earlybird
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2010-04-09 09:54
(5512 d 21:08 ago)

Posting: # 5059
Views: 9,652
 

 Meta-analysis [General Sta­tis­tics]

Dear D_Labes,

I am not a R user, but as I learned you can do meta-analysis (combined p-values analysis) of studies (hint: BE guideline: Chapter 4.1.8 / "Alternatively when relevant a combined analysis of all studies can be provided in addition to the individual study analysis."

Or how do you solve that in SAS?

Greetings
earlybird


Edit: Opened as a new thread (was linked to Survey: R use in BE/BA, category changed. [Helmut]
d_labes
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Berlin, Germany,
2010-04-09 10:35
(5512 d 20:27 ago)

@ earlybird
Posting: # 5060
Views: 8,867
 

 Meta-analysis in SAS

Dear earlybird,

❝ I am not a R user, but as I learned you can do meta-analysis (combined p-values analysis) of studies (hint: BE guideline: Chapter 4.1.8 / "Alternatively when relevant a combined analysis of all studies can be provided in addition to the individual study analysis."


❝ Or how do you solve that in SAS?


Although I have not done any serious meta-analysis in SAS upto now I guess it is possible. All is possible with
[image] :-D
See for instance SUGI 27: SAS® Tools for Meta-analysis

Regards,

Detlew
Helmut
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2010-04-09 22:33
(5512 d 08:29 ago)

@ d_labes
Posting: # 5070
Views: 8,889
 

 Meta-analysis vs. naïve pooling

Dear D. Labes & earlybird!

SUGI 27: SAS® Tools for Meta-analysis


Is it really that easy? See the example at page 2:

Suppose we have [...] two identical studies, following the same protocol, using the same treatments, using the same response variable, and suppose once again that we can obtain the data. We could then fit a mixed model (if we wanted to treat study as a random effect), using PROC MIXED, or an ANOVA model (if we wanted to treat study as a fixed effect), using PROC GLM.


It took me while to find suitable data in my files - who repeats a study without any modifications? This was the closest I could get: AUC-data, same protocol (clinical site, sampling schedule, analytical method,...). Different batches of test and reference were used (actually the reference came from two countries).

Single studies
Fixed: sequence+treatment+period
Random: subject(sequence)
Study 1: n=12, 99.93% (94.46% - 105.71%), CVintra 7.61%
Study 2: n=13, 91.00% (85.26% -  97.12%), CVintra 9.24%


Naïve pooling (study not in the model)
Fixed: sequence+treatment+period
Random: subject(sequence)
Pooled 1: n=25, 95.05% (90.86% -  99.43%), CVintra 9.31%

Interesting: The CV is higher than in either study despite the higher sample size.

OK, let's add the study to the model...
Fixed: sequence+treatment+period
Random: subject(sequence)+study
Pooled 2: n=25, 95.05% (90.85% -  99.43%), CVintra 9.31%

Aha No.1 :confused:

And code all as fixed...
Fixed: sequence+treatment+period+subject(sequence)+study
Pooled 3: n=25, 95.05% (90.86% -  99.43%), CVintra 9.31%

Aha No.2

Besides some minor differences in the second decimal of the lower CL all models came up the same. Why all the fuzz with sequential designs, alpha-adjustements and the like - if I can simply throw all data into the big pot, stir it up, and voilá...

Again: Is it really that easy?
Both studies were already evaluated, the alpha is 'consumed' - any professional statisticians out there?

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ElMaestro
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Denmark,
2010-04-10 00:02
(5512 d 07:00 ago)

@ Helmut
Posting: # 5071
Views: 8,587
 

 Meta-analysis vs. naïve pooling

Hi HS,

I do not have the definitive answer, but I have a comment and a question.

Comment:
Study will be a between-subject factor. Thus it should not influence the intra/residual. Adding "study" as a factor thus might not mean much in terms of the outcome as compared to an anova and the subsequent CI without that factor.

Question:
Can you show a bit more? I wonder why the combined CV's (9.31%) are higher than those from the two individual studies. Were the subjects uniquely coded - i.e. "Subject 1" was uniquely assigned to either study 1 or 2 etc?


Best regards
EM.

Pass or fail!
ElMaestro
Helmut
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2010-04-10 00:11
(5512 d 06:51 ago)

@ ElMaestro
Posting: # 5072
Views: 8,597
 

 Meta-analysis vs. naïve pooling

Dear ElMaestro!

❝ Study will be a between-subject factor. Thus it should not influence the intra/residual. Adding "study" as a factor thus might not mean much in terms of the outcome as compared to an anova and the subsequent CI without that factor.


