Pharmacokinetic Evaluation of the Data
For single-dose studies, including a fasting study or a food intervention study, the pharmacokinetic analyses include calculation for each subject of the area under the curve to the last quantifiable concentration (AUC0t) and to infinity (AUC0∞), tmax, and Cmax. Additionally, the elimination rate constant, k, the elimination half-life, t1/2, and other parameters may be estimated. For multiple-dose studies, pharmacokinetic analysis includes calculation for each subject of the steady-state area under the curve, (AUC∞t), tmax, Cmin, Cmax, and the percent fluctuation [100 × (Cmax – Cmin)/Cmin]. Proper statistical evaluation should be performed on the estimated pharmacokinetic parameters.
Statistical Evaluation of the Data
Bioequivalence is generally determined using a comparison of population averages of a bioequivalence metric, such as AUC and Cmax. This approach, termed average bioequivalence, involves the calculation of a 90% confidence interval for the ratio of averages (population geometric means) of the bioequivalence metrics for the test and reference drug products (Schuirmann, 1987; FDA Guidance, 2001).
Many statistical approaches (parametric tests) assume that the data are distributed according to a normal distribution or “bell-shaped curve” (see Appendix A). The pharmacokinetic parameters such as Cmax and AUC may not be normally distributed and the true distribution is difficult to ascertain because of the small number of subjects used in a bioequivalence study. The distribution of data that have been transformed to log values resembles more closely a normal distribution compared to the distribution of non-log-transformed data.
Two One-Sided Tests Procedure
The two one-sided tests procedure is also referred to as the confidence interval approach (Schuirmann, 1987). This statistical method is used to demonstrate if the bioavailability of the drug from the test formulation is too low or high in comparison to that of the reference product. The objective of the approach is to determine if there are large differences (ie, greater than 20%) between the mean parameters.
The 90% confidence limits are estimated for the sample means. The interval estimate is based on Student's t distribution of the data. In this test, presently required by the FDA, a 90% confidence interval about the ratio of means of the two drug products must be within ±20% for measurement of the rate and extent of drug bioavailability. For most drugs, up to a 20% difference in AUC or Cmax between two formulations would have no clinical significance. The lower 90% confidence interval for the ratio of means cannot be less than 0.80, and the upper 90% confidence interval for the ratio of the means cannot be greater than 1.20. When log-transformed data are used, the 90% confidence interval is set at 80% to 125%. These confidence limits have also been termed the bioequivalenceinterval (Midha et al, 1993). The 90% confidence interval is a function of sample size and study variability, including inter- and intrasubject variability.
For a single-dose, fasting or food intervention bioequivalence study, an analysis of variance (ANOVA) is usually performed on the log-transformed AUC and Cmax values. There should be no statistical differences between the mean AUC and Cmax parameters for the test (generic) and reference drug products. In addition, the 90% confidence intervals about the ratio of the means for AUC and Cmax values of the test drug product should not be less than 0.80 (80%) nor greater than 1.25 (125%) of that of the reference product based on log-transformed data. Table 15-5 summarizes the statistical analysis for average bioequivalence. Presently, the FDA accepts only average bioequivalence estimates are used to establish bioequivalence of generic drug products.
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Table 15-5 Statistical Analysis for Average Bioequivalence
- Based on log-transformed data
- Point estimates of the mean ratios
- Test/reference for AUC and Cmax are between 80% to 125%
- AUC and Cmax
- 90% confidence intervals (CI) must fit between 80% and 125%
- Bioequivalence criteria
- Two one-sided tests procedure
- Test (T) is not significantly less than reference
- Reference (R) is not significantly less than test
- Significant difference is 20% (α = 0.05 significance level)
- T/R = 80/100 = 80%
- R/T = 80% (all data expressed as T/R so this becomes 100/80 = 125%)
- The statistical model typically includes factors accounting for the following sources of variation: sequence, subjects nested in sequences, period, and treatment
An analysis of variance (see ANOVA) is a statistical procedure (see Appendix A) used to test the data for differences within and between treatment and control groups. A bioequivalent product should produce no significant difference in all pharmacokinetic parameters tested. The parameters tested statistically usually include AUC0t, AUC0∞, and Cmax obtained for each treatment or dosage form. Other metrics of bioavailability have also been used to compare the bioequivalence of two or more formulations. The ANOVA may evaluate variability in subjects, treatment groups, study period, formulation, and other variables, depending on the study design. If the variability in the data is large, the difference in means for each pharmacokinetic parameter, such as AUC, may be masked, and the investigator might erroneously conclude that the two drug products are bioequivalent.
A statistical difference between the pharmacokinetic parameters obtained from two or more drug products is considered statistically significant if there is a probability of less than 1 in 20 times or 0.05 probability (p ≤ .05) that these results would have happened on the basis of chance alone. The probability, p, is used to indicate the level of statistical significance. If p < .05, the differences between the two drug products are not considered statistically significant.
To reduce the possibility of failing to detect small differences between the test products, a power test is performed to calculate the probability that the conclusion of the ANOVA is valid. The power of the test will depend on the sample size, variability of the data, and desired level of significance. Usually the power is set at 0.80 with a β = 0.2 and a level of significance of 0.05. The higher the power, the more sensitive the test and the greater the probability that the conclusion of the ANOVA is valid.