Bioequivalence and Bioavailability Forum

bvoggu
☆

2010-08-18 09:49
(5373 d 12:18 ago)

Posting: # 5801
Views: 10,469

least square mean calculation [General Statistics]

Dear all
My name is Bharat kumar (Trainee in pharmacokinetics dept.)
In our company, calculations of least square mean were done according to SAS only.
But i want to learn all those manually in excel.

Up to my knowledge... LSM will be calculated by doing average of parameter of one treatment in period 1 and average of same in period 2, followed by dividing the sum of both averages by 2 (2 in case of two periods, right?).
My questions are:

While doing calculations with same formula, i am getting correct values for AUCt, Cmax but for AUCinf i am getting different values.
Anybody will help me about this issue???
what is the formula for calculation of standard error of difference?
Please suggest me a book especially for statistical part of PK?

—
Regards,
Bharat

Helmut
★★★

Vienna, Austria,
2010-08-18 16:15
(5373 d 05:52 ago)

@ bvoggu
Posting: # 5803
Views: 9,475

least square mean calculation

Post reply

Dear Bharat,

please search the forum before posting. What about this thread (and linked examples)?

❝ 1. While doing calculations with same formula, i am getting correct values for AUCt, Cmax but for AUCinf i am getting different values.

This is strange. Are you sure that you have complete data for AUC_inf?
Maybe you have complete datasets for AUC_t, C_max and are calculating geometric means instead of adjusted (=LSM) means in all cases. Remember that simple mean = adjusted mean only for complete (balanced) datasets. Please check.

❝ 3. Please suggest me a book especially for statistical part of PK?

See this post. Newer editions of some textbooks are published as of today.

—
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

bvoggu
☆

2010-08-19 11:24
(5372 d 10:43 ago)

(edited on 2010-08-20 07:58)
@ Helmut
Posting: # 5806
Views: 9,758

least square mean calculation

Post reply

Dear Helmut,
Thank you very much for immediate response
I did calculation for least square mean of test and reference product in a 2X2 cross over study (TR Vs RT), but i am getting correct values for Cmax and AUCt only, but not for AUCinf. Please check with the following data if possible...


SubID Period Treatment Sequence  AUCt     AUCinf

XR03    1       R         RT     7833     7926.2

XR04    1       R         RT     7622.2   7730.3

XR07    1       R         RT     6477.7   6546.2

XR10    1       R         RT    10528.1  10682.1

XR11    1       R         RT    10968.6  11269.8

XR14    1       R         RT     8472.2   8535.6

XR16    1       R         RT    11593.9  11786.0

XR18    1       R         RT     7353.6   7473.4

XR20    1       R         RT     6090.6   6137.7

XR03    2       T         RT     6484.3   6601.6

XR04    2       T         RT     8587.1   8739.8

XR07    2       T         RT     4201.9   4262.8

XR10    2       T         RT     9566.9   9741.1

XR11    2       T         RT    12203.3  12404.6

XR14    2       T         RT     8495.7   8575.0

XR16    2       T         RT    10392.5  10554.7

XR18    2       T         RT     7859.7   8021.7

XR20    2       T         RT     7463.3   7549.4

XR01    2       R         TR     9982.6  10101.9

XR02    2       R         TR     6774     6879.6

XR05    2       R         TR     6065.1   6247.4

XR09    2       R         TR     7789.5   7913.9

XR13    2       R         TR     6253.9   6390.1

XR15    2       R         TR     5965.3   6056.8

XR17    2       R         TR     5593.2   5682.8

XR01    1       T         TR     9902.2  10044.0

XR02    1       T         TR     6684     6906.9

XR05    1       T         TR     5813.7   5903.5

XR09    1       T         TR     7975     8116.1

XR13    1       T         TR     6925     7026.4

XR15    1       T         TR     5995.3   6075.5

XR17    1       T         TR     6094.7   6191.3

Calculation according to mine is AUCt-LSM 8.919 (T), 8.927 (R)
Calculation according to SAS default programme for AUCt-LSM 8.919 (T), 8.927(R)
But for AUCinf my results are-8.929 (R) and 8.974 (T)
But SAS programme results are-8.942 (R) and 8.936 (T)
I am not getting why these are different :confused:

excuse me for such a lengthy data....
Please clarify me that a balanced design is nothing but number of sub facing TR is equal to number of sub facing RT right?
what is the formula for calculation of standard error of difference?

