ElMaestro
★★★

Denmark,
2020-07-22 13:17
(703 d 02:52 ago)

Posting: # 21776
Views: 2,943

## The grandiose shocker of 2020 [General Sta­tis­tics]

Hi all,

may I shock you a bit or subject you to some degree of provocation?
You are not going to like it, initially. You are going to love me later (certainly not now). Possibly much later. The choice is yours. I am not forcing anyone's hand or vote. You need to think hard if you've got the nerves for this (or at least a sh!tload of spare Schützomycin that you can down eventually).
Once the dust settles, and your blood pressure comes a little down your first instinct will be to tell me it is wrong and secondly that it isn't useful (the latter will be true if your mental reference and intellectual horizon are solely defined through the current regulations)

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2020-07-22 13:51
(703 d 02:18 ago)

@ ElMaestro
Posting: # 21777
Views: 2,414

## The most obscure post ever

Hi ElMaestro,

congratulations, this is the most obscure post you ever made! What the heck are you talking about?

» You are going to love me later (certainly not now). Possibly much later.

Be assured of my love. Not just right now but at first sight.

Dif-tor heh smusma 🖖
Helmut Schütz

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

Denmark,
2020-07-22 14:34
(703 d 01:35 ago)

(edited by ElMaestro on 2020-07-22 14:50)
@ Helmut
Posting: # 21778
Views: 2,443

## Here goes

Hi Hötzi,

» Be assured of my love. Not just right now but at first sight.

Thank you.

OK, here goes:
1. In a recent previous thread dealing with RRT/RTR/TRR designs, I showed how it is entirely possible to work with the covariance matrix without summing it as ZGZt+R.
I have been doing a little work on that for some time.

2. I have been lying awake for some time over s2WR and s2WB - what the fuck are these things?
(They are between-subject variances, for .... yes, for what exactly, given that we have treatment as fixed effect in the BE model???)

3. Then s2BTR (also called other stuff) - what the f#ck is that between-thingy really?
(It is the covariance of T with R, but what the heck is that in reality???? I am aware what a covariance is, how a covariance is defined (average sum of product of differences in expected minus observed values), but what the f#ck is s2TR at the end of the day from a practical perspective in a model with treatment?

It basically boils down to one single good question for me: What is the practical relevance of S2BR, s2BT, s2BTR, when the BE model already includes treatment as a fixed effect, and if I can't bend my head around that part, so how would I rather do it instead?

I actually started thinking it over, and I would much rather work with a single between-subject variance component. I can totally see how within subjects there will be a diffentiated variance according to the treatment measured, but across subjects, no I can't readily see why there would be a difference between S2BR, s2BT, s2BTR when treatment is modeled as fixed in the model.

So, and I had this idea a few years back, I think I hinted at it on a post in this forum but I can't find the link, in a replicated design, it makes great sense to me just to have s2WR, s2WT and a single component for the betweens. This is my little provocation.
I was happy to look up how Chow & Liu see it; see e.g. formula 2.5.1 and 9.1.1 in the 3rd edition: A single variance component between subjects is also suggested -or implied- there. This has a tremendously useful consequence for TRR/RTR/RRT designs: With these three components in V, and nothing else, V becomes invertible and the model has a quantifiable likelihood. And therefore, even though T is not replicated we can still estimate s2wt in a TRR/RTR/RRT design (!!!). But if you think about it, you will see it makes good sense (happy to take that discussion further if need be, but for starters: we never look directly at within subject contrasts when we fit a BE model, regardless of how replicated the design is, and regardless of whether we do mixed models or all fixed, just think about it).

Again, I am not saying anything here is compliant with a guideline/guidance. I am solely looking at the foundations of my own knowledge and not trying to build a house/walls/roof from it. The perspective from all this is potentially good news for those who are into inhaled products for FDA submission.

Here's my result with EMA's dataset II, if it is of interest:
 Var.Component  Ini.value      Value          varWT 0.01240137 0.01833538          varWR 0.01240137 0.01211072           varB 0.03576077 0.04080577

Now, can you all show your love and repeat after me: "Anders, you are a friggin genius"

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2020-07-22 15:37
(703 d 00:32 ago)

@ ElMaestro
Posting: # 21779
Views: 2,408

## Yeah but, no but, yeah but…

Hi ElMaestro,

I must confess that I don’t have the slightest idea what you have done here. Not surprising. Hazelnut-sized brain < walnut-sized brain. However:

» I was happy to look up how Chow & Liu see it; see e.g. formula 2.5.1 and 9.1.1 in the 3rd edition
$$Y_{ijk}=\mu+S_{ik}+P_j+F_{(j,k)}+{\color{Red}{C_{(j-1,k)}}}+e_{ijk} \tag{2.5.1=9.1.1}$$Did you implement the first-order carryover as well? If yes, try it without. Might explain the differences below.

» Here's my result with EMA's dataset II, if it is of interest:
»  Var.Component  Ini.value      Value
»          varWR 0.01240137 0.01211072

library(replicateBE) CV.wR <- 0.01*method.A(data = rds02, print = FALSE, details = TRUE)[["CVwR(%)"]] cat("varwR", signif(log(CV.wR^2+1), 7), "\n") varwR 0.01240137

With your previous REML-code I got 0.01324648 and following the FDA’s approach (intra-subject contrasts) I got 0.01298984 (in Phoenix, SAS, and by my -code). Hence, I see two problems:
1. Your result does not match the FDA’s approach. Your previous result is even closer (+2.0%) than the new one (–6.8%).
2. Even if it would match, how would you code the FDA’s mixed model for ABE in ?
That’s the most important question.

