1. Kyiv, 2005-10-061 TRAINING WORKSHOP ON PHARMACEUTICAL QUALITY, GOOD MANUFACTURING PRACTICE & BIOEQUIVALENCE Statistical Considerations for Bioequivalence Studies Prepared by John Gordon, Ph.D. Presented by Hans Kemmler White Sands, 23 August 2006 e-mail: john_gordon@hc-sc.gc.ca

2. Kyiv, 2005-10-062 Introduction Performance will never be identical –Two formulations –Two batches of the same formulation? –Two tablets within a batch? Purpose of bioequivalence (BE) –Demonstrate that performance is not “significantly” different –Same therapeutic effect –What constitutes a ‘significant’ difference?

3. Kyiv, 2005-10-063 Introduction cont. Agencies must define a standard consisting of the following: –Bioavailability metrics –One or more acceptance criteria for each metric –Number and type of metrics may vary Dependent on drug formulation

4. Kyiv, 2005-10-064 Metrics for BE studies Concentration vs. time profiles –Area under the curve (AUC) –Maximal concentration (Cmax) –Time to Cmax (Tmax) Statistical measures of BE metrics –Mean –Variance

5. Kyiv, 2005-10-065 Logarithmic Transformations Distribution of BE metrics –Skewed to the right –Consistent with lognormal distribution Proportionate effects

6. Kyiv, 2005-10-066 Example What would be the expected drop in AUC if a patient received 20% less drug? Subject 1 –Original AUC = 100 units –20% drop = 20 units Subject 2 –Original AUC = 1000 units –20% drop = 200 units

7. Kyiv, 2005-10-067 Example cont. Log transformation –Absolute intrasubject differences become independent of patient’s AUC Log(80) – log(100) = log(800) – log(1000) Log transformation for concentration dependent measures –Accepted by regulatory agencies

8. Kyiv, 2005-10-068 Analysis of Variance ANOVA Most common technique of analysis and estimation Lognormal distribution –Raw data must be log transformed –Comparison of means and variances of transformed data –Geometric mean –Results reported in original scale

9. Kyiv, 2005-10-069 ANOVA Hypothesis Testing Null hypothesis test –No formulation difference Convey little detail Statistically significant difference –Clinically significant? Imprecise estimates (high variability) –No statistically significant difference

10. Kyiv, 2005-10-0610 Confidence Intervals (CI) Inference from study to wider world Range of values within which we can have a chosen confidence that the population value will be found Study findings expressed in scale of original data measurement

11. Kyiv, 2005-10-0611 Confidence Intervals cont. Width of CI indication of (im)precision of sample estimates Width partially dependent on: –Sample size –Variability of characteristic being measured Between subjects Within subjects Measurement error Other error

12. Kyiv, 2005-10-0612 Confidence Intervals cont. Degree of confidence required –More confidence = wider interval In other words, width of CI dependent on: –Standard error (SE) Standard deviation, sample size –Degree of confidence required

13. Kyiv, 2005-10-0613 Confidence Intervals cont. Statistical analysis of pharmacokinetic measures –Confidence intervals –Two one-sided tests

14. Kyiv, 2005-10-0614 Typical BE Assessment Criteria 90% confidence interval Ratio of geometric means Acceptance criteria: 80 – 125% Log transformed AUC T & C max

15. Kyiv, 2005-10-0615 Statistical Approaches for BE Average bioequivalence Population bioequivalence Individual bioequivalence

16. Kyiv, 2005-10-0616 Statistical approaches cont. Average BE –Conventional method –Compares only population averages –Does not compare products variances –Does not assess subject x formulation interaction

17. Kyiv, 2005-10-0617 Statistical approaches cont. Population and individual BE –Include comparisons of means and variances Population BE –Assesses total variability of the measure in the population Individual BE –Assesses within subject variability –Assesses subject x formulation interaction

18. Kyiv, 2005-10-0618 Design Considerations Non-replicated designs –Most common –Crossover designs –Two-formulation, two-period, two- sequence, crossover design –Average or population BE approaches –Parallel designs

19. Kyiv, 2005-10-0619 Design Considerations Replicated designs –Can be used for all approaches –Critical for individual BE approach –Suggested replicated design Two-formulation, four-period, two- sequence T R R T

20. Kyiv, 2005-10-0620 Statistical effects in model Sequence effect Subject (SEQ) effect Formulation effect Period effect Carryover effect Residual

21. Kyiv, 2005-10-0621 Outliers Statistical outliers Valid clinical/physiological justification Re-testing?

22. Kyiv, 2005-10-0622 Add-on designs All studies should be powered appropriately If study fails the standard –Reformulate –Undertake larger study –Add-on study Consistency testing Group-sequential designs –Penalty for ‘peeking’ at results