## Group effects FDA/EMA [Two-Stage / GS Designs]

Hi everybody and nobody!

I am pointing to the 2x2 crossover studies in groups due to logistic reasons (capacity of clinical unit, etc.).

Many discussions about groups were done here but recently I was asked to calculate effect of groups in one failed study (study acc. to EMA guidelines, in protocol/report without group effect testing - two groups within the week). (But no problem when "everything possible" is analysed in a failed study with getting more informations for sponsor's next decision.)

Nevertheless there is nothing stated from EMA on testing of such groups (or did I miss something?).
For FDA there is CDER or known letter mentioned many times dealing with groups*treatments. So everyone can follow it to analyse the model for FDA.
For EMA groups are not intended to testing. ?

I have opinion that group effect is not important in 2x2 crossover with proper planning/realization. (Moreover I have never seen group testing for EMA and I like the sentence "With one week between groups I would never ever thought a milli­second of setting up a group model." from this post.)

Following model (from the post I replay to) sounds right but only sounds or is?
» » 2. What kind of statistical model is preffered for Europe ..
» » Something like that:
» » Fixed: sequence, period, treatment, group, subject(sequence)
»
» Sounds right to me, and I've had thumbs up in sc.advices.

Actually groups and sequences are nested in Subjects so there is no difference in results of BE from the standard model without groups (difference can be only in sequence effect and of course "in new" effects Groups and in Subjects(Groups*Sequences), so in between-subject variability also).

Moreover optional statement as: "If Groups differ significantly, they can't be pooled and BE must be calculated in one group only." smells fishy to me (I heard this bad idea somewhere, maybe misunderstanding due to inaccuracy).

Group effect in such model has one property similar as period effect (not only that sometimes it happens significant). Group effect as well as Period effect is not able affect BE decision (in this simple model).
You know if you calculate data from one period by 1000 nothing change in BE decision, only period significance (+intercept+total) is different. No change at Formulations, Subjects, Error. Not problem unless the study is extremely imbalanced.
In the same way Group effect in such defined model is not able affect BE decision - if you multiply data from one group by 1000, there is no change in Formulations individual ratios, at ANOVA effects Formulations, Periods, Sequence and MSE. The difference is only in ANOVA group effect (will be significant) + Subjects (due to group is nested within the subjects).
I checked that property in the next example. (The same size of groups and no dropouts is not required for this property I think, even though in my testing example below it is so. Multiplication by 1000 will be always used for same number of T and R values even in case of dropouts or whatever - sure imbalancing would change sequence effect, but not BE decision I expect.)

I prepared example (no real data ... to get "unlucky" results).
data=read.delim("http://tj-prazdroj.lesyco.cz/download/groups.txt")

Firstly I calculated classical GLM model without groups. (according to EMA)
Effects = Formulations, Periods, Sequences, Subjects(Sequences).

Results:
CVintra = 27.4%
PE (LL,UL) = 1.0127 (0.9236,1.1103)
Great results in 80-125%, I can congratulate myself! x)

No change after adding effect Groups to the model:
Effects = Formulations, Periods, Sequences, Groups, Subjects(Sequences*Groups).

Of course everybody and nobody get the same results as above - due to Sequences and Groups are nested in Subjects, i.e. only effects Formulations, Periods, Subjects (as sum of between-subjects effects) take role for intra-subject CV, GMR of T/R and CI.

The effect Groups seems to be not significant as per ANOVA table (p=0.1230537).
So it sounds good, everyone can write statement about Groups are not significant and data could be pooled (when using this simple model with Groups).

The Phantom Menace for this example is to use another model. (according to FDA)
Effects = Formulations, Periods(Groups), Sequences, Sequences*Groups, Subjects(Sequences*Groups), Groups, Formulations*Groups.
(GLM with random statement for Subjects was used)

Results:
CVintra = 25.7%
PE (LL,UL) = 1.0127 (0.9284,1.1045)

But with significant Formulations*Groups interaction (p=0.008066805 < 0.1). There is recommendation to not to pool the data and calculate BE separately in one of the groups (if this model planned for the decision of pool or not to pool).
Because the data are written by me randomly and then changing and changing to get the nice and not nice results at the same. The groups separately provide us with next BE results:

Group 1:
data1=subset(data,data[,"Groups"]==1)
CVintra = 30.9%
PE (LL,UL) = 0.8774 (0.7554,1.0191)

Group 2:
data2=subset(data,data[,"Groups"]==2)
CVintra = 19.4%
PE (LL,UL) = 1.1689 (1.0626,1.2858)

I only want to make more clear and more visibile what can be hidden behind the "no significant group effect".

If group testing was required by EMA I would prefer test for group*treatment interaction. But I am still convinced that group effect is not required to test in standard 2x2 crossover study. For me it seems similar to have 2x2 crossover study on 24 subjects in 1 group and test for Period*Treatment interaction (e.g. in model Period*Treatment, Sequence, Subjects(Sequence) - if Period*Treatment significant, use data from one period as in parallel design. It will be certainly significant if ratio T/R (i.e. ratio with means of different subjects) in period 1 will be around 1.25 and T/R in period 2 will be 0.80 (not probable to have opposite (reciprocal) ratio, but periods are often more separated in time than groups and who knows after several months in case of long washout).

Best regards,
zizou

Note: All calculations were done using GLM (in R and/or SPSS).