Bioequivalence and Bioavailability Forum

rana ☆ India, 2013-03-01 14:20 (4063 d 19:09 ago) Posting: # 10139 Views: 11,523	Intra subject variability vs Inter subject variability [General Statistics] Post reply
	Hi Mr. Helmut, In what cases we do observe an intersubject variability is less than intrasubject variability? Regards, Rana. Edit: Category changed. [Helmut]

Helmut
★★★

Vienna, Austria,
2013-03-01 17:12
(4063 d 16:18 ago)

@ rana
Posting: # 10140
Views: 10,285

CVinter < CVintra: happens sometimes…

Post reply

Hi Rana,

❝ In what cases we do observe an intersubject variability is less than intrasubject variability?

No idea. Happens in ~ <10% of studies. Note: You might have to switch to an all fixed-effects model in SAS and Phoenix/WinNonlin.

P.S.: Top-level posts please to the entire group – not to a person (this is a Forum – not a Chat-room). :-D

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ElMaestro
★★★

Denmark,
2013-03-01 21:51
(4063 d 11:38 ago)

@ Helmut
Posting: # 10142
Views: 10,028

CVinter < CVintra: happens sometimes…

Post reply

Oh ye mighty caveman,

❝ Note: You might have to switch to an all fixed-effects model in SAS and Phoenix/WinNonlin.

Interesting. I am not extremely well versed with either package but am curious to learn why this would need be done. Could you explain a little, please?
Is it a convergence/optimizer thing? And would it in SAS be something other than PROC GLM cf. the bogus statement?

Muchas gracias.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2013-03-02 00:10
(4063 d 09:19 ago)

@ ElMaestro
Posting: # 10143
Views: 10,281

CVinter < CVintra: happens sometimes…

Post reply

Ahoy, matey!

❝ Interesting. I am not extremely well versed with either package but am curious to learn why this would need be done. Could you explain a little, please?

I know SAS only from hearsay. From Pharsight’s Support Site:

Solution for WinNonlin Bioequivalence Warning 11094: Negative final variance component

The negative final Variance Component warning most likely indicates that, if using Subj(Seq) as a random effect, the within-subject variance (residual) is greater than the between-subject variance. Probably a more appropriate model is to move Subj(Seq) out of the random model and into the fixed model, i.e.,

Sequence+Subject(Sequence)+Formulation+Period

❝ Is it a convergence/optimizer thing?

Don’t think so. If you give me some days I will dig out a data set.*

❝ And would it in SAS be something other than PROC GLM cf. the bogus statement?

Duno. Detlew?

As an appetizer one dataset where CV_intra ~5×CV_inter. Folinic acid after 15 mg IR calcium folinate, SD, fasting, LLOQ 5 ng/mL (0.95% of C_max), all extrapolated areas <20% (median 6.9%), n=24 (n_RT=11, n_TR=13):
Subject Period Treatment Sequence AUC_t 1 1 R RT 8551.8 1 2 T RT 4538.3 2 1 T TR 2199.6 2 2 R TR 11036.4 3 1 R RT 3498.7 3 2 T RT 10710.5 4 1 T TR 3419.9 4 2 R TR 6447.8 5 1 T TR 4523.4 5 2 R TR 5190.9 6 1 R RT 6744.1 6 2 T RT 5244.8 8 1 T TR 7043.7 8 2 R TR 3786.6 9 1 T TR 3948.0 9 2 R TR 7159.8 10 1 R RT 4723.4 10 2 T RT 2275.2 11 1 T TR 1768.7 11 2 R TR 2380.9 12 1 R RT 9048.8 12 2 T RT 6669.6 13 1 T TR 8922.0 13 2 R TR 2443.8 14 1 R RT 3817.9 14 2 T RT 3841.7 15 1 R RT 9801.1 15 2 T RT 3286.6 16 1 T TR 4159.6 16 2 R TR 3217.2 17 1 T TR 5566.6 17 2 R TR 9262.4 18 1 R RT 13406.3 18 2 T RT 7070.3 20 1 T TR 5030.5 20 2 R TR 6086.9 21 1 T TR 3989.6 21 2 R TR 3019.1 22 1 R RT 7644.5 22 2 T RT 10794.6 23 1 R RT 6152.1 23 2 T RT 3448.3 24 1 T TR 5519.4 24 2 R TR 5583.8 25 1 R RT 10842.8 25 2 T RT 11058.5 26 1 T TR 5879.7 26 2 R TR 5539.5
PHX could fit subjects(sequence) as random without any tweaks. CV_intra 49.15%, CV_inter 9.991%. Somehow surprising since the individual T/R-ratios range from 19.9–365%!

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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d_labes
★★★

Berlin, Germany,
2013-03-02 16:57
(4062 d 16:32 ago)

@ Helmut
Posting: # 10144
Views: 10,075

CVinter < CVintra or negative variance component?

Post reply

Dear guys!

❝ ❝ Interesting. I am not extremely well versed with either package but am curious to learn why this would need be done. Could you explain a little, please?

