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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
• Fletcher, Roger (1987), Practical methods of optimization (2nd ed.), New York: John Wiley & Sons, ISBN 978-0-471-91547-8
• Giesbrecht, F. G., and Burns, J. C. (1985), "Two-Stage Analysis Based on a Mixed Model: Large-sample Asymptotic Theory and Small-Sample Simulation Results," Biometrics, 41, 853-862.
• Gurka, Matthew. (2006). Selecting the Best Linear Mixed Model under REML. The American Statistician. 60. 19-26. 10.1198/000313006X90396.
• Henderson, C. R., et al. “The Estimation of Environmental and Genetic Trends from Records Subject to Culling.” Biometrics, vol. 15, no. 2, 1959, pp. 192–218. JSTOR, www.jstor.org/stable/2527669.
• Hrong-Tai Fai & Cornelius (1996) Approximate F-tests of multiple degree of freedom hypotheses in generalized least squares analyses of unbalanced split-plot experiments, Journal of Statistical Computation and Simulation, 54:4, 363-378, DOI: 10.1080/00949659608811740
• Jennrich, R., & Schluchter, M. (1986). Unbalanced Repeated-Measures Models with Structured Covariance Matrices. Biometrics, 42(4), 805-820. doi:10.2307/2530695
• Laird, Nan M., and James H. Ware. “Random-Effects Models for Longitudinal Data.” Biometrics, vol. 38, no. 4, 1982, pp. 963–974. JSTOR, www.jstor.org/stable/2529876.
• 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