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Mixed model solution for replicate designed bioequivalence study. This can be used to obtained results with methods C (random effects with interaction), given by the EMA in Annex I. Statistical model formed with accordance FDA Guidance for Industry: Statistical Approaches to Establishing Bioequivalence, APPENDIX F.

Install:

using Pkg; Pkg.add("ReplicateBE")

Install latest version directly:

using Pkg; Pkg.clone("https://github.com/PharmCat/ReplicateBE.jl.git")

Using:

using ReplicateBE
be = ReplicateBE.rbe!(df, dvar = :var, subject = :subject, formulation = :formulation, period = :period, sequence = :sequence);
ci = confint(be, 0.1)

Where:

• dvar::Symbol - dependent variable;
• subject::Symbol - subject;
• formulation::Symbol - formulation/drug;
• period::Symbol - study period;
• sequence::Symbol - sequence.

How to get results?

#Fixed effect table:
fixed(be)

#Type III table
typeiii(be)

Output example:

Bioequivalence Linear Mixed Effect Model (status: converged)

-2REML: 329.257    REML: -164.629

Fixed effect:
───────────────────────────────────────────────────────────────────────────────────────────
Effect           Value         SE          F          DF        t           P|t|
───────────────────────────────────────────────────────────────────────────────────────────
(Intercept)      4.42158       0.119232    1375.21    68.6064   37.0838     4.02039E-47*   
sequence: 2      0.360591      0.161776    4.96821    62.0      2.22895     0.0294511*     
period: 2        0.027051      0.0533388   0.257206   122.73    0.507155    0.612956       
period: 3        -0.00625777   0.0561037   0.012441   153.634   -0.111539   0.911334       
period: 4        0.036742      0.0561037   0.428886   153.634   0.654894    0.513515       
formulation: 2   0.0643404     0.0415345   2.39966    62.0      1.54908     0.126451       
───────────────────────────────────────────────────────────────────────────────────────────
Intra-individual variance:
formulation: 1   0.108629    CVᵂ:   33.87   %   
formulation: 2   0.0783544   CVᵂ:   28.55   %

Inter-individual variance:
formulation: 1   0.377846
formulation: 2   0.421356
ρ:               0.980288   Cov: 0.391143   

Confidence intervals(90%):
formulation: 1 / formulation: 2
Ratio: 93.77, CI: 87.49 - 100.5 (%)
formulation: 2 / formulation: 1
Ratio: 106.65, CI: 99.5 - 114.3 (%)

Validation information: here, validation results you can find in table.

All API docs see here.

Random dataset function is made for generation validation datasets and simulation data. Description here.

Struct information see here.

Best acknowledgments to D.Sc. in Physical and Mathematical Sciences Anastasia Shitova a.shitova@qayar.ru for support, datasets and testing procedures.

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Author: Vladimir Arnautov aka PharmCat Copyright © 2019 Vladimir Arnautov mail@pharmcat.net