Dif-tor heh smusma 🖖
Helmut Schütz

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

Denmark,
2020-07-22 17:53
(702 d 22:16 ago)

(edited by ElMaestro on 2020-07-22 18:20)
@ Helmut
Posting: # 21780
Views: 2,367

## Yeah but, no but, yeah but…

Hi Hötzi,

» I must confess that I don’t have the slightest idea what you have done here. Not surprising. Hazelnut-sized brain < walnut-sized brain. However:
»
» » I was happy to look up how Chow & Liu see it; see e.g. formula 2.5.1 and 9.1.1 in the 3rd edition
» $$Y_{ijk}=\mu+S_{ik}+P_j+F_{(j,k)}+{\color{Red}{C_{(j-1,k)}}}+e_{ijk} \tag{2.5.1=9.1.1}$$Did you implement the first-order carryover as well? If yes, try it without. Might explain the differences below.

No no, the carry-over part of it was scrapped years ago. It is of historical interest and of no concern here. I did not model it, as you saw in the code posted last week. I model sequence. Note that the verbal distinction between sequence and carry is of no importance, has no bearing, to my purpose of starting this thread.

» » Here's my result with EMA's dataset II, if it is of interest:
» »  Var.Component  Ini.value      Value
» »          varWR 0.01240137 0.01211072
»

Again, this is not about compliance with a guidance/guideline.
The Value above is the result from the optimizer. The Ini.value is the guess.

» library(replicateBE)» CV.wR <- 0.01*method.A(data = rds02, print = FALSE, details = TRUE)[["CVwR(%)"]]» cat("varwR", signif(log(CV.wR^2+1), 7), "\n")» varwR 0.01240137
» Anything goes. (© Paul Feyerabend)

I do not know what this is about?

» With your previous REML-code I got 0.01324648 and following the FDA’s approach (intra-subject contrasts) I got 0.01298984 (in Phoenix, SAS, and by my -code). Hence, I see two problems:
1. Your result does not match the FDA’s approach. Your previous result is even closer (+2.0%) than the new one (–6.8%).
»
2. Even if it would match, how would you code the FDA’s mixed model for ABE in ?
» That’s the most important question.

Again, I am not trying to code anything in relation to a guidance. At least not a current one. For example, I do not know how yet to do Satterthwaite dfs, this isn't a direction I am taking at all. It may be of importance to you, but to me not in any way my purpose of the thread.

In a sense, my post just made clear that:
1. I don't see the relevance of s2BR, s2BT, s2BTR individually, in a mixed model where we already have treatment as fixed. I would combine them all in one single between-variance estimate, s2B, as I see no particular reason they would be assumed different.
2. When combining them all in s2B we will get model convergence (V is invertible) which results in a valid and qualified estimate of s2wt, even though T is not replicated (the reason is that R is replicated and we collapse the between variance components to a signle one).

These are two little things that have no particular relevance to current published guidances.
Note that point 1 above is entirely in line with Chow & Liu's model. I have not seen the BE model specified anywhere with more than one between-variance component. Have you? Where?
Why would we fit something with individual between-(co)variances when T and R have fixed levels (apart from the fact that it may be easy to code something along such lines in SAS, WNL, SPSS, and hence it also appears to be a component of guidances)?

So, forget the guidances and look at the horizon.

Is this more easy/intuitive/informative to read:
 Var.Component Ini.guesses   Estimate          varWT     0.01200 0.01833529          varWR     0.01230 0.01211073           varB     0.01234 0.04080585

Pass or fail!
ElMaestro
PharmCat
★

Russia,
2020-07-29 21:11
(695 d 18:58 ago)

@ ElMaestro
Posting: # 21799
Views: 2,001

## Here goes

Hello Maestro, hello all!

As if echoing you... Don't deny right away, at least in an hour... Provocational post

All thoughts about S2BR, s2BT, s2BTR separately is erroneous or incomplete. This all is part of V. All model notations also explain nothing. You can get some variance component, but without other this nothing matter. This is my very very very humble opinion. But why we need V except to get some specific component for special reason? First of all we need to calculate SE for vector of fixed effect. It can be done simple: sqrt(LCL') where L is "contrast vector" and C is variance-covariance matrix of fixed effect. C can be found like this: SUMi(Xi'Vi-1Xi)-1

There are misunderstanding in mixed models. Many people thoughts, that each line of data is observation. It really is in models without repeating. But in models with repeating all data for each subject is statistically independent observation for multivariate normal random variable with variance-covariance matrix V. V is indivisible and all attempts to obtain components are meaningless, if only because the structure of this matrix itself is just an assumption. If we consider V holistically, then it makes some sense.
jag009
★★★

NJ,
2020-07-24 18:52
(700 d 21:17 ago)

@ ElMaestro
Posting: # 21789
Views: 2,224

## The grandiose shocker of 2020

Hi ElMaestro,

» may I shock you a bit or subject you to some degree of provocation?

You on drugs?
J
ElMaestro
★★★

Denmark,
2020-07-24 19:01
(700 d 21:08 ago)

@ jag009
Posting: # 21790
Views: 2,217

## The grandiose shocker of 2020

Hi jag,

» You on drugs?

Not at all - my doctor prescribed me some antibiotics for gonorrea last week, but it seems my specific strain is multiresistant, so I stopped taking those meds. But thanks for asking.

Pass or fail!
ElMaestro