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RegisterSample size for PK linearity [Power / Sample Size]
posted by Helmut 
– Vienna, Austria, 2009-05-19 15:19 (5829 d 12:42 ago) – Posting: # 3702
Views: 19,853
Dear Kro!
Keep terminology high: since you don’t know the relationship beforehand, you should call it a PK proportionality study. Dose linearity is a subcategory.
In the most simple case run a 4-way cross-over, normalize PK-responses (10, 30, 40 doses) to the 20 mg dose, and evaluate BE at 80–125%. A Bonferroni-correction of the alpha-level was advised by the German BfArM and was acceptable in a recent MRP in 15 EU member states. Your would perform three comparisons; therefore α/3 = 0.05/3 or 96.6% confidence intervals instead of 90% CIs. The overall patient’s risk is kept at <0.05, since 1 – (1 – 0.05/3)³ = 0.0492. See also this thread and Martin’s suggestions of another approach.
I’m not sure what you mean by ‘a deviation of 20% between doses being acceptable’. If you run model I (1 and/or 2) you get a common slope which can have any value (depending on the units of dose and PK response). So a 20% deviation from what?
If you opt for the Bonferroni-approach, run a sample size estimation as usual based on the expected T/R-ratio (generally 0.95), CVintra, and α 0.05/3 (instead of 0.05).
Example (T/R 0.95, power 80%), total cross-over sample sizes):
Sample sizes are larger in order to compensate for simultaneous testing.
❝ I would like to estimate a sample size for a PK linearity study.
Keep terminology high: since you don’t know the relationship beforehand, you should call it a PK proportionality study. Dose linearity is a subcategory.
- Dose linearity
- A straight line (PK response v.s. dose) through the origin = no significant (p>0.05) difference of the intercept from zero = 95% confidence interval of the intercept includes zero.
- A straight line, but with nonzero intercept.
- Dose proportionality
Any relationship other than linear; generally a power model.
❝ The study design plans to test 4 different doses (10, 20, 30 and 40).
❝ I need to test the bioequivalence for each dose, compared to the reference dose which is 20.
In the most simple case run a 4-way cross-over, normalize PK-responses (10, 30, 40 doses) to the 20 mg dose, and evaluate BE at 80–125%. A Bonferroni-correction of the alpha-level was advised by the German BfArM and was acceptable in a recent MRP in 15 EU member states. Your would perform three comparisons; therefore α/3 = 0.05/3 or 96.6% confidence intervals instead of 90% CIs. The overall patient’s risk is kept at <0.05, since 1 – (1 – 0.05/3)³ = 0.0492. See also this thread and Martin’s suggestions of another approach.
❝ In addition I need to calculate the linear correlation slope for the four doses, a deviation of 20% between doses being acceptable.
I’m not sure what you mean by ‘a deviation of 20% between doses being acceptable’. If you run model I (1 and/or 2) you get a common slope which can have any value (depending on the units of dose and PK response). So a 20% deviation from what?
❝ What is the required methodology and what is the formula to calculate the sample size?
If you opt for the Bonferroni-approach, run a sample size estimation as usual based on the expected T/R-ratio (generally 0.95), CVintra, and α 0.05/3 (instead of 0.05).
Example (T/R 0.95, power 80%), total cross-over sample sizes):
α
CV% 0.05000 0.01667
10.0 8 10
12.5 10 14
15.0 12 16
17.5 16 22
20.0 20 28
22.5 24 34
25.0 28 40
27.5 34 48
30.0 40 56Sample sizes are larger in order to compensate for simultaneous testing.
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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:
- Sample size for PK linearity Kro 2009-05-19 10:56 [Power / Sample Size]
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- Sample size for PK linearityHelmut 2009-05-19 13:19
- Sample size for PK linearity Kro 2009-05-19 13:56
- Sample size for PK linearity Helmut 2009-05-19 15:09
- Sample size for PK linearity ElMaestro 2009-05-26 17:26
- Weighting scheme Helmut 2009-05-26 19:52
- Sample size for PK linearity mjons 2011-12-08 18:03
- Sample size for PK linearity Lucas 2014-09-11 21:41
- Sample size for PK linearity - power model d_labes 2014-09-12 15:01
- Power dose proportionality - power model - Correction d_labes 2014-10-01 09:09
- Sample size for PK linearity d_labes 2014-09-13 15:05
- Sample size for PK linearity Lucas 2014-10-13 20:36
- Sample size for PK linearity d_labes 2014-10-14 09:26
- Sample size for PK linearity Lucas 2014-10-14 15:24
- Sample size for PK linearity d_labes 2014-10-14 09:26
- Sample size for PK linearity Lucas 2014-10-13 20:36
- Sample size for PK linearity - power model d_labes 2014-09-12 15:01
- Sample size for PK linearity ElMaestro 2009-05-26 17:26
- Sample size for PK linearity Helmut 2009-05-19 15:09
- dose proportionality vs. dose linearity martin 2009-05-25 08:46
- dose proportionality vs. dose linearity Helmut 2009-05-25 14:59
- Sample size for PK linearity Kro 2009-05-19 13:56
- Sample size for PK linearityHelmut 2009-05-19 13:19
Ing. Helmut Schütz