Right.

❝ Can you show a bit more?


Just leaving the office. Maybe next year. ;-)

❝ I wonder why the combined CV's (9.31%) are higher than those from the two individual studies.


Surprised me too.

❝ Were the subjects uniquely coded - i.e. "Subject 1" was uniquely assigned to either study 1 or 2 etc?


Yes. Codes were
study (1-2)
treatment (test/reference)
subject (001-013 in study 1, and 101-112 in study 2)
period (1-2)

P.S.: Nice signature.

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ElMaestro
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Denmark,
2010-04-10 00:20
(5512 d 06:42 ago)

@ Helmut
Posting: # 5073
Views: 8,683
 

 Meta-analysis vs. naïve pooling

Ahoy!

❝ Yes. Codes were

❝ study (1-2)

❝ treatment (test/reference)

❝ subject (001-013 in study 1, and 101-112 in study 2)

❝ period (1-2)


There's a period 1 and 2 in both studies, so one could code it as the period-by-study interaction in analyses where study is included. I have not thought this fully through and if I tried my brain would prolly just idle because I am not a statistician.

❝ P.S.: Nice signature.


Dank je wel.

Best regards
EM.

Pass or fail!
ElMaestro
Helmut
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2010-04-10 02:49
(5512 d 04:13 ago)

@ ElMaestro
Posting: # 5074
Views: 8,844
 

 Meta-analysis vs. naïve pooling

Ahoi, ElMaestro!

❝ […] I have not thought this fully through […] because I am not a statistician.


Me not either. Maybe codes for period should be simply 1-4.

Pooled: n=25, 95.19% (91.11% - 99.46%), CVintra 9.03%

Results identical for all models (yeah, treatments still within). Well, how to set up your interaction?

Goede wind!

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ElMaestro
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Denmark,
2010-04-10 10:13
(5511 d 20:49 ago)

(edited on 2010-04-10 12:34)
@ Helmut
Posting: # 5075
Views: 8,591
 

 Meta-analysis vs. naïve pooling

Goede morgen,

❝ Well, how to set up your interaction?


I only know R (Study:Per)1.
But it could also be faked by calling the periods of the second study "3" and "4" etc. Then no need to specify the interaction, I think.

EM.

Addendum: Just re-read your post - you are suggesting exactly the same if I interpret your post right?


1: Sorry wrote Trt:Per at first - typo.
Helmut
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2010-04-10 16:46
(5511 d 14:16 ago)

@ ElMaestro
Posting: # 5076
Views: 8,531
 

 Yes, but...

Ahoi!

❝ Just re-read your post - you are suggesting exactly the same if I interpret your post right?


Yes. After RTFM and setting up the model with a study × period interaction term, I'm getting exactly the same results as with faked four periods.

There are only minor differences between the 'faked 4 period' and interaction set-ups, probably due to numerical issues. More significant digits below:
Faked Periods:  95.1926% (91.1103% - 99.4578%), CVintra 9.02706%
Period × Study: 95.1915% (91.1007% - 99.4660%), CVintra 9.04355%


Apart from the technical issues, my main concern remains alpha in the combined analysis.
:ponder:

Though a sailor and a scuba-instructor supposedly are familiar with murcky waters, I guess we would need some statistical consultancy here.

Wist het anker! :pirate:

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ElMaestro
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Denmark,
2010-04-11 13:44
(5510 d 17:17 ago)

@ Helmut
Posting: # 5077
Views: 8,480
 

 Yes, but...

Hi HS,

❝ I guess we would need some statistical consultancy here.


Completely agree. Wouldn't it be wonderful if for example sdavis joined in with a comment here in this forum, in this thread, dealing with this topic?

Best regards
EM.
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2010-04-11 16:27
(5510 d 14:35 ago)

@ ElMaestro
Posting: # 5078
Views: 8,583
 

 Yes, but...

Dear ElMaestro!

Yes, Simon is a nice and clever lad - not only here, but also in the real world. But this problem is not specific for WinNonlin.

I'm not sure whether Simon is monitoring all posts here. If you think it would be nice joining us - contact him.

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d_labes
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Berlin, Germany,
2010-04-12 15:32
(5509 d 15:30 ago)

@ Helmut
Posting: # 5087
Views: 8,484
 

 Meta-analysis alpha

Dear Helmut!

❝ Is it really that easy?

❝ ... Why all the fuzz with sequential designs, alpha-adjustements and the like - if I can simply throw all data into the big pot, stir it up, and voilá...


❝ Again: Is it really that easy?

