Confidence intervals bioequivalency testing

In a series of papers (23-26), Polli and colleagues proposed alternative direct curve comparison metrics on this level. In their papers, attention was focused on two aspects (i) are means or medians more suitable for comparison and (ii) how can symmetric confidence intervals be constructed that are invariant when exchanging reference and test In addition, this work was devoted to bioavailability and bioequivalence, i.e., time profiles in vivo, but the conclusions apply likewise to in vitro-release profiles. 

The statistical evaluation of bioequivalence studies should be based on confidence interval estimation rather than hypothesis testing (Metzler, 1988, 1989 Westlake, 1988). The 90% confidence interval approach, using 1 —2a (where a = 0.05), should be applied to the individual parameters of interest (i.e. the pharmacokinetic terms that estimate the rate and extent of drug absorption) (Martinez Berson, 1998). Graphical presentation of the plasma concentrationtime curves for averaged data (test vs. reference product) can be misleading, as the curves may appear to be similar even for drug products that are not bioequivalent. 

The statistical method for testing pharmacokinetic bioequivalence is based upon the determination of the 90% confidence interval around the ratio... 

Products are considered to be bioequivalent, if the 90% confidence interval of average ratios of AUC and between test and reference products... 

Another argument can be given in favour of conventional 95% confidence limits which removes discussion from the context of formal decision making. Suppose that, with no particular object in mind, we were to assert that the true bioequivalence ratio was some value y. If we were to test this assertion conventionally we would do so at the 5% level two-sided by adopting the value y for our true difference under the null hypothesis. The data will either cause us to accept or to reject the hypothesis. By changing the value of y we can establish all values which are accepted or rejected. The accepted range of values forms a 95% confidence interval and, to use the conventional logic of the... 

Westlake was a pioneer in bioequivalence, being one of the first to draw explicit attention to the way in which hypothesis testing was being inappropriately used to assert equivalence. (Failure to reject the hypothesis of exact equivalence was being used as a reason for asserting it.) At one time this approach to calculating confidence intervals was widely employed. It soon attracted criticism, however, and was eventually abandoned by Westlake himself, who subsequently recommended the 90% conventional confidence limits symmetric about the point estimate (Westlake, 1981). 

The current evaluation criteria are based on the two one-sided test approach, also commonly referred to as the Confidence Interval Approach or Average Bioequivalence, which determines whether the average values for the pharmacokinetic parameters measured after the administration of test and reference products are comparable. This approach involves the calculation of a 90% confidence interval about the ratio of the averages of T and R products for AUC and values. To establish bioequivalence, the AUC and of the T product should not be less than 0.80 (80%) or greater than 1.25 (125%) of the R product based on log-transformed data (i.e., a bioequivalence limit of 80 to 125%). For some time prior to the use of log-transformed data, the nontransformed data were used to assess bioequivalence. In 1989, it was realized that log transformation of the data enables a comparison based on the ratio of the two averages rather than the difference between the averages in an additive manner." Moreover, most biological data correspond to a log-normal distribution rather than to a normal distribution. 

The assessment of bioequivalence is based on 90% confidence intervals for the ratio of the population geometric means (test/reference) for the parameters under consideration. This method is equivalent to two one-sided tests with the null hypothesis of bio-inequivalence at the 5% significance level. Two products are declared bioequivalent if upper and lower limits of the confidence interval of the mean (median) of log-transformed AUC and Cmax each fall within the a priori bioequivalence intervals 0.80-1.25. It is then assumed that both rate (represented by Cmax) and extent (represented by AUC) of absorption are essentially similar. Cmax is less robust than AUC, as it is a single-point estimate. Moreover, Cmax is determined by the elimination as well as the absorption rate (Table 2.1). Because the variability (inter- and intra-animal) of Cmax is commonly greater than that of AUC, some authorities have allowed wider confidence intervals (e.g., 0.70-1.43) for log-transformed Cmax, provided this is specified and justified in the study protocol. 

Does this confidence interval fall within the FDA limits of 0.80-1.25 (80-125%) The answer is "Yes" (at the low end, the answer is "Yes, by a whisker.") So, the generic has passed its bioequivalence test with respect to AUC values. 

According to the EMA two products are considered to be bioequivalent when they contain the same active substance and when their respective bioavailabilities (rate and extent) after administration in the same molar dose and via the same route, lie within acceptable predefined limits. These limits are set to ensure comparable in vivo performance, i.e. similarity in terms of safety and efficacy. The design and number of studies that is to be carried out to establish bioequivalence depends on the physico-chemical and pharmacokinetic properties of the active substance. In this respect reference is made to the BCS classification of the active substance. For BCS class I active substances it may even be possible to obtain a waiver for the in vivo studies (a so-called biowaiver), whereas for the active substances showing more complex pharmacokinetic behaviour extensive studies are to be carried out. In general bioequivalence will be determined from the parameters Cmax and AUC. Two products are considered to be bioequivalent when the 90 % confidence interval of the ratio of test and reference product falls within the 85-125 % acceptance interval. However, for the required design of the bioequivalence study and statistical evaluation details for a specific active substance reference is made to the appropriate (most recent) guideline on this subject [2, 3]. 

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