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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

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

Basic methods

All API docs see here.

Random Dataset

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

Structures

Struct information see here.

Acknowledgments

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

References

• FDA Guidance for Industry: Statistical Approaches to Establishing Bioequivalence, 2001
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• Lindstrom & J.; Bates, M. (1988). Newton—Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data. Journal of the American Statistical Association. 83. 1014. 10.1080/01621459.1988.10478693.
• Mogensen et al., (2018). Optim: A mathematical optimization package for Julia. Journal of Open Source Software, 3(24), 615,doi: 10.21105/joss.00615
• Patterson, S. D. and Jones, B. (2002), Bioequivalence and the pharmaceutical industry. Pharmaceut. Statist., 1: 83-95. doi:10.1002/pst.15
• Revels, Jarrett & Lubin, Miles & Papamarkou, Theodore. (2016). Forward-Mode Automatic Differentiation in Julia.
• Schaalje GB, McBride JB, Fellingham GW. Adequacy of approximations to distributions of test statistics in complex mixed linear models. J Agric Biol Environ Stat. 2002;7:512–24.
• Van Peer, A. (2010), Variability and Impact on Design of Bioequivalence Studies. Basic & Clinical Pharmacology & Toxicology, 106: 146-153. doi:10.1111/j.1742-7843.2009.00485.x
• Wolfinger et al., (1994) Computing gaussian likelihoods and their derivatives for general linear mixed models doi: 10.1137/0915079
• Wright, Stephen, and Jorge Nocedal (2006) "Numerical optimization." Springer

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