New simulations & some desultory thoughts [BE/BA News]

posted by Helmut Homepage – Vienna, Austria, 2023-06-29 13:34 (358 d 12:15 ago) – Posting: # 23634
Views: 2,684

Hi Divyen & all,

I simulated IR ibuprofen.

One-compartment model, D = 400 mg, V = 7 L (lognormal distribution, CV 40%), ƒ = 0.9 (uniform distribution 0.8 – 1.0), t½ = 2 h. Associated k10-values (lognormal distribution, CV 25%). Seven formulations with tmax 1.25 h (Reference), at the lower (1.000 h) and upper (1.562 h) ‘limits’, fast (1.125 h, 1.188 h), and slow (1.316 h, 1.389 h). Associated k01-values (lognormal distribution, CV 35%), analytical error (normal distribution, CV 7.5%), LLOQ set to 5% of the reference’s error-free model Cmax. Concentrations <LLOQ before tmax set to zero, and after to NA. Lots of samples…
16 subjects in order to achieve ≥80% power for Cmax (CV 18%, T/R 0.95).

Lengthy [image]-script (302 LOC) upon request. I got:

Simulation settings: 2,500 studies with 16 subjects
  Sampling every five minutes up to 2 × tmax of R (2.50 h),
  exponentially increasing intervals to tlast (16 h) = 38 samples.
    0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70,
    75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135,
    140, 145, 150 min, 3.5, 4, 5.5, 7, 9.5, 12.5, 16 h
  Seven formulations
  L  = lower limit: tmax = 1.000 h, ka = 2.190 / h, t½,a = 19.0 min
  T1 = fastest    : tmax = 1.125 h, ka = 1.822 / h, t½,a = 22.8 min
  T2 = fast       : tmax = 1.188 h, ka = 1.672 / h, t½,a = 24.9 min
  R  = Reference  : tmax = 1.250 h, ka = 1.539 / h, t½,a = 27.0 min
  T3 = slow       : tmax = 1.316 h, ka = 1.417 / h, t½,a = 29.4 min
  T4 = slowest    : tmax = 1.389 h, ka = 1.296 / h, t½,a = 32.1 min
  U  = upper limit: tmax = 1.562 h, ka = 1.065 / h, t½,a = 39.0 min

Simulation results:
  L = lower limit
    Median  : 1.0833 h (Range: 0.7500 - 1.4583 h)
    Skewness: +0.4452  (Bias: +0.0833)
  T1 = fastest
    Median  : 1.2083 h (Range: 0.8750 - 1.6250 h)
    Skewness: +0.4093  (Bias: +0.0833)
  T2 = fast
    Median  : 1.2917 h (Range: 0.9167 - 1.7917 h)
    Skewness: +0.3858  (Bias: +0.1042)
  R  = Reference
    Median  : 1.3333 h (Range: 1.0000 - 1.7917 h)
    Skewness: +0.3505  (Bias: +0.0833)
  T3 = slow
    Median  : 1.4167 h (Range: 1.0000 - 1.8750 h)
    Skewness: +0.2960  (Bias: +0.1009)
  T4 = slowest
    Median  : 1.5000 h (Range: 1.1250 - 2.0000 h)
    Skewness: +0.2594  (Bias: +0.1111)
  U = upper limit
    Median  : 1.6667 h (Range: 1.2500 - 2.2500 h)
    Skewness: +0.0878  (Bias: +0.1042)

Comparisons:
  passed ‘±20% median criterion’ (80.00-125.00%)
    L  = lower limit: 52.1%
    T1 = fastest    : 80.9%
    T2 = fast       : 90.4%
    T3 = slow       : 91.2%
    T3 = slowest    : 84.8%
    U  = upper limit: 57.0%


The positive skewness of tmax-values confirmed the theoretical considerations of the two Lászlós.1 Interesting that the skewness decreased with increasing tmax. All medians were positively biased when compared to the models’ true values.

What changed to the simulations I presented in the comments to the guidance?

Simulation settings: 2,500 studies with 16 subjects
  Sampling every five minutes up to 2 × tmax of R (1.00 h),
  exponentially increasing intervals to tlast (16 h) = 18 samples.
    0, 10, 20, 25, 30, 35, 40, 45, 50, 55, 60 min, 1.5, 2, 3.5,
    5, 7, 11, 16 h
  Seven formulations
  L  = R –5 min   : tmax = 25 min, ka = 7.828 / h, t½,a = 5.31 min
  T1 = pretty fast: tmax = 27 min, ka = 7.037 / h, t½,a = 5.91 min
  T2 = fast       : tmax = 28 min, ka = 6.527 / h, t½,a = 6.37 min
  R  = Reference  : tmax = 30 min, ka = 6.074 / h, t½,a = 6.85 min
  T3 = slow       : tmax = 32 min, ka = 5.650 / h, t½,a = 7.36 min
  T4 = pretty slow: tmax = 33 min, ka = 5.233 / h, t½,a = 7.95 min
  U  = R +5 min   : tmax = 35 min, ka = 4.881 / h, t½,a = 8.52 min

Simulation results:
  L = R –5 min
    Median  : 0.5000 h (Range: 0.3333 - 0.6667 h)
    Skewness: +0.4994  (Bias: +0.0833)
  T1 = pretty fast
    Median  : 0.5417 h (Range: 0.3750 - 0.7500 h)
    Skewness: +0.4606  (Bias: +0.0917)
  T2 = fast
    Median  : 0.5417 h (Range: 0.3750 - 0.7500 h)
    Skewness: +0.4086  (Bias: +0.0667)
  R  = Reference
    Median  : 0.5833 h (Range: 0.4167 - 0.8333 h)
    Skewness: +0.3538  (Bias: +0.0833)
  T3 = slow
    Median  : 0.5833 h (Range: 0.4167 - 0.8333 h)
    Skewness: +0.2857  (Bias: +0.0570)
  T4 = pretty slow
    Median  : 0.6250 h (Range: 0.4167 - 0.8333 h)
    Skewness: +0.2113  (Bias: +0.0694)
  U = R +5 min
    Median  : 0.6667 h (Range: 0.4583 - 0.8750 h)
    Skewness: +0.1550  (Bias: +0.0833)

Comparisons:
  passed ‘±20% median criterion’ (80.00-125.00%)
    L  = R –5 min   : 73.7%
    T1 = pretty fast: 83.2%
    T2 = fast       : 87.1%
    T3 = slow       : 88.3%
    T3 = pretty slow: 82.6%
    U  = R +5 min   : 76.8%



  1. Tóthfálusi L, Endrényi L. Estimation of Cmax and Tmax in Populations After Single and Multiple Drug Ad­mi­ni­stra­tion. J Pharma­co­kin Pharma­codyn. 2003; 30(5): 363–85. doi:10.1023/b:jopa.0000008159.97748.09.
  2. Commission of the EC. Note for Guidance. Inves­ti­ga­tion of Bioavailability and Bioequivalence. Appendix III: Tech­ni­cal Aspects of Bioequivalence Statistics. Brussels. December 1991. Online.
  3. EMEA, CPMP. Note for Guidance on the Inves­ti­ga­tion of Bioavailability and Bioequivalence. London. 26 July 2001. Online.

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