❝ Both studies were already evaluated, the alpha is 'consumed' - any professional statisticians out there?


Since I'm only a bloody raw recruit in statistics and since I haven't done serious meta-analysis up to now I can't answer these questions really professional.

But what I have read scarcely about that topic there is actually no such thing in meta-analysis like alpha-adjustment or alpha-spending.
How should it be? Meta analysis was invented for pooling studies (mostly from literature) which generally are not under control of the meta-analyst and had generally already been evaluated with some alpha. Therefore there is little or no room for alpha-spending at all. Thats why meta-analyses are not generally accepted as confirmatory proof.

But there are regulatory concerns, f.i. in CPMP/EWP/2330/99 "Points to consider with 1. meta-analysis 2. one pivotal study". On page 2 is stated:
"When a meta-analysis is included in an application it should be performed in accordance with a protocol specifying
...
-Statistical methods (including methods for investigation of heterogeneity). In case where the meta-analysis provides the pivotal evidence for an indication, a p-value more extreme then the conventional significance level of 0.05 would generally required, and narrow confidence intervals for the treatment effect would be expected. The required degree of significance will be judged on a case by case basis considering factors such as amount of supportive data, plausibility of hypothesis tested and whether the analysis is pre-specified or not."

Emphasis by me.

BTW: I would incorporate a treatment by study interaction in the model as test of heterogeneity.
BTW2: What big differences did you expect with such a very low intra-subject variability?
BTW3: See Chow/Liu "Design and Analysis ...", Chapter 16 "Meta-analysis for bioequivalence review" to be more confused :-D.

Regards,

Detlew
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2010-04-12 16:25
(5509 d 14:37 ago)

@ d_labes
Posting: # 5088
Views: 8,531
 

 Meta-analysis alpha

Dear D. Labes!

Agree with your points (e.g., not confirmatory). I did not know this EMA-document, THX.
Interesting Section II.1.3:

A retrospective meta-analysis of only two studies originally intended to stand on their own is not expected to add any useful information. In particular, a meta-analysis can­not be used to reconcile the conflicting results of one positive and one inconclusive study.


❝ BTW: I would incorporate a treatment by study interaction in the model as test of heterogeneity.


OK.

❝ BTW2: What big differences did you expect with such a very low intra-subject variability?


I didn't expect anything. This was just the only dataset I had coming closest to two identical studies. As said in my previous post it is unlikely to repeat a study with any modifications.

❝ BTW3: See Chow/Liu "Design and Analysis ...", Chapter 16 "Meta-analysis for bioequivalence review" to be more confused :-D.


Oh. :surprised:

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d_labes
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Berlin, Germany,
2010-04-12 17:03
(5509 d 13:59 ago)

@ Helmut
Posting: # 5091
Views: 8,396
 

 2-Study Meta-analysis

Dear Helmut!

❝ Interesting Section II.1.3:

A retrospective meta-analysis of only two studies originally intended to stand on their own is not expected to add any useful information. In parti­cu­lar, a meta-analysis cannot be used to reconcile the conflicting results of one positive and one inconclusive study.


THX for highlighting this. IMHO its not so very sound, not to say ... urrgh (cervix blocked to to keep a civil tongue :-D), especially if the study sizes differ to a greater extent.

Fortunately this is weaker formulated in the new BE guidance, text pointed to by earlybird, page 16: "Alternatively, when relevant, a combined analysis of all studies can be provided in addition to the individual study analyses. It is not acceptable to pool together studies which fail to demonstrate bioequivalence in the absence of a study that does."
Hopefully this overrules.

Regards,

Detlew
Helmut
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2010-04-12 17:18
(5509 d 13:44 ago)

@ d_labes
Posting: # 5093
Views: 8,437
 

 2-Study Meta-analysis

Dear D. Labes!

❝ […] cervix blocked to to keep a civil tongue :-D


Cervix?! Not larynx?

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d_labes
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Berlin, Germany,
2010-04-12 17:33
(5509 d 13:29 ago)

@ Helmut
Posting: # 5094
Views: 8,626
 

 Anatomical miracle

Dear Helmut!

❝ Cervix?! Not larynx?


Oh, what a shame. False page in my anatomy atlas :-(.
(Leo "Hals")

Regards,

Detlew
Helmut
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2010-04-12 17:40
(5509 d 13:22 ago)

@ d_labes
Posting: # 5095
Views: 8,451
 

 Anatomical miracle

Dear D. Labes!

❝ Oh, what a shame. False page in my anatomy atlas :-(.


Maybe correct image of the body, but upside down.
Hint: if you experience difficulties in reading the text - turn around. ;-)

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