Bioequivalence and Bioavailability Forum • Sample size for PK linearity

Sample size for PK linearity - power model [Power / Sample Size]

posted by d_labes – Berlin, Germany, 2014-09-12 17:01 (3887 d 09:24 ago) – Posting: # 13499
Views: 15,337

❝ Hello Helmut!

Not interested in an answer of others?

❝ If I'm going to use the Power Model, I think I should use this reference. Can you suggest me which software does that calculation?

I'm only aware of a solution in SAS given in the Patterson/Jones book for the case of crossover studies:

data a;

  * total number of subjects (needs to be a multiple of number

    of sequences, seq);

  * p is the number of periods;

  n=12; seq=3; p=3;

  * significance level;

  a=0.05;

  * true dose proportionality;

  beta=1;

  * sigmaW = within-subject standard deviation;

  sigmaW=0.25;

  * css is the corrected sum of squares of doses;

  * s assumes period effects are orthogonal to dose;

  css=CSS(log(1),log(2),log(8));

  s=sigmaW/sqrt(n*css);

  * error degrees of freedom for cross-over with n subjects in total

    assigned equally to seq sequences;

  n2=(n*p)-(n+p-1)-1;

  * t = acceptance limit;

  theta=1.25;

  r=8/1;

  t=log(theta)/log(r);

run;

data b; set a;

  * calculate power;

  t1=tinv(1-a,n2); t2=-t1;

  nc1=(sqrt(n))*((beta-(1-t))/s);

  nc2=(sqrt(n))*((beta-(1+t))/s);

  df=n2;

  prob1=probt(t1,df,nc1);

  prob2=probt(t2,df,nc2);

  answer=prob2-prob1;

  power=answer*100; 

run;

proc print data=b; run;

I'm not quite sure if this all is correct.
Only power is calculated. Use this with different n's until you get your desired power. But for crossover designs you get high power with small numbers already. The above code with n=12 gives power=1!

BTW:
If you have the paper you linked to I would happy to get a copy. Then it may eventually possible to incorporate it into R-package PowerTOST.

S Patterson and B Jones
Bioequivalence and Statistics in Clinical Pharmacology
Chapman & Hall/CRC, Boca Raton (2006)
page 239

—
Regards,

Detlew

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 modeld_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
  - dose proportionality vs. dose linearity martin 2009-05-25 08:46
    - dose proportionality vs. dose linearity Helmut 2009-05-25 14:59