yckim
☆

2008-05-27 15:04

Posting: # 1874
Views: 6,364

## Mean calculation method in unbalanced cross-over study [Software]

Dear all,

I found the difference of mean calculation method between equivtest 1.0 and 2.0. Equivtest 1.0 calculates (mean_seq1+mean_seq2)/2 instead of {(mean_seq1*n1)+(mean_seq2*n2)}/(n1+n2). The company confirmed Equivtest 2.0 is right. Which is the right one in your opinion? Is the other method absolutely wrong? I would also like to know the theoretical basis.

Best regards,

Yu Chul Kim
Korea, Republic of
Helmut
★★★

Vienna, Austria,
2008-05-27 15:41
(edited by HS on 2008-05-27 19:47)

@ yckim
Posting: # 1875
Views: 5,745

## EquivTest v1 / v2 / PK

Dear Yu!

» I found the difference of mean calculation method between equivtest 1.0 and 2.0.

Fascinating! I have both versions on my machine and will check it sometime...

» Equivtest 1.0 calculates (mean_seq1+mean_seq2)/2 instead of {(mean_seq1*n1)+(mean_seq2*n2)}/(n1+n2). The company confirmed Equivtest 2.0 is right. Which is the right one in your opinion?

In the case of an unbalanced study (n1 # n2) only the latter.

» Is the other method absolutely wrong?

If the design is balanced (n1 = n2), the second formula reduces to the first one. In technical terms, the second one is wrong for unbalanced studies; the bias will depend on both the overall size of the study (n1+n2) and the degree of unbalance (ratio of n1/n2).

» I would also like to know the theoretical basis.

There are some examples in Chow & Liu (2001).

--
Edit: Sorry, I don't have version 1 any more. Both EquivTest02.00 (2001) and EquivTest/PK (2006) use the correct formula - which is also given in the manuals (look for TOST).

Cheers,
Helmut Schütz

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

2008-05-28 01:39

@ Helmut
Posting: # 1876
Views: 5,574

## EquivTest v1 / v2 / PK

Dear HS

However, I am a little confused about followings.

» In the case of an unbalanced study (n1 # n2) only the latter.

» In technical terms, the second one is wrong for unbalanced studies; the bias will depend on both the overall size of the study (n1+n2) and the degree of unbalance (ratio of n1/n2).

You said the method of equivtest 2.0 is right in the former while it is wrong in the latter. Please clarify it.

Thank you.

Best regards,

Yu Chul Kim

Edit: Standard quotes restored. [Helmut]
Helmut
★★★

Vienna, Austria,
2008-05-28 11:55

@ yckim
Posting: # 1878
Views: 5,534

## Weighted mean

Dear Yu!

» You said the method of equivtest 2.0 is right in the former while it is wrong in the latter. Please clarify it.

You are right, I did not express myself clearly.
EquivTest v2 and /PK are using the correct formula in all situations (n1=n2 and n1#n2), whereas the formula of v1 is only correct for n1=n2. The formula of v1 is wrong for unbalanced studies (n1#n2).

BTW, the correct method is the 'weighted mean'; an example:
x1 of n1 numbers [1,2,3] is (1+2+3)/3 = 2,
x2 of n2 numbers [4,5] is (4+5)/2 = 4.5.
The weighted mean xw for two groups is defined with (x1n1+x2n2)/(n1+n2), giving (2×3+4.5×2)/(3+2) = 3.
The 'mean of the means' (x1+x2)/2 irrespective of the size of groups (EquivTest 1) leads to (2+4.5)/2 = 3.25.
The bias (in our case +0.25) can be positive or negative, but always drags the overall-mean towards the mean of the smaller group.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
d_labes
★★★

Berlin, Germany,
2008-05-28 16:35

@ Helmut
Posting: # 1879
Views: 5,552

## Least square mean

Dear HS, dear Yu,

I think it is necessary to have the concise context of the formulas before discussing in depth.

I do not own Equivtest. But a bet a big coin that because sequence means are mentioned and equivalence studies are mostly done with cross-over designs, that we are talking about the evaluation of such cross-over studies.

The formula
  (x1+x2)/2
then looks to me as that what is called a 'Least square mean'.

Helmuts simple data give with
 Proc GLM;   class sequence;   model numbers=sequence;   estimate 'Overall LSMean' intercept 1; run;                           Standard Parameter  Estimate         Error    t Value    Pr > |t| ------------------------------------------------------------ LSMean    3.25000000    0.41666667      7.80     0.0044 

If the numbers are treatment differences in one subject, then the above code is for evaluation of the overall treatment difference in Senn's basic estimator approach.

Stephen Senn
Cross-over trials in clinical research
Wiley, 2002, chapter 3.

Regards,

Detlew
yckim
☆

2008-06-03 07:46

@ d_labes
Posting: # 1899
Views: 5,573

## Least square mean

Dear HS and d_labes

There seems to be opinions that 'mean of the means' (least square mean?) is right in cross-over study. Even Equiv 2.0 use the term of 'least square mean'. In addition, many texts on statistics use the 'mean of the means' formula. Please help me clearly understand which method is right and the rationale.

Best regards,

YCKim
JPL
☆

Vienna,
2008-06-03 09:10

@ yckim
Posting: # 1900
Views: 5,729

## Least square mean

Dear Yu,

in fact Least Square Means (LSMeans) are not an issue of X-over studies only but of unbalanced data. For the balanced case LSMeans and Means agree, for the unbalanced case, LSMeans account for the size of the group the LSMeans is determined of. Find a basic example here: http://www.uidaho.edu/ag/statprog/sas/workshops/glm/lsmeans.htm

Regards,
JPL
vish14184
★

India,
2008-06-04 06:54

@ JPL
Posting: # 1905
Views: 5,420

## Least square mean

Dear all,

In SAS geometric mean calculated by using exp(lnLSM) that value differ from the geometric mean calculated using excel.

i want to know that why this values are differ?

Regards
Vishal Nakrani
JPL
☆

Vienna,
2008-06-04 08:44

@ vish14184
Posting: # 1907
Views: 5,641

## Least square mean

Dear Vishal,

the main difference ist that you use a LSMean in the first case, whereas Excel really does not calculate LSMeans and therefore does not produce geometric LSMeans.

Regards,

JPL
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