A new statistical procedure for testing equivalence in two-group comparative bioavailability trials

How to establish equivalence between treatments: a one-sided clinical trial in paediatric oncology

The design of clinical trial to establish the equivalence of two treatments differs from that of an efficacy trial. The conventional null hypothesis of equivalent treatment efficacy is replaced by a null hypothesis of inequivalence which must be tested by appropriate statistics. In addition, the maximum allowable value of the true difference between the efficacy of two equivalent treatments must be specified. In oncology, such a trial is necessary when a standard treatment is replaced by a new less toxic one of equivalent efficacy. The statistical formulation is one-sided. A trial comparing two pre-operative treatments in childhood nephroblastoma is presented here and analysed according to this methodology.

The influence of food on the pharmacokinetics and ACE inhibition of cilazapril

1. The influence of food on the pharmacokinetics and angiotensin-converting enzyme (ACE) inhibitory effects of oral 5 mg doses of cilazapril was investigated in a two-way crossover study in 16 volunteers. 2. Plasma and urine concentrations of cilazaprilat, the active diacid metabolite of cilazapril, and plasma ACE activity were determined by a radio-enzymatic method. 3. Cmax decreased by 30% (P less than 0.05) with a delay in (t)max of 1 h (P less than 0.05) and area under curve (AUC) was decreased by 14% (P less than 0.05). The elimination rate was unaltered. 4. Onset of ACE inhibition was delayed by approximately 30 min but degree and duration were unaffected. 5. The effect of food on the bioavailability of cilazapril at this dose would not be expected to be clinically significant.

The bioavailability of Tamoplex (tamoxifen). Part 3. A steady-state study in breast cancer patients

The bioavailability of two tamoxifen preparations (Tamoplex and Nolvadex) was compared in a multiple dose two-way cross-over design in twelve breast cancer patients. The formulations were found to be bioequivalent. Mean steady-state serum levels of tamoxifen and N-desmethyltamoxifen were 133 ng/ml and 242 ng/ml, respectively, at a single daily dose of three tablets of Tamoplex 10 mg and 128 ng/ml and 248 ng/ml, respectively, at a single daily dose of three tablets of Nolvadex 10 mg. While there was a large interpatient as well as intrapatient variability in steady-state levels of tamoxifen and N-desmethyltamoxifen, their ratio appeared to be constant in the individual patient.

A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability

The statistical test of hypothesis of no difference between the average bioavailabilities of two drug formulations, usually supplemented by an assessment of what the power of the statistical test would have been if the true averages had been inequivalent, continues to be used in the statistical analysis of bioavailability/bioequivalence studies. In the present article, this Power Approach (which in practice usually consists of testing the hypothesis of no difference at level 0.05 and requiring an estimated power of 0.80) is compared to another statistical approach, the Two One-Sided Tests Procedure, which leads to the same conclusion as the approach proposed by Westlake based on the usual (shortest) 1-2 alpha confidence interval for the true average difference. It is found that for the specific choice of alpha = 0.05 as the nominal level of the one-sided tests, the two one-sided tests procedure has uniformly superior properties to the power approach in most cases. The only cases where the power approach has superior properties when the true averages are equivalent correspond to cases where the chance of concluding equivalence with the power approach when the true averages are not equivalent exceeds 0.05. With appropriate choice of the nominal level of significance of the one-sided tests, the two one-sided tests procedure always has uniformly superior properties to the power approach. The two one-sided tests procedure is compared to the procedure proposed by Hauck and Anderson.

