htmn
☆    

2008-08-19 13:29
(5700 d 21:49 ago)

Posting: # 2196
Views: 22,335
 

 Least-squares mean, geometric least-square means [General Sta­tis­tics]

Dear all,
Please let me introduce myself first: I am a beginner in BA/BE study field, working for just-established BE center. Therefore, my question might annoy you, please forgive me and understand for me that I have tried my best to improve my basic knowledge on BA/BE and I have searched thoroughly all topic in this forum.
The problem of our center is: all of us are pharmacists, we do not have deep knowledge in statistic. 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!). With a very basic requirement of FDA for bioequivalence, we still do not understand what have to do, please help us:
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.
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? Could you please tell us step by step the equation to calculate? Because, even if we are able to use the software Bear, we still have to validate it, i.e calculate manually to compare the results. Also, I myself, really want to understand clearly what LS-means is so I am confident to talk about it. I have read http://www.uidaho.edu/ag/statprog/sas/workshops/glm/lsmeans.htm
but still not understand very well, especially when we have a big data.
I am really sorry for such long question. Hopefully you are not too tired to read my poor English. Really waiting for your help. Thank you in advance!
Helmut
★★★
avatar
Homepage
Vienna, Austria,
2008-08-19 15:51
(5700 d 19:27 ago)

@ htmn
Posting: # 2197
Views: 19,148
 

 Least-squares mean, geometric least-square means

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 (tmax: 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, Cmax,...). 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. :-D
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…

Dif-tor heh smusma 🖖🏼 Довге життя Україна! [image]
Helmut Schütz
[image]

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
htmn
☆    

2008-08-19 21:20
(5700 d 13:57 ago)

@ Helmut
Posting: # 2199
Views: 15,624
 

 Least-squares mean, geometric least-square means

Dear HS,
Thank you very much for your quick help. I feel very lucky to find out this forum bcoz I found many valuable answers to my problems (many, many problems and do not know whom to ask).

❝ 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:


Thank you for your advice! At the moment we are doing only simple study, 2x2 single-dose, crossover design for domestic companies. However, we are planning to do more complicated study (we have received several orders from sponsors to do study for modified-release products with both single and multiple-dose)

❝ If you want to write software for all these methods starting from scratch, this would be a rather tough and time-consuming job (- I wouldn't recommend it except to masochists).


:-D I never thought I will write any software in my life, especially statistical one. I am not good at computer and always struggle with statistic (however, I am really interested in statistics for BE).

❝ 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).


My center is a governmental one so it is not easy to buy something. We have asked for buying a software many times but not be approved. Actually, it is our fault as my personal thought: we are using Excel to do statistic and keep giving the results of bioequivalence to sponsor (;-) secret pls, I won't tell you where I am from) so everything seems OK and why have to buy a software, use Excel! Now, when foreign company from developed countries come and ask us to do study for them and the harmonization between countries force us to change. Actually, I think the way we are using Excel at the moment may be accepted bcoz we are at starting steps,there is no regulations for BA/BE study yet in my country. However, it won't be accepted in the future, definitely! We are not calculating anything mentioned in a real BE study: no geometric mean, no LS means, no inter, intra-subject variability, no power of the study...We do not know how to solve our situation at the moment: no software, no proper training (our center is at the highest level in my country, so can not change experience with other centers, going oversea is too luxury for us), no books (All the books in the lists you have recommended not easy to be found in my city bcoz they are expensive and not many people work in this field so those books are not available), no access to the good database (such as Science Direct or Wiley InterScience); luckily the Internet speed is faster recently. You may feel funny but it is the fact of a developing country. (Sorry if I bother you too much with long story, just want you to be in sympathy if I have any too simple questions later)

❝ I'm too short in time to give you the entire procedure - vacation approaching :-)


Terribly sorry for occupying your time again. Wishing you a great vacation! However, please spend some time to answer my and others' questions - we are really waiting for your help! (I am really impressive with huge works done by you in this forum with the answers to almost all questions) I will read carefully all the posts and documents you suggested and definitely, I will come up with plenty questions which need your help!

❝ 2. Your English is better than some I've read from 'native' speakers...


Hope that you did not regret to tell me as above. You gave me confidence so I am writing "a thesis" to reply you :-P. Thank you very much for your compliment!
Best regards,
HTMN.
Helmut
★★★
avatar
Homepage
Vienna, Austria,
2008-08-20 00:01
(5700 d 11:17 ago)

@ htmn
Posting: # 2200
Views: 16,192
 

 Excel or not Excel, that's the question!

Dear HTMN!

❝ My center is a governmental one so it is not easy to buy something. We have asked for buying a software many times but not be approved.


I think that both Pharsight (WinNonlin) and Thermo (Kinetica) do have academic licenses and licenses for governmental bodies as well which are much cheaper than the regular licenses. Just ask them.

❝ […] we are using Excel to do statistic…


Yes, why not; I also use it to get a quick look. Nasty things start when validation comes into play – which is simply impossible to perform on Excel.
Furthermore, Micro$oft implemented some statistical functions in a rather weird way. For example if you want to get the inverse t-distribution (you need it in calculating the confidence interval) you have to multiply the α-value by two in order to get the right result. See this article containing a lot of useful links.

Since you already have R installed, see this post. Chapter 7 of Millard and Krause (2001) deals with the 2×2 design (available for download). The S+ code can easily (OK, almost easily) adapted for use in R. Then you even have something I’m still missing in all commercial programs: intra- and inter-subject residuals…

❝ […] You may feel funny but it is the fact of a developing country. (Sorry if I bother you too much with long story, just want you to be in sympathy if I have any too simple questions later)


I take you very seriously. When I started in 1980 in Austria, the situation was comparable. Just a few books about PK (not a single one on BE), regularily waiting two weeks for a lousy photocopy of some reference, no fax, the internet wasn’t invented yet, no software at all (not even spreadsheets, no text processors - standard was the IBM electric typewriter and corrective tape). It was the time of programing the TI-59; one of my friends at the Austrian Health Authority while struggling with his brand-new Commodore PET 4000 (1 MHz, 32 KB RAM) couldn't believe that the company I was with, could afford an HP 9836 (8 MHZ, 2 MB RAM, 2 floppy disc drives, BASIC, Pascal, HP-UX, a thermoprinter for the bargain of € 25,000.–)…
And yes, nobody to talk to (we founded the first independent CRO in Austria in 1984).

❝ […] please spend some time to answer my and others' questions - we are really waiting for your help! (I am really impressive with huge works done by you in this forum with the answers to almost all questions)


Not only me, there are quite a lot of others which are equally experienced. The compliment goes also to them!

❝ I will read carefully all the posts and documents you suggested and definitely, I will come up with plenty questions which need your help!


Yes, do so, but be prepared that sometimes it will take some time to get an answer.
I’m running the forum in my spare time – which is limited. ;-)

Dif-tor heh smusma 🖖🏼 Довге життя Україна! [image]
Helmut Schütz
[image]

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
UA Flag
Activity
 Admin contact
22,957 posts in 4,819 threads, 1,636 registered users;
114 visitors (0 registered, 114 guests [including 6 identified bots]).
Forum time: 10:18 CET (Europe/Vienna)

With four parameters I can fit an elephant,
and with five I can make him wiggle his trunk.    John von Neumann

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5