❝

❝ I know SAS only from hearsay. From Pharsight’s Support Site:

❝

Solution for WinNonlin Bioequivalence Warning 11094: Negative final variance component

❝

❝ The negative final Variance Component warning most likely indicates that, if using Subj(Seq) as a random effect, the within-subject variance (residual) is greater than the between-subject variance. Probably a more appropriate model is to move Subj(Seq) out of the random model and into the fixed model, i.e.,

❝

❝ Sequence+Subject(Sequence)+Formulation+Period

Sorry. What was the question (see subject line)?

❝ ❝ Is it a convergence/optimizer thing?

❝

❝ Don’t think so. If you give me some days I will dig out a data set.*

Can play with the data if my SAS is again in reach to me.

Meanwhile I think it is an optimizer thing. Using ML or REML usually implies that variance-covariance terms are fitted with the constraints that they must be >= 0. At least in SAS this is the default setting which must be overred if you want an unconstrained solution. Maybe the WinNonlin doesn't obey this reasonable rule? And therefore the between-subject variance may come out as negative. Or what is meant here?

BTW: Liu & Chow have a chapter dealing with negative between-subject variance in the context of ordinary ANOVA (i.e. using the least square optimizer in fitting the model with all effects fixed). Don't remember the chapter number exactly. This is implemented in Bear I think, see ANOVA_stat.txt "prob: the probability for obtaining a negative estimate of inter-subject variability".

❝ ❝ And would it in SAS be something other than PROC GLM cf. the bogus statement?

❝

❝ Duno. Detlew?

Sorry. What was the question :confused:

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2013-03-02 19:46
(4062 d 13:43 ago)

@ d_labes
Posting: # 10145
Views: 9,926

Sometimes both…

Post reply

Hideehoo!

❝ Sorry. What was the question (see subject line)?

Rana asked:

❝ In what cases we do observe an intersubject variability is less than intrasubject variability?

And I answered that I have no idea why. Sounds counterintuitive first, but it happens.

❝ ❝ ❝ Is it a convergence/optimizer thing?

❝ ❝ Don’t think so. If you give me some days I will dig out a data set.*

❝ Can play with the data if my SAS is again in reach to me.

Stupid enough PHX/WNL has no problems with this dataset. A while ago I explored some of my studies. Checked the six most extreme ones where CV_intra > CV_inter. All could be fitted with a mixed-effects model. Crazy when you want a software to crash and it doesn’t. Will try to find a problematic dataset (no promises).

❝ Using ML or REML usually implies that variance-covariance terms are fitted with the constraints that they must be >= 0. At least in SAS this is the default setting which must be overred if you want an unconstrained solution.

Same in PHX/WNL.

❝ Maybe the WinNonlin doesn't obey this reasonable rule? And therefore the between-subject variance may come out as negative. Or what is meant here?

I’ve I recall it right (where the hell is my dataset?), the analysis is performed but the warning is thrown.

❝ BTW: Liu & Chow have a chapter dealing with negative between-subject variance in the context of ordinary ANOVA (i.e. using the least square optimizer in fitting the model with all effects fixed). Don't remember the chapter number exactly.

7.3.1

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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ElMaestro
★★★

Denmark,
2013-03-02 23:22
(4062 d 10:08 ago)

@ Helmut
Posting: # 10146
Views: 9,992

Must be the optimizer for Mixed Effects Muddles

Post reply

Hi Helmut,

❝ Sequence+Subject(Sequence)+Formulation+Period

❝ ❝ Is it a convergence/optimizer thing?

❝

❝ Don’t think so. If you give me some days I will dig out a data set.*

Ah, now it is beginning to dawn on me what the heck is going on.
I am fairly certain this must be an optimizer problem associated only with a mixed effects model; some initial guesses are necessary to get started and of course the optimiser might sometimes pick something with higher between-s than within-s. Then everything could go south if the initial guess is too wrong. If I recall correctly the REML value has a vertical (yes oddly not not horizontal) attractor asymptote when the guesses are too wrong.
So I guess nothing to do with PROC GLM + "random" statement.

But then again why would anyone fit a 2,2,2-BE study with REML. It can be solved pseudo-exactly without an optimizer Al Gore Rhythm. And it involves all effects as fixed, even in the case of PROC GLM + "random".

—
Pass or fail!
ElMaestro

d_labes
★★★

Berlin, Germany,
2013-03-05 13:57
(4059 d 19:32 ago)

@ ElMaestro
Posting: # 10154
Views: 9,622

Fixed Effects Muddleties

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Hi ElMaestro,

❝ But then again why would anyone fit a 2,2,2-BE study with REML. It can be solved pseudo-exactly without an optimizer Al Gore Rhythm. And it involves all effects as fixed, even in the case of PROC GLM + "random".

IMHO you can't talk about inter-subject variance if using an "all effects as fixed" EMAphylistic model. In such a model there is only one error source, the residual error.

