Statistical considerations

1. Statistical considerations Drs. Jan Welink Training workshop: Assessment of Interchangeable Multisource Medicines, Kenya, August 2009

2. Statistical considerations

3. Bioequivalence The primary concern in bioequivalence assessment is to limit the risk of a false declaration of equivalence. Statistical analysis of the bioequivalence trial should demonstrate that the clinically significant difference in bioavailability is unlikely….. [WHO working document multisource (generic) pharmaceutical products: Guidelines on registration requirements to establish interchangeability, Nov. 2005]

4. Bioequivalence 2 pharmaceutical products Test Reference Bioequivalent??

5. Bioequivalence Cmax AUC Tmax Important PK parameters Cmax: the observed maximum concentration of a drug  measure of the rate of absorption AUC: area underthe concentration-time curve  measure of the extent of absorption tmax: time at which Cmax is observed  measure of the rate of absorption

6. Statistical considerations How similar is similar?

7. Statistical considerations

8. Statistical considerations Statistical test should take into account… • The consumer (patient) risk of erroneously accepting bioequivalence (primary concern health authorities) • Minimize the producer (pharmaceutical company) risk of erroneously rejecting bioequivalence • Choice: • two one-side test procedure • confidence interval ratio T/R 100 (1-2) •  set at 5% (90% CI)

9. Statistical considerations

10. Statistical considerations Consumer Risk • The risk of declaring two product BE when they’re not is called the ‘consumer risk’ • In statistical terms, this is a Type I error • The risk of rejecting the null hypothesis when it’s true • The consumer risk is set at 5%

11. Statistical considerations Producer Risk • The risk of declaring two products NOT BE when they truly are BE is called the ‘producer risk’ • In statistical terms, this is a Type II error • The risk of accepting the null hypothesis when it’s false

12. Statistical considerations The risks are related • If the consumer risk is reduced, the producer risk increases • In statistical terms, if you lower the acceptable risk of making a Type I error, the risk of making a Type II error increases

13. Statistical considerations Average Bioequivalence: two drug products are bioequivalent ‘on the average’ when the (1-2α) confidence interval around the Geometric Mean Ratio falls entirely within 80-125% (regulatory control of specified limit)

14. Statistical considerations Some International Criteria

15. Statistical considerations

16. Statistical considerations Least Square Means from ANOVA t-statistic with 0.05 in one tail Standard Error

17. Statistical considerations BE Limits • The concept of the 20% difference is the basis of BE limits (goal posts) • If the concentration dependent data were linear, the BE limits would be 80-120% • On the log scale, the BE limits are 80-125% • The 90%CI must fit entirely within specified BE limits e.g. 80-125%

18. Statistical considerations Variables..: • Log transformation: • For all concentration dependent pharmacokinetic variables (AUC and Cmax) • Analysis of log-transformed data by means of ANOVA (analysis of variance) • includes usually formulation, period, sequence or carry-over, and subject factors • parametric test (normal theory)

19. Statistical considerations • The sources of variance in the model are • Product • Period • Sequence • Subject (Sequence) • Residual variance These account for all the inter-subject variability This estimates Intra-subject variability

20. Statistical considerations • The width of the 90%CI depends on • The magnitude of the WSV (ANOVA-CV (residual variance)) • The number of subjects in the BE study • The bigger the WSV (within- or intra-subject variability), the wider the CI • If the WSV is high, more subjects are needed to give statistical power compared with when the WSV is low

21. Statistical considerations intra-subject variability analytical variability unexplained random variability subject by formulation interaction ANOVA CV

22. Statistical considerations 125 100 80

23. Statistical considerations why log-transformation:

24. Statistical considerations Why parametric testing and not non-parametric: applicant: after log transformation not normal distributed! • based upon test for normality, however these are insensitive and it concerns a small study • normally after log transformation AUC and Cmax are normal distributed • reason for non-normality should be explained

25. Outliers • ‘Outliers’ • Definition: • aberant/irregular values (e.g. no plasma concentration, ‘late’ high concentrations….)

26. Outliers • ‘Outliers’ • Explanation: • vomiting? • non-compliant volunteers? • bioanalytical failure? • individual pharmacokinetics? • protocol violations? • ……

27. Outliers • ‘Outliers’ • Handling: • “…pharmacokinetic data can only be excluded based on non-statistical reasons that have been defined previously in the protocol. • Exclusion of data can never be accepted on the basis of statistical analysis or for pharmacokinetic reasons alone, because it is impossible to distinguish between formulation effects and pharmacokinetic effects. • Results of statistical analyses with and without the excluded subjects should be provided.” (excerpt from Q&A Doc Ref: EMEA/CHMP/EWP/40326/2006)

28. Power calculation

29. End