Bioequivalence and Bioavailability Forum

Dear htmn,

welcome to the club!

❝ The problem of our center is: all of us are pharmacists, we do not have deep knowledge in statistic.

'True' statisticians are a minority in this field anyhow; most of us originate from a quite disperse background - I've seen pharmacists, chemists, physicians, microbiologists, etc. If I remember it correctly, one of the authors (G. Bozler) of the powerful PK/PD-Modeling software TopFit is a physicist...

❝ Also, we do not have any statistical software (I found the free software "bear" introduced in this forum and am trying to apply it at the moment - thank you for introducing!).

OK, if you only want to go with software in the public domain I must warn you. R is a wonderful statistical environment - but with a very steep learning curve. Both a lot of statistical knowledge and object-oriented programming skills are a must. 'bear' is still in it's developing phase (e.g., just three sampling points used for the estimation of the terminal phase) and only suitable for a conventional 2×2 cross-over design after single administration.
If you want to deal with studies keeping a global perspective in mind, you must be able to evaluate at least the following type of studies / apply the following statistical methods:

• higher order cross-over studies (>2 formulations),
  
• multiple dose studies,
  
• studies on dose proportionality (power model),
  
• nonparametric methods (t_max: EU, ASEAN states, Australia, South Africa, Brazil, …),
  
• studies in a replicate design.

If you want to write software for all these methods starting from scratch, this would be a rather tough and time-consuming job (I've done it myself starting in 1980, but only because nothing was available except NONLIN and SAAM for mainframe computers - I wouldn't recommend it except to masochists). Consider going with one of the general-purpose PK/PD/BE-software packages instead despite they are expensive, the support is slow, etc... The industrial standard is WinNonlin, a little bit cheaper is Kinetica (at the priece of a somehow weird user interface).

❝ 1. In Guidance for Industry: Statistical Approaches to Establishing Bioequivalence - FDA, 2001, page 10: The 90% CI for the difference in the means of the log-transformed data should be calculated using methods appropriate to the experimental design. The antilog of the confidence limits obtained constitute the 90% CI for the ratio of the geometric means between the T and R products.

❝ So, the first CI for the difference in the means... calculate with which mean:arithmetic?

❝ We only think that calculate CI of the geometric mean ratio means using geometric mean, can't understand why have to do antilog.

Maybe this post helps. First you log-transform all data subjected to a multiplicative model (AUC, C_max,...). Then you run an ANOVA on these log-transformed data. Antilogs of arithmetic means of log-transformed data equal geometric means of raw data (untransformed):
Example for two values:
x₁ 0.95 ln(x₁) -0.05129
x₂ 0.90 ln(x₂) -0.10536
arithmetic mean of logs (-0.05129,-0.10536) = ((-0.05129)+(-0.10536))/2 = -0.078327
antilog(-0.078327) = 0.925
geometric mean(0.95,0.90) = sqrt(0.95 x 0.90) = 0.925
The commonly applied acceptance range (AR) of [0.80,1.25] of the reference in the untransformed domain (that's the one non-mathematicians are thinking in) is transformed into [ln(0.80) = -0.2231, ln(1.25) = +0.2231]. The AR which is not symetrical about 1 (-0.20,+0.25) in the untransformed domain becomes symetrical around 0 [ln(1) = 0]. Since nobody except mathematicians feels comfortable with logs, the confidence interval and the point estimate are back-transformed (taking antilogs) after the analysis.

❝ 2. In the report format of ASEAN, it is required to have a table: - Table - Analysis of Variance, Geometric least-squares means for each pharmacokinetic parameters.

❝ We do not know how to calculate geometric least-square means?

The software should do it for you.
If your data set is balanced (i.e., the same nuber of subjects in sequence TR as in sequence RT, or in other words no drop-outs in the study): (geometric) LSM = geometric mean.

❝ Could you please tell us step by step the equation to calculate?

I'm too short in time to give you the entire procedure - vacation approaching - please see either Chow & Liu (2000) or Hauschke et al. (2007).

❝ I am really sorry for such long question. Hopefully you are not too tired to read my poor English.

1. No problem!
   
2. Your English is better than some I've read from 'native' speakers…