Comparative BA-calculation for the EMA's Average Bioequivalence with Expanding Limits (ABEL)
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Comparative BA-calculation for the EMA’s Average Bioequivalence with Expanding Limits (ABEL)

The library supports methods given in the EMA’s Q&A document for reference-scaling according to the EMA’s Guideline on the Investigation of Bioequivalence. Potential influence of outliers on the variability of the reference can be assessed by boxplots of studentized and standardized residuals as suggested at a joint EGA/EMA workshop.

  • Method A

    A linear model of log-transformed PK responses and effects sequence, subject(sequence), period, and treatment – where all effects are fixed (i.e., ANOVA). Estimated via function lm() of library stats.

    log(PK) ~ sequence + subject(sequence) + period + treatment, data = data
  • Method B

    A linear mixed model of log-transformed PK responses and effects sequence, subject(sequence), period, and treatment – where subject(sequence) is a random effect and all others are fixed.

    log(PK) ~ sequence + period + treatment, random = ~1|subject, data = data

    Two options

    • Estimated via function lme() of library nlme. Uses degrees of freedom equivalent to SAS’ DDFM=CONTAIN and Phoenix/WinNonlin’s DF Residual. Implicitly preferred according to the Q&A document.
    • Estimated via function lmer() of library lmerTest. Uses Satterthwaite’s degrees of freedom.
  • Conventional (unscaled) Average Bioequivalence (ABE) – optionally with tighter limits required for NTIDs – can be calculated as well.

Tested designs

  • 4-period (full) replicates
    • TRTR | RTRT
    • TRRT | RTTR
    • TTRR | RRTT
    • TRTR | RTRT | TRRT | RTTR¹
    • TRRT | RTTR | TTRR | RRTT¹
  • 2-period (full) replicate
    • TR | RT | TT | RR²
  • 3-period (full) replicates
    • TRT | RTR
    • TRR | RTT
  • 3-period (partial) replicates
    • TRR | RTR | RRT
    • TRR | RTR³

¹ Confounded effects (design not recommended).

² Balaam’s design (not recommended due to poor power characteristics).

³ Extra-reference design; biased in the presence of period effects (design not recommended).

Cross-validation: Results of reference data sets agree with ones obtained in SAS (9.3, 9.4) and Phoenix WinNonlin (6.4, 7.0, 8.0).

Program offered for Use without any Guarantees and Absolutely No Warranty. No Liability is accepted for any Loss and Risk to Public Health Resulting from Use of this R-Code.