for validating newly developed alternative toxicity methods for routine use developed by the Interagency Coordinating Committee on the Validation of Alternative Methods provides relevant guidance for assessing in vitro methods, but method validation should not be the only litmus test for inclusion of bioavailability data in risk assessments.     

High-performance liquid chromatographic assay of indomethacin and its application in pharmacokinetics in healthy volunteers

A new sensitive high-performance liquid chromatographic method for indomethacin from plasma on a reversed-phase column (C_1$$$) has been developed. The method involves precipitation of plasma with perchloric acid followed by diethyl ether extraction. The assay is quantitative down to 0.25 μg ml⁻¹ from a 200-μl aliquot of plasma with a detection limit of 0.1 μg ml⁻¹ and a recovery of approximately 90%.

The method was applied to single-dose studies with volunteers under various dietary restrictions. The results of these studies indicated that intrasubject variability within these regimens may be as important a factor as the intersubject variability already documented for this drug. These results have important implications in the determination of bioavailability and pharmacokinetic parameters of this drug.     

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.     

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.     

Simulation of Spatial and Temporal Variability of Chronic Copper Toxicity to Daphnia magna and Pseudokirchneriella subcapitata in Swedish and British Surface Waters

Water Quality Criteria (WQC) for metals are usually based on single species laboratory toxicity data. The influence of water characteristics of the surface waters on bioavailability to freshwater organisms is hence neglected, along with regional and temporal variability of these water characteristics. A methodology is presented to account for regional and temporal variability in the WQC setting for copper in the United Kingdom and Sweden. Bioavailability models were applied in a Monte-Carlo approach to account for temporal variability and a Geographic Information System was used to account for geographical variability on the chronic copper toxicity to Daphnia magna and Pseudokirchneriella subcapitata. Fifth percentiles of distributions of the No Observed Effect Concentration (NOEC) for both model species were derived in both study regions. For P. subcapitata, it was demonstrated that this fifth percentile can vary by a factor 10 in the UK study region. The ratio of these NOEC fifth percentiles (D. magna percentile divided by P. subcapitata percentile) was used to compare the ecotoxicity of copper to two model species. This ratio showed the highest variability (a factor 5) within the Swedish study region. The findings of this research stress the need for the use of region-specific WQC for copper.     

Assessing the Bioavailability and Risk from Metal-Contaminated Soils and Dusts

Exposure to contaminated soil and dust is an important pathway in human health risk assessment. Physical and chemical characteristics and biological factors determine the bioaccessibility/bioavailability of soil and dust contaminants. Within a single sample, contamination may arise from multiple sources of toxic elements that may exist as different species that impact bioavailability. In turn, the bioaccessibility/bioavailability of soil and dust contaminants directly impacts human health risk. Research efforts focusing on development and application of in vitro and in vivo methods to measure the bioaccessibility/bioavailability of metal-contaminated soils have advanced in recent years. The objective of this workshop was to focus on developments in assessing the bioaccessibility/bioavailability of arsenic-contaminated soils, metals’ contamination in urban Canadian residences and potential children's exposures to toxic elements in house dust, an urban community-based study (i.e., West Oakland Residential Lead Assessment), bioavailability studies of soil cadmium, chromium, nickel, and mercury and human exposures to contaminated Brownfield soils. These presentations covered issues related to human health and bioavailability along with the most recent studies on community participation in assessing metals’ contamination, studies of exposures to residential contamination, and in vitro and in vivo methods development for assessing the bioaccessibility/bioavailability of metals in soils and dusts.