I am getting these difference bcz of excel, Please clarify SAS and Excel results are different to some extent right? and please provide me calculation upto LSM with one of our's members formula
(mean_seq1+mean_seq2)/2 for balanced design or (mean_seq1*n1)+(mean_seq2*n2)}/(n1+n2) for unbalanced design (I thought that second formula is best because our data is unbalanced). But I am getting result only with first formula not with second. Please clarify this.

—
Regards,
Bharat

Helmut
★★★

Vienna, Austria,
2010-08-19 14:36
(5372 d 07:31 ago)

@ bvoggu
Posting: # 5809
Views: 9,335

SE: SAS / PHX-WNL / manual

Post reply

Dear Bharat,

please add a column with the subject's ID. Edit your original post instead of posting a new one. THX.

❝ Please clarify me that a balanced design is nothing but number of sub facing TR is equal to number of sub facing RT right?

Yes.

❝ what is the formula for calculation of standard error of difference?

SE_(T-R)=sqrt[2×MSE_residual/(n₁+n₂)], where n₁ and n₂ are the numbers of subjects in sequences 1 and 2.

Edit: I played around with your dataset. I coded the subjects ID to 1-9, 1-9, 10-16, 10-16. I don't have SAS, but in Phoenix/WinNonlin v6.1 I could confirm SAS's results, both for AUC_t and AUC_inf.
Interestingly I got for SE_(T-R):

          PHX     'manual'

AUC_t  0.0381181 0.0378191 

AUC_inf  0.0378947 0.0375974

Can one of our SAS-owners please check these results? Maybe my formula is wrong.

—
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

d_labes
★★★

Berlin, Germany,
2010-08-19 18:18
(5372 d 03:49 ago)

@ Helmut
Posting: # 5811
Views: 9,319

Standard error

Post reply

Dear Helmut, dear Bharat,

❝ Edit: I played around with your dataset. I coded the subjects ID to 1-9,

❝ 1-9, 10-16, 10-16. I don't have SAS, but in Phoenix/WinNonlin v6.1 I could

❝ confirm SAS's results, both for AUC_t and AUC_inf.

❝ Interestingly I got for SE_(T-R):

❝ PHX 'manual'

❝ AUC_t 0.0381181 0.0378191

❝ AUC_inf 0.0378947 0.0375974

❝ Can one of our SAS-owners please check these results?

Of course I will do you the favor.

          PHX     'manual' "The power to know"

AUC_t  0.0381181 0.0378191  0.03811805

AUC_inf  0.0378947 0.0375974  0.03789467

❝ Maybe my formula is wrong.

Seems so

.
Try the following:

   SE_(T-R)=sqrt(0.5*MSE_residual*(1/n₁+1/n₂))

AUCinf:  =sqrt(0.5*0.01130855*(1/9+1/7))= 0.03789467

.

Bahrat! Have a look at ElMaestros first sentence! Eventually that is your problem.

BTW: My SAS LSMeans are equal to Bahrats SAS LSMeans :cool:

. That is finest software validation! SAS gives the same results regardless if in India or in Germany! Also it seems to make no difference if Bahrat or D. Labes calculates. Also it is not known which release of "Superior software" they use. That is highly satisfactory :lol:

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2010-08-19 18:33
(5372 d 03:34 ago)

@ d_labes
Posting: # 5812
Views: 9,256

Standard error

Post reply

Dear D. Labes!

❝ ❝ Maybe my formula is wrong.

❝

❝ Seems so :-D .

