SE of ∆ [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2020-10-02 22:29 (200 d 18:38 ago) – Posting: # 21966
Views: 788

Dear Detlew,

» I think all the confusion comes from that sigmaw, sigmad, sigmadelta values including their estimates which are used by all the authors cited within this thread in a different meaning.

Quite possible.

» I'm not able to figure out who is who, what is what. Sorry.

F**ing terminology.

» The only thing I'm convinced of is that your formula (2) above is correct.
» If you write the confidence interval for the BE decision as
» PE(T-R) +- SD(d)*tval(0.95, df)

Exactly.

» The rest of your algebra is straight forward.
» And correct if you ask me ;-).

THX. Now three people agree. I even didn’t trust my rusty algebra and asked Maxima for help:

[image]


» BTW: the formula (2) is not the error term in the 2×2×2 crossover.

How would you call it? We use \((3)\) in PowerTOST’s BE_CI.R line 30:

sqrt(mse*ades$bkni*nc)

where for design = "2x2" ades$bkni is 0.5 and nc is sum(1/n[1]+1/n[2]).
If we agree that \(\small{\widehat{\sigma}_\textrm{w}=\sqrt{MSE}}\) * we end up with \((2)\):

      For the special case of a two-treatment, two-period crossover study in which \(\small{n_\textrm{1}}\) subjects receive the test formulation in period one and the reference formulation in period two, while \(\small{n_\textrm{2}}\) subjects receive the reference formulation in period one and the reference formulation in period two, the unbiased estimator is given by $$\small{Est.=\frac{\left(\bar{X}_\textrm{T1}+\bar{X}_\textrm{T2} \right)}{2}-\frac{\left(\bar{X}_\textrm{R1}+\bar{X}_\textrm{R2} \right)}{2}}$$ where
      \(\small{\bar{X}_\textrm{T1}=}\) the observed mean of the \(\small{n_\textrm{1}}\) observations of the test formulation in period one.
      \(\small{\bar{X}_\textrm{T2}=}\) the observed mean of the \(\small{n_\textrm{2}}\) observations of the test formulation in period two.
      \(\small{\bar{X}_\textrm{R1}=}\) the observed mean of the \(\small{n_\textrm{2}}\) observations of the reference formulation in period one.
      \(\small{\bar{X}_\textrm{R2}=}\) the observed mean of the \(\small{n_\textrm{1}}\) observations of the reference formulation in period two.
The standard error of this estimator is $$\small{SE=s\sqrt{\frac{1}{2}\left (\frac{1}{n_\textrm{1}}+\frac{1}{n_\textrm{2}} \right)}}$$ where […] \(\small{s}\) is the square root of the “error” mean square from the crossover analysis of variance, based on \(\small{\nu}\) degrees of freedom.




Dif-tor heh smusma 🖖
Helmut Schütz
[image]

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

Complete thread:

Activity
 Admin contact
21,419 posts in 4,475 threads, 1,510 registered users;
online 15 (0 registered, 15 guests [including 8 identified bots]).
Forum time: Wednesday 17:07 CEST (Europe/Vienna)

In the Middles Ages the lingua franca of science was Latin.
Nowadays the language of science is bad English.    Anonymous

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