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Applying Multilevel Models in E valuation of Bioequivalence in Drug Trials

Applying Multilevel Models in E valuation of Bioequivalence in Drug Trials. Min Yang Prof of Medical Statistics Nottingham Clinical Trials Unit School of Community Health Sciences University of Nottingham (20/05/2010) (min.yang@nottingham.ac.uk). Contents.

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Applying Multilevel Models in E valuation of Bioequivalence in Drug Trials

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  1. Applying Multilevel Models in Evaluation of Bioequivalence in Drug Trials Min Yang Prof of Medical Statistics Nottingham Clinical Trials Unit School of Community Health Sciences University of Nottingham (20/05/2010) (min.yang@nottingham.ac.uk)

  2. Contents • A review of FDA methods for ABE, PBE and IBE • A brief introduction to multilevel-level models (MLM) • MLM for ABE • MLM for PBE • MLM for IBE • Comparison between FDA and MLM methods on an example of 2x4 cross-over design • Further research areas • Questions

  3. Bioequivalence evaluation in drug trials • Statistical procedure to assess inter-exchangeability between a brand drug and a copy of it • Major outcome measures: ▬ Blood concentration of an active ingredient in the area under curve: (AUC) ▬ Maximum concentration of the ingredient in blood: (Cmax) ▬ Time to reach the maximum concentration in blood: (Tmax) Logarithm transformation of these outcomes is usually performed

  4. Standard testing design (FDA guidance) • A generic copy of a drug for test (T) versus the established drug as reference (R) • Cross-over experimental design (two drugs on same subject with washout periods) • Assessing three types of bioequivalence ▬Average bioequivalence (ABE) by 22 design ▬ Population bioequivalence (PBE) by 24 design ▬ Individual bioequivalence (IBE) by 24 design

  5. Standard assessment criterion Comprising of three parts: • A set of statistical parameters for specific assessment • Confidence interval (CI) of those parameters • Predetermined clinical tolerant limit

  6. Assessing ABE • Tolerable mean difference between drugs T and R ▬ statistical parameters: ▬ Confidence interval: ▬ Criterion: Diff. in mean ABE upper limit, ln(1.25) = 0.2231 ABE lower limit, ln(0.8) = -0.2231

  7. Assessing PBE • Difference in the distribution between drugs (assuming Normal distribution) ▬ Statistical parameters: Difference between total variance of T and R

  8. Assessing PBE (cont.) ▬ Criterion: PBE limit, a constant Parameter to control for total variance (0.04 typically)

  9. Assessing PBE (cont.) ▬ The linear scale of the criterion ▬ 95% CI of the scale ▬ To satisfy

  10. Assessing IBE • Individual difference (similar effects of same individual on both drugs) Corr. (T, R) Between individual variation Within individual variance

  11. Assessing IBE (cont.) IBE limit, preset constant ▬ Criterion ▬ Linear scale of the criterion ▬ Calculate 95%CI of the scale and to satisfy Parameter to control for within-subj. variance

  12. Limitations of FDA methods • Estimators of Moment method (less efficient, not necessarily sufficient) • Complex design? • Joint bioequivalence of AUC, Cmax and Tmax? • Covariates effects?

  13. FDA calculation of CI for IBE criteria scale

  14. FDA calculation of CI for IBE criteria scale (cont.) • Assuming chi-square distribution for each var. term

  15. FDA calculation of CI for IBE criteria scale (cont.) Let 95%CI upper limit:

  16. Alternative method?

  17. Data structure of cross-over designs 2  2 for a sequence/block

  18. Data structure of cross-over design (cont.) 2  4 for a sequence/block

  19. Data structure of cross-over design (cont.)

  20. Sources of variation • Between sequences/individuals • Within sequence/individual • Between periods (repeated measures over time) • Between treatment groups (treatment effect)

  21. Common methodological issues • Cluster effect within individual (random effects analysis for repeated measures) • Missing data over time (losing data) • Imbalanced groups due to patient dropout or missing measures (analysis of covariate)

  22. Basic 2-level model for repeated measures Model 1 • ith time point for jth individual, • x = 0 for drug R, 1 for drug T • Between individual variance • Within individual variance • Intercept: mean for drug R • Slope: mean diff. between T & R • u0j residuals at individual level • eij residuals at time level Mean diff. of jth individual from population

  23. Lay interpretation of multilevel modelling Y=βX + τU = fixed effects + variance components • An analytic approach that combines regression analysis and ANOVA (type II for random effects) in one model. • It takes advantage of regression model for modelling covariate effects. • It takes advantage of ANOVA for random effects and decomposing total variance into components: For a 2-level model, two variance components as between and within individual variances (SSt = SSb + SSw), Intra-Class Correlation (ICC) = SSb/SSt

  24. How MLM works for BE evaluation?

  25. Assessing ABE under multilevel models (MLM) • Estimate and test the slope estimate • Calculate 90% CI of the estimate • Compare with ABE limit [-0.2231, 0.2231] • In addition, adjusting for covariates if necessary.

  26. Two-level model for PBE (Model 2) • Between individuals (level 2) variance: • Within individual (level 1) variance:

  27. Two-level model for PBE (cont.) Total variance of drug T: Total variance of drug R:

  28. Assessing PBE (cont.) • The linear scale of the FDA criterion • 95% CI of the scale • To satisfy

  29. Two-level model for IBE • Linear scale of FDA criteria for IBE: The difference of within-individual variance and the interaction of individual and drug effects: random effects of drug effect between individuals.

  30. Variance components in Model 2

  31. Two-level model for IBE (cont.) • Diff. of within-individual var. estimated by • Interactive term estimated by

  32. Assessing IBE • Linear scale of the FDA criterion • Calculate 95%CI of the scale, to satisfy

  33. An example of anti-hypertension drug trial*

  34. ABE between FDA method and MLM (Model 1)

  35. Model estimates

  36. Variance components between FDA & MLM

  37. PBE parameters between FDA & MLM

  38. IBE parameters between PDA & MLM

  39. Merits of MLM • Straightforward estimation of the criterion scale for ABE, PBE or IBE • Expandable to cover complex cross-over designs • Capacity of adjusting covariates • Capacity in assessing multiple outcomes jointly (multilevel multivariate models) • Missing data (MAR) was not an issue due to ‘borrowing force’ in model estimation procedure

  40. Further research areas in MLM • Comparison of statistical properties of parameter estimates between FDA Moment approach and MLM (simulation study) • Calculating CI of criteria scale point estimate for PBE and IBE (MCMC or Bootstrapping) assessing single outcome • Calculating CI of criteria scale point estimates for multiple outcomes

  41. Thank you!

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