New simulations & some desultory thoughts [BE/BA News]
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 -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?
- The chance to pass is higher due to the upper limit of 125% (instead of 120%).
As mentioned by other stakeholders, the approach favors slower formulations – even more than with the draft’s 120% limit. Surprisingly we read on page 16: - It is not agreed that slower formulations will be developed to use a wider acceptance range since quicker formulations are desired from a clinical and marketing point of view.
However, is a Δ of ±8 minutes really clinically relevant for a pain-killer? I doubt it.
- […] if Tmax is expected 30 minutes after administration, sampling should be at e.g. 10, 20, 25, 30, 35, 40, etc., which would allow to conclude that the difference is less than 5 minutes if the Tmax is observed in the same or an adjacent sampling time.
- ‘T’ is the SI symbol for the absolute temperature. Use the correct SI symbol ‘t’ for time, at least for consistency with the overarching guideline.
- The assessment of the range is more subjective. If all the values except one are the same, the ranges would be considered acceptable. Therefore, only if differences are evident and worse for the test product, the range could be used for a regulatory decision.
- The comparison of the medians does not intend to preserve the type 1 error [sic] but to exclude formulations with different onset of action.
- […] the power of a statistical test (usually be performed using a confidence interval), and consequently the sample size needed, will depend on the requested equivalence range and significance level (the allowed type-1 error rate). Equivalence range could be wider than the range that is applied for point estimate. Also, the allowed type-1 error rate (or equivalently, the coverage probability of the confidence interval) may be less strict than for AUC and Cmax. This would allow for assessing the consumers risk for Tmax but on a different level than for AUC and Cmax. Still an agreement on both, equivalence range and significance level to be used, may be difficult to achieve.
- It is considered that while the Hodges-Lehmann estimator is an adequate estimator to compare Tmax of Test (generic) and Reference (innovator) products […] the present revision of the product specific guideline concerns […] not introducing a new method particularly one for which EMA experience in regulatory submissions is limited.
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%
- 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.
- Commission of the EC. Note for Guidance. Investigation of Bioavailability and Bioequivalence. Appendix III: Technical Aspects of Bioequivalence Statistics. Brussels. December 1991. Online.
- EMEA, CPMP. Note for Guidance on the Investigation of Bioavailability and Bioequivalence. London. 26 July 2001. Online.
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz
The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Complete thread:
- EMA: New product-specific guidances Helmut 2022-04-08 15:17 [BE/BA News]
- How would you implement it? ElMaestro 2022-04-09 11:45
- Confuse a Cat Inc. Helmut 2022-04-09 18:40
- Confuse a Cat Inc. ElMaestro 2022-04-09 21:47
- Confuse a Cat Inc. Ohlbe 2022-04-11 11:29
- Confuse a Cat Inc. Helmut 2022-04-11 13:59
- So many questions, so few answers Helmut 2022-04-11 13:03
- Preliminary simulations Helmut 2022-04-30 14:59
- Preliminary simulations ElMaestro 2022-04-30 19:10
- Preliminary simulations Helmut 2022-05-01 15:56
- Revisions of the PSGLs final Helmut 2023-06-23 13:29
- Revisions of the PSGLs final dshah 2023-06-28 14:43
- EMA: No problems with many sampling time points… Helmut 2023-06-28 15:59
- New simulations & some desultory thoughtsHelmut 2023-06-29 11:34
- SCNR. A heretic alternative. Helmut 2023-06-30 11:50
- Revisions of the PSGLs final dshah 2023-06-28 14:43
- Preliminary simulations ElMaestro 2022-04-30 19:10
- Simulated distributions Helmut 2022-05-02 13:43
- Confuse a Cat Inc. Ohlbe 2022-04-11 11:29
- Confuse a Cat Inc. ElMaestro 2022-04-09 21:47
- Confuse a Cat Inc. Helmut 2022-04-09 18:40
- How would you implement it? ElMaestro 2022-04-09 11:45