If one is interested in inter-subject variance (to what end ever) a mixed model evaluated via real mixed model software is indispensable.

Although it makes no or little difference in case of balanced datasets with no missings. I have played with Helmut's dataset:

               CVinter    CVintra

Proc GLM       9.9912%    49.1476%

Proc Mixed     9.9912%    49.1476%


GLM: s²inter = (MS_sub(seq)-MS_error)/2; s²intra = MS_error

Mixed: variance terms directly read from Covariance parameters

CV = sqrt(exp(s²)-1)

BTW: @Helmut - No message / warning whatsoever during fit of the mixed model (subject(sequence) as random effect, all other fixed) with Proc Mixed.

—
Regards,

Detlew

ElMaestro
★★★

Denmark,
2013-03-05 14:06
(4059 d 19:23 ago)

@ d_labes
Posting: # 10155
Views: 9,665

Fixed Effects Muddleties

Post reply

Hi d_labes,

How was the holiday?

❝ IMHO you can't talk about inter-subject variance if using an "all effects as fixed" EMAphylistic model. In such a model there is only one error source, the residual error.

I completely agree and I think we mean the same - my point was that previously in this forum there was some confusion abut PROC GLM with the "random" statement giving the impression that a random effects (plural) model was applied. This isn't the case cf Bogus. I just wished to make sure this issue wasn't somehow derived from that confusion.

❝ If one is interested in inter-subject variance (to what end ever) a mixed model evaluated via real mixed model software is indispensable.

For a 2,2,2-BE design one can go via a normal linear model where the subject MS will do if subject is included as a term.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2013-03-05 16:53
(4059 d 16:36 ago)

@ d_labes
Posting: # 10156
Views: 9,685

Fixed Effects Muddleties

Post reply

Dear Detlew,

❝ IMHO you can't talk about inter-subject variance if using an "all effects as fixed" EMAphylistic model. In such a model there is only one error source, the residual error.

❝ If one is interested in inter-subject variance (to what end ever) a mixed model evaluated via real mixed model software is indispensable.

Yep.

❝ Although it makes no or little difference in case of balanced datasets with no missings. I have played with Helmut's dataset:

Well, my dataset is complete but imbalanced.

❝ CVinter CVintra

❝ Proc GLM 9.9912% 49.1476%

❝ Proc Mixed 9.9912% 49.1476%

❝ GLM: s²inter = (MS_sub(seq)-MS_error)/2; s²intra = MS_error

❝ Mixed: variance terms directly read from Covariance parameters

❝ CV = sqrt(exp(s²)-1)

Got exactly your values. Since Pharsight abandoned ANOVA in WinNonlin 3.2 (was standard till 3.1) everything now ‘sits on top’ of REML. It’s a little bit tricky* to get CV_inter from the fixed effects model since PHX doesn’t report the MSEs in this case – have to be reconstructed from the table of F-values and the residual variance. :-(

In the next release (1.4) Pharsight might bring back ANOVA-tables and test statements like in Proc GLM…

❝ BTW: @Helmut - No message / warning whatsoever during fit of the mixed model (subject(sequence) as random effect, all other fixed) with Proc Mixed.

Stupid enough I couldn’t find a dataset which gives this warning. Don’t remember whether I have seen it previously. I will ask Pharsight – maybe they have an example.

* Workaround for the fixed effects model:

Partial Tests → Data Wizard Filter: Exclude Units, Numer_DF, Denom_DF, P_value
Result → Join Worksheets Worksheet 2: Final Variance Parameters Sort: Dependent
Result → Data Wizard Custom Transformation, Formula: if(Hypothesis = 'int', Estimate, F_stat*Estimate), New Column Name: MS Filter: Replace where [Hypothesis] = 'int' with 'Error', Exclude F_stat, Parameter Proporties: Estimate → MSerror Custom Transformation, Formula: if(Hypothesis = 'Error', 100*sqrt(exp(MSerror)-1), ''), New Column Name: CVintra Custom Transformation, Formula: if(Hypothesis = 'Sequence*Subject', 100*sqrt(exp((MS-MSerror)/2)-1), ''), New Column Name: CVinter Filter: Exclude MSerror

Gives:

   Hypothesis         MS       CVintra    CVinter

Error             0.21635983  49.147639

Sequence          1.0368565

Sequence*Subject  0.23622554             9.9911704

Formulation       0.39246506

Period            0.054789184

Note that PHX’ Partial Tests are expected to agree with SAS’ Type III LSMs in most of cases (whereas Sequential Tests ≡ SAS’ Type I).

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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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

Intra subject variability vs Inter subject variability [General Sta­tis­tics]

CVinter < CVintra: happens sometimes…

CVinter < CVintra: happens sometimes…

CVinter < CVintra: happens sometimes…

CVinter < CVintra or negative variance component?

Sometimes both…

Must be the optimizer for Mixed Effects Muddles

Fixed Effects Muddleties

Fixed Effects Muddleties

Fixed Effects Muddleties

Intra subject variability vs Inter subject variability [General Statistics]