Bioequivalence and Bioavailability Forum

Power dose proportionality - power model - Correction [Power / Sample Size]

posted by d_labes  – Berlin, Germany, 2014-10-01 11:09 (3868 d 15:06 ago) – Posting: # 13627
Views: 16,853

Dear all,

have posted here the above SAS code from the book Patterson/Jones for calculating power for dose proportionality studies evaluated via power model.

As already stated this code gives extraordinary high power for low n's already. The authors state "These are typically very powerful designs for the assessment of dose proportionality, and interested readers will find that power for the above design approaches 100%. Although as few as six normal healthy volunteers will serve to provide a very robust dose-proportionality assessment in most settings, it is recommended that cross-over studies supporting a regulatory file include at least 10 to 12 subjects to ensure application of the central-limit theorem is appropriate."

My gut feeling was that the power obtained is too high and that there must be a bug.
This feeling was supported by the following:

• I would expect that the power equals the power obtained via the ordinary formulas for a 2x2x2 crossover, assuming true ratio=1, if we calculate for 2 doses only.
  But this is not the case.
  Example sigmaW=0.25 (CV=25.39567%), N=12 and doses 1, 4:
  power = 100% with the SAS code
  power(2x2x2) with true ratio 1 = 33.0069%
  
• In the paper of Hummel et al.¹ formulas via the normal distribution (large sample approximation I think) are given for the power of the parallel group design. I could not reproduce the values obtained via these formulas if I adapt the above SAS code to parallel group design (different df and different css). Again the values are much higher with the SAS code.
  
• The paper of Sethuraman et al.² gives examples for sample sizes also not compatible with the power calculated via the cited SAS code.

A closer look revealed that the non-centrality parameters have to changed to:
  nc1=((beta-(1-t))/s);
  nc2=((beta-(1+t))/s);
i.e. without the term sqrt(n) and voila, all above issues vanish.

Morals of the story: Even the pope may err .

BTW: New version of R-package PowerTOST³ is out now. From the NEWS: "... Contains further experimental functions for power calculations / samplesize estimation for dose proportionality studies using the Power model".
Experimental in the sense that I have pending a discussion with the authors of above SAS code. But meanwhile I'm quite sure that the implementation in PowerTOST is correct.

BTW2: PowerTOST contains more new goodies to be discovered .

---

¹Hummel et al.
"Exploratory assessment of dose proportionality: review of current approaches and proposal for a practical criterion"
Pharm. Stat. Vol. 8(1):38-49 (2007)

²Sethuraman VS, Leonov S, Squassante L, Mitchell TR, Hale MD
"Sample size calculation for the Power Model for dose proportionality studies"
Pharm. Stat. Vol. 6(1):35-41 (2007)

³Detlew Labes and Helmut Schuetz (2014).
PowerTOST: Power and Sample size based on two one-sided t-tests (TOST) for (bio)equivalence studies.
R package version 1.2-01.

Complete thread:

• Sample size for PK linearity Kro 2009-05-19 10:56 [Power / Sample Size] 
  • Sample size for PK linearity Helmut 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 - Correctiond_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
    • dose proportionality vs. dose linearity martin 2009-05-25 08:46
      • dose proportionality vs. dose linearity Helmut 2009-05-25 14:59