Relative bioavailability of rimantadine HCl tablet and syrup formulations in healthy subjects

Twenty healthy male subjects completed an open-label randomized crossover design to assess the bioavailability of 100 mg of rimantadine HCl in tablet and syrup forms relative to an oral solution. Blood samples were drawn and rimantadine plasma concentrations were determined by a GC-MS method. The maximum plasma concentration (Cmax), the time to Cmax (tmax), the area under the plasma concentration-time curve (AUC), and k were compared among treatments using an analysis of variance and the Hauck-Anderson test for bioequivalence. The Hauck-Anderson test was satisfied when the syrup and solution were compared. The relative bioavailability of the syrup was 96%. Both Cmax and AUC were significantly (p less than 0.05) increased (23 and 17%, respectively) when the tablet was compared with the solution. The relative bioavailability of the tablet was 117%. This outcome was unusual and could not be explained. However, this was not anticipated to be of clinical consequence since the majority of the safety and efficacy of rimantadine HCl was established using a tablet.

Prediction of steady-state bioequivalence relationships using single dose data I-linear kinetics

Simulated data using a linear one- and two-compartment body model with different absorption characteristics were used to evaluate the ability of single dose bioavailability data to predict the relationships that exist at steady state. This was done by comparing the confidence intervals obtained from single and multiple dose data sets for the parameters of Tmax, Cmax, and area under the curve from time zero to infinity (AUC0-infinity). As a consequence of Tmax and Cmax decreasing and increasing from single to multiple dosing regimens, the confidence intervals for these parameters reflected these changes. The 90 per cent confidence interval expressed as a percentage of the reference mean increased or decreased for Tmax dependent upon the ratio of Ka test/Ka reference, and decreased for Cmax while the interval for AUC0-infinity exhibited no predictable pattern and appeared to be influenced by the amount of error in the data set. Alteration of either the dosing interval or the fraction absorbed did not affect the pattern of change in the confidence intervals for Tmax and Cmax, but the latter did result in a decrease in the interval for AUC0-infinity. Analysis of the confidence intervals for Tmax, Cmax and AUC0-infinity in bioequivalency studies for quinidine gluconate and procainamide hydrochloride following administration of single and multiple doses to different subjects appeared to be consistent with the patterns observed for the simulated data sets.

The bioavailability of oral nifedipine formulations: a statistical and simulation approach

The bioequivalence of three oral forms of nifedipine was assessed in a triple crossover study on 12 healthy volunteers. Single 10 mg dose was given and ten blood samples were drawn during the first 8 h after administration. Highly sensitive gas chromatographic method was used for the nifedipine assay. Pharmacokinetic parameters which describe bioavailability and general kinetic behaviour of the drug (AUC, Cmax, tmax, beta, MRT) were calculated from individual plasma profiles. They were subjected to statistical analysis (paired t-test, Hauck's inverted t-test, and Westlake's method of confidence intervals). Analogue-hybrid simulation and identification was used to generate plasma profiles of nifedipine after single and multiple dosing. Averaged plasma concentrations were used for this purpose. The three formulations studied were bioequivalent in terms of the rate of absorption. The simulation proved to be an efficient tool to substitute in vivo multiple dosing studies for assessment of bioavailability. The specific statistical methods should be preferred in bioequivalence data evaluation due to their greater power and inclusion of extraneous bioequivalence limits interval. Despite the differences among the formulations studied, each one of them should be viewed according to its intended clinical use.

A proposal for interpreting and reporting negative studies

An issue of continuing interest is the interpretation and reporting of 'negative' studies, namely studies that do not find statistically significant differences. The most common approach is the design-power method which determines, irrespective of the observed difference, what differences the study could have been expected to detect. We propose an alternative approach, the application of equivalence testing methods, where we define equivalence to mean that the actual difference lies within some specified limits. This approach, in contrast to the design-power approach, provides a way of quantifying (with p-values) what was actually determined from the study instead of saying what the study may or may not have accomplished with some degree of certainty (power). For example, a possible outcome of the equivalence testing approach is the conclusion at the 5 per cent level that two means (or proportions) do not differ by more than some specified amount. The equivalence testing approach applies to any study design. We illustrate the method with a cancer clinical trial and an epidemiologic case-control study. In addition, for those studies in which one cannot specify limits a priori, we propose the use of equivalence curves to summarize and present the study results.