BEQool ★ 20240627 14:25 (46 d 20:40 ago) Posting: # 24042 Views: 1,787 

Hello all! Would anyone know what are the equations to calculate standard deviation of a study for different study designs (2x2, 2x3x3, 2x2x3, 2x2x4)? For example, standard error of a study for a given parameter is given in Phoenix Winnonlin with "Diff_SE" in the "Average Bioequivalence" tab but I cannot either find or calculate its standard deviation. I assume it has something to do with coefficients and number of subjects in sequences like in known.designs() but I cant get my head around it BEQool 
Helmut ★★★ Vienna, Austria, 20240627 15:29 (46 d 19:35 ago) @ BEQool Posting: # 24043 Views: 1,603 

Hi BEQool, ❝ Would anyone know what are the equations to calculate standard deviation of a study … — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
BEQool ★ 20240628 09:35 (46 d 01:29 ago) @ Helmut Posting: # 24045 Views: 1,586 

❝ ❝ Would anyone know what are the equations to calculate standard deviation of a study … ❝ I’m not sure what you mean by that. Can you reword/explain please? Sorry for the confusion, I meant standard deviation of a difference between treatments for a certain parameter. Now that I am thinking about it again, is it just the square root of MSE and therefore doesnt depend on the design? BEQool 
ElMaestro ★★★ Denmark, 20240630 00:08 (44 d 10:57 ago) @ BEQool Posting: # 24046 Views: 1,516 

Hi BEQool, ❝ Would anyone know what are the equations to calculate standard deviation of a study for different study designs (2x2, 2x3x3, 2x2x3, 2x2x4)? ❝ For example, standard error of a study for a given parameter is given in Phoenix Winnonlin with "Diff_SE" in the "Average Bioequivalence" tab but I cannot either find or calculate its standard deviation. ❝ I assume it has something to do with coefficients and number of subjects in sequences like in If I am not mistaken, you are looking for the standard error of the treatment difference, which is used to construct a 12*alpha Confidence interval. I agree, this is not all that easy. One thing is to apply an easy equation from Chow & Liu which works well in the case of a simple 222BE design, but it can get more obscure if the design gets a little complex. For a general approach, you can derive the covariance matrix, V, for the fixed effects. If X is your model matrix (=design matrix) and you have fitted your model and extracted your MSE from that model, then you simple have V=MSE*(X'X)^{1} If treatment A is indicated by the column a in X, and treatment B is in the column b of X, then V[a,a] is the SE of A and V[b,b] is the SE of B. V[a,b]=V[b,a] is the covariance of the two, hence: SE_{diff}=SE_{A}+SE_{B}2Cov_{AB} If you program in R here is a little snippet for you to play with, and it may be handy for you to have the emmeans package installed. R turns out to have a very handy function called vcov which directly gives us V without us having to do the underlying matrix algebra. I hope the following is illustrative:
library(emmeans) You can extend this as necessary. Be careful about intercepts and the order of factors in your lm. — Pass or fail! ElMaestro 
BEQool ★ 20240701 09:25 (43 d 01:39 ago) @ ElMaestro Posting: # 24047 Views: 1,468 

Hello ElMaestro, thank you for your indepth answer, I will take a deeper look into it. ❝ If I am not mistaken, you are looking for the standard error of the treatment difference, which is used to construct a 12*alpha Confidence interval. I am not exactly looking for the standard error of the treatment difference but instead for its standard deviation. I am using Phoenix WinNonlin and standard error of the treatment difference is already given with "Diff_SE". I would like to find out how to get (if it is possible) standard deviation of the treatment difference from the standard error of the treatment difference "Diff_SE" (or is there some other way?). BEQool 
ElMaestro ★★★ Denmark, 20240701 09:38 (43 d 01:26 ago) @ BEQool Posting: # 24048 Views: 1,460 

Hi BEQool, ❝ I am not exactly looking for the standard error of the treatment difference but instead for its standard deviation. I am using Phoenix WinNonlin and standard error of the treatment difference is already given with "Diff_SE". I would like to find out how to get (if it is possible) standard deviation of the treatment difference from the standard error of the treatment difference "Diff_SE" (or is there some other way?). Yeah, that is confusing, too. We have all kinds of standard deviations, but the one we usually learn about is the standard deviation of a sample. But if we have a sample, then we also have a mean from it, and the standard deviation of that mean is called a standard error. When statisticians derive a standard deviation of a mean (in contrast to a sample), then they tend to call that a standard error. My suspicion is they are solely doing it to confuse people like me. So, I think the answer to your question is that the SE of the difference is the standard deviation of the difference. I can't help with WNL at all. What it does, how it does it and how it presents results to the user is entirely outside my competences. — Pass or fail! ElMaestro 
BEQool ★ 20240701 10:41 (43 d 00:24 ago) @ ElMaestro Posting: # 24049 Views: 1,444 

❝ My suspicion is they are solely doing it to confuse people like me. Yes you are not alone in this ❝ So, I think the answer to your question is that the SE of the difference is the standard deviation of the difference. ❝ I can't help with WNL at all. What it does, how it does it and how it presents results to the user is entirely outside my competences. Thank you! I will also ask this on Certara forum if they have different perspective. BEQool 
mittyri ★★ Russia, 20240701 13:18 (42 d 21:46 ago) @ BEQool Posting: # 24051 Views: 1,440 

Hi BEQool, ❝ I will also ask this on Certara forum if they have different perspective. ElMaestro is right — Kind regards, Mittyri 
ElMaestro ★★★ Denmark, 20240703 15:37 (40 d 19:28 ago) @ ElMaestro Posting: # 24060 Views: 1,336 

Hi all, typo above: ❝ SE_{diff}=SE_{A}+SE_{B}2Cov_{AB} It should be more like: SE_{diff}^{2}=Var_{A}+Var_{B}2Cov_{AB} — Pass or fail! ElMaestro 