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yuvrajkatkar ★ Pune, Maharashtra (India), 2010-03-19 10:36 (5574 d 21:24 ago) Posting: # 4935 Views: 22,358 |
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Dear Sir, I am not getting why we used geometric least square means instead of mean in BA/BE studies. what is the significance behind this and what is the difference between geometric least square means and mean? I need ur guidence. — Best Regards, Yuvraj |
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ElMaestro ★★★ Denmark, 2010-03-19 12:06 (5574 d 19:54 ago) @ yuvrajkatkar Posting: # 4936 Views: 20,613 |
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Hi yuvrajkatkar ❝ I am not getting why we used geometric least square means instead of mean in BA/BE studies. We are working with logarithmic tranforms of the Cmax- and AUC-values, and we have a keen interest in the means of those. However, once we backtransform the mean of the logged values we end up with a quantity that can be thought of as the geometric mean. Example (somewhat simplified): Consider these three AUCs for Test: 10.1, 12.4, 11.4 And for Ref : 11.5, 11.6, 13.2Log means are logT=2.42 and logR=2.49 (natural logs here, but 10-based can be used too). The difference between the two is: log(T)-log(R)=-0.0699. But hey, the grumpy old math teacher with bad breath in hi-school tought us that we can write that as log(T/R)=-0.0699, so we backtransform this and get T/R=0.932. Now try and check the geometric means of T and R (untransformed). They are 11.26 and 12.08. If you take their ratio you find that the Geometric mean ratio is 0.932 just as we got above. I personally never think of geometric mean ratios; it is confusing to me. I think of them as backtransformed mean-log ratios. Hope this makes sense. Best regards EM. |
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Helmut ★★★   Vienna, Austria, 2010-03-19 15:39 (5574 d 16:20 ago) @ ElMaestro Posting: # 4941 Views: 20,754 |
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Ahoy ElMaestro, hi Yuvraj! ❝ ❝ I am not getting why we used geometric least square means instead of mean in BA/BE studies. ❝ ❝ [...] we end up with a quantity that can be thought of as the geometric mean. ❝ Example (somewhat simplified): ❝ Consider these three AUCs for Test: 10.1, 12.4, 11.4 ❝ And for Ref Just for the record: The term “least squares means” is ‘invented’ by ![[image]](img/uploaded/image2.gif) .In statistical textbooks you may find the term “adjusted means”. Adjusted means are used if the design is imbalanced (in the balanced case, geometric means = adjusted means). If in ElMaestro’s example we don’t have the third values for the test, the geometric mean for test will be 11.2, but without knowing the design and running the model we have no idea what the adjusted mean is. — Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png) Helmut Schütz ![[image]](https://static.bebac.at/img/CC by.png) The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
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ElMaestro ★★★ Denmark, 2010-03-19 17:06 (5574 d 14:53 ago) @ Helmut Posting: # 4942 Views: 20,543 |
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Hi again, ❝ Adjusted means are used if the design is imbalanced (in the balanced case, geometric means = adjusted means). Agreed, adjusted means (LSMeans) introduce another source of confusion. Let's say we have a BE-study unbalanced so as to have different numbers of subjects in the sequences (and/or the groups cf recent discussion). LSMeans are averages of averages in the sequences (groups). Example: If the mean of log AUC is 10.0 in sequence 1 (n=10) and the mean of log AUC is 2.0 in sequence 2 (n=2) then the LSMean is 0.5*(10.0+2.0)=7.0. Whether LSMeans are more meaningful than Means is debated widely, but since LSMeans were invented by SAS those statisticians who leaned on SAS during their education tend to favour LSMeans over Means. Fortunately we don't all have to be sheep - unless we want to submit our dossiers to EU regulators of course  . Type III SS is a good further example of this phenomenon.In the example above one would argue that the value in sequence 1 is better estimated (n=10) than the value in sequence 2 (n=2) so it would seem unfair to weight them equally when we work out an overall meaningful mean. Terrible wording, sorry. I do not have the answer as to why LSMeans would be more relevant than Means, or the other way around for that matter. Best regards, EM. |
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ElMaestro ★★★ Denmark, 2010-03-21 01:05 (5573 d 06:55 ago) @ ElMaestro Posting: # 4947 Views: 20,757 |
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Erm... ❝ If the mean of log AUC is 10.0 in sequence 1 (n=10) and the mean of log AUC is 2.0 in sequence 2 (n=2) then the LSMean is 0.5*(10.0+2.0)=7.0. *cough* Sorry. EM. |
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