❝ Try the following:

❝ SE_(T-R)=sqrt(0.5*MSE_residual*(1/n₁+1/n₂))

THX, my manual doesn't give the formula at all and I was to lazy to look it up somewhere else.
So I improvised... :not really:

—
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

bvoggu ☆ 2010-08-20 12:51 (5371 d 09:16 ago) @ d_labes Posting: # 5817 Views: 9,154	Standard error Post reply
	❝ `SE_(T-R)=sqrt(0.5MSE_residual(1/n₁+1/n₂))` ❝ `AUCinf: =sqrt(0.50.01130855(1/9+1/7))= 0.03789467`. Hello Mr. Labes I am very thankful for your response and may I know how to calculate MSE residuals here??? — Regards, Bharat

d_labes
★★★

Berlin, Germany,
2010-08-20 16:57
(5371 d 05:10 ago)

@ bvoggu
Posting: # 5819
Views: 9,181

Not with EXCEL

Post reply

Dear Bharat,

❝ ... may I know how to calculate MSE residuals here???

MSE_residual is the Mean square of the error term from an appropriate ANOVA with the terms (effects) treatment, period, sequence and subject within sequence in the ANOVA model.

Although it is in principle possible I would not recommend to do this in M$ EXCEL :no:

. See this and related posts.
If you need a cheaper alternative then [image]

consider using R.

If you insist in using a spreadsheet consider the evaluation via intra-subject contrasts T-R. See Senn, Chapter 3 or Chow and Liu, Chapter 3.3.

S Senn
Cross-over Trials in Clinical Research
John Wiley & Sons, Chichester (2nd ed. 2002)

S-C Chow and J-p Liu
Design and Analysis of Bioavailability and Bioequivalence Studies
Marcel Dekker, New York (3rd ed. 2009)

—
Regards,

Detlew

ElMaestro
★★★

Denmark,
2010-08-18 16:46
(5373 d 05:21 ago)

@ bvoggu
Posting: # 5804
Views: 9,589

least square mean calculation

Post reply

Dear Bharat,

❝ Up to my knowledge... LSM will be calculated by doing average of parameter of one treatment in period 1 and average of same in period 2, followed by dividing the sum of both averages by 2 (2 in case of two periods, right?).

In the simplest case, average the sequences rather than the periods.
If you are looking for a sneakier way of finding the values, then you need to extract the treatment effects from the fitted effect vector (often called greek beta).

—
Pass or fail!
ElMaestro

bvoggu
☆

2010-08-20 09:41
(5371 d 12:26 ago)

@ ElMaestro
Posting: # 5814
Views: 9,245

least square mean calculation

Post reply

❝ If you are looking for a sneakier way of finding the values, then you need to extract the treatment effects from the fitted effect vector (often called greek beta).

Hi Mr.Gent
I didn't get you about sneakier way of finding. Because I am a beginner please clarify clearly...
In my data I am calculating the least square mean of reference and treatment separately. In my opinion you are telling about overall least square mean, right?.

—
Regards,
Bharat

ElMaestro
★★★

Denmark,
2010-08-20 11:34
(5371 d 10:33 ago)

@ bvoggu
Posting: # 5815
Views: 9,199

LSMeans

Post reply

Dear Bharat,

❝ I didn't get you about sneakier way of finding. Because I am a beginner please clarify clearly...

Sorry if I was not expressing myself in a clear fashion.
The normal linear model, written in matrix notation would look like this:

y=Xb+e

y is the vector of abserved values (log Cmax for example).
X is model matrix.
b is the coefficient vector.
e is the vector containg the residuals.

If you have software that fits this model, then it minimses e^te (the sum of squares) by playing around with the values in the b vector. By laws of matrix logic, b has as many rows as X has columns, and that is one for each value to be fitted. From this you can extract values (LSMeans) for Test and Reference. Note that when a model with intercept is fitted, there is typically just one column in X that corresponds to an LSMean value; to find the other in such cases you will have to add and subtract a little in order to figger the other LSMean out.

Oh dear, this was not at all clear. Sorry.

—
Pass or fail!
ElMaestro

least square mean calculation [General Sta­tis­tics]

least square mean calculation

least square mean calculation

SE: SAS / PHX-WNL / manual

Standard error

Standard error

Standard error

Not with EXCEL

least square mean calculation

least square mean calculation

LSMeans

least square mean calculation [General Statistics]