Datacollector
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United Kingdom,
2019-07-27 12:09

Posting: # 20448
Views: 1,160
 

 Good News, Bad News [Study As­sess­ment]

I was involved with a regular 2 way crossover with a non endogenous compound which is not very exotic. The good news was that the study comfortably met the usual bioequivalence criteria. The less good news was that there were significant period and sequence effects for both AUC and Cmax. We are assured we can ignore the sequence effect as the usual conditions for so doing apply. Looking at the period data (treating as two parallel studies) we find the T/R point estimator lies considerably below the acceptance range, while for period 2, it is rather higher than the BE acceptance range. This has given rise to some concern. Does the observation of the difference between periods negate the finding of equivalence? I should be grateful for any advice or suggestions. I don't have any obvious reason to suspect the design or conduct of the study.


Edit: Please follow the Forum’s Policy[Helmut]
Helmut
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Vienna, Austria,
2019-07-27 13:15

@ Datacollector
Posting: # 20449
Views: 1,097
 

 Good News only

Hi Datacollector,

» […] a regular 2 way crossover […] comfortably met the usual bioequivalence criteria.

Congratulations.

» The less good news was that there were significant period and sequence effects for both AUC and Cmax.

AUC and Cmax are highly correlated. If you see significant effects for one likely you see them for the other as well.

» We are assured we can ignore the sequence effect as the usual conditions for so doing apply.

Correct. A statistically significant sequence effect (better unequal carry-over because equal carry-over doesn’t matter) can be caused by
  • a true sequence effect,
  • a true carry-over effect,
  • a true formulation-by-period interaction,
  • a randomization failure,
or any possible combination of them. OK, the last one can be assessed in an audit/inspection. These effects are ‘confounded’ (i.e., cannot be separated by a statistical method in a non-replicative design). Hence, they can only be avoided by design (sufficiently long washout). It was shown by Freeman* that analysis of period data gives biased estimates and a potentially inflated type I error. It took the EMA 21 years to incorporate that in the BE-GL:

A test for carry-over is not considered relevant and no decisions regarding the analysis (e.g. analysis of the first period only) should be made on the basis of such a test. The potential for carry­over can be directly addressed by examination of the pre-treatment plasma concentrations in period 2 (and beyond if applicable).


» Looking at the period data (treating as two parallel studies) …

Given the above, why did you do that at all? The sequence effect is not relevant. Even more, the period effect is adjusted for in the crossover model anyway (it means out).

» … we find the T/R point estimator lies considerably below the acceptance range, while for period 2, it is rather higher than the BE acceptance range.

Are you looking for an explanation?
Since the two periods are now evaluated as parallel designs there are tons of reasons. If a study would have been planned (!) as a parallel design, the usual conditions should have been observed: It is of utmost importance to keep groups as similar as possible (sex, body weight, age-dependent clearance, …). If the drug is subjected to polymorphic metabolism, pheno- (or even better geno-) typing should be done. This was not the case – and with good reasons. Since in a crossover subjects act as their own reference, we don’t have to care about all that. It is quite possible that – by pure chance – groups were not similar: You think that your are comparing treatments but actually you are comparing treatments + unknown (!) group differences. Confounded effects again. Meaningless.

» … This has given rise to some concern.

By whom and why?

» Does the observation of the difference between periods negate the finding of equivalence?

Nope.


  • Freeman PR. The performance of the two-stage analysis of two-treatment, two-period cross-over trials. Stat Med. 1989;8(12):1421–32. doi:10.1002/sim.4780081202.

Cheers,
Helmut Schütz
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Datacollector
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United Kingdom,
2019-07-27 13:34

@ Helmut
Posting: # 20450
Views: 1,062
 

 Good News only, but not according to some

Hi Helmut,
Thanks for your kind and considered response.
To answer your question on the origin of the concerns-
I was not at first unduly concerned- the study was submitted. However, a well regarded EU regulatory agency has raised objections on public health grounds. Treatment by period interaction has been mentioned. I can't see how that could arise given that the design of the study is fine and assuming there was no major issue in the conduct of the study. I can only infer that the agency suspects that the study has not been executed correctly but is not prepared to say so in black and white. Have you encountered this kind of response?

Thanks & Regards
Helmut
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Vienna, Austria,
2019-07-27 13:48

@ Datacollector
Posting: # 20451
Views: 1,065
 

 ’Some’ should read the GL (and again, and again)

Hi Datacollector,

» […] a well regarded EU regulatory agency has raised objections on public health grounds. Treatment by period interaction has been mentioned. I can't see how that could arise given that the design of the study is fine and assuming there was no major issue in the conduct of the study. I can only infer that the agency suspects that the study has not been executed correctly …

OK, then the agency should trigger an inspection1 rather than just ‘suspect’ sumfink. Again: Statistics2 cannot help. BTW, it is yet another – all too common – misconception that the p-value gives the prob­ability that the Null-hypothesis is true.

» … but is not prepared to say so in black and white.

Well, they are happy to speculate in black and white. As I wrote before, only a failure in randomization can be assessed in an inspection. Everything else: No way.

» Have you encountered this kind of response?

Yes. By the German BfArM three days (‼) ago. :thumb down:

Potential serious risk to public health not already raised by the RMS as major objection.
However, regarding ████, serious concerns on the results from BE-study ████ remain.




  1. Though I don’t see a clear reason in “Guidance on triggers for inspections of bioequivalence trials: Quick scan”.
  2. Even raising the question is some kind of double moral standards. We are not allowed to exclude anything based on statistics alone (not even reanalyse a sample). Quod licet Iovi, non licet bovi?

Cheers,
Helmut Schütz
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ElMaestro
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Belgium?,
2019-07-27 13:50

@ Datacollector
Posting: # 20452
Views: 1,070
 

 Good News only, but not according to some

Hi DC,

can you show me a plot or table of:
ln(T) in period 1
ln(T) in period 2
ln(R) in period 1
ln(R) in period 2
you can use LSMeans.

Many thanks.

I could be wrong, but...
Best regards,
ElMaestro
Helmut
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Vienna, Austria,
2019-07-27 16:55

@ ElMaestro
Posting: # 20453
Views: 1,026
 

 My stuff

Hi Elmaestro,

like DC’s the study I have on my desk passed with flying colors. Balanced sequences, equal number of subjects in both periods.
p-values for AUC: 0.576 (treatment), 7.17·10–8 (subjects), 2.42·10–8 (sequence), 0.0321 (period).
Geometric means ±SD. R in blue and T in red:

[image]

If there is no true formulation-by-period interaction and no random variation lines should intersect exactly midway. The deviation we see here is negligible.

Cheers,
Helmut Schütz
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ElMaestro
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Belgium?,
2019-07-27 17:38

@ Helmut
Posting: # 20454
Views: 1,010
 

 My stuff

Hi Hötzi,

this is either an element of chance or something else. Clearly.:-D:-D:-D

I could be wrong, but...
Best regards,
ElMaestro
Datacollector
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United Kingdom,
2019-07-27 19:13

@ ElMaestro
Posting: # 20455
Views: 1,000
 

 My stuff

Hello Helmut & Elmaestro,

Mine is Bfarm also

Not sure if this is still wanted, but just in case (AUC data only)...
Period 1      lnauc         
subj  seq   r             subj  seq   t
1     RT    10.10502423   2     TR    8.461196855
4     RT    9.858151112   3     TR    8.049084725
5     RT    10.1570727    6     TR    9.134989797
8     RT    10.30224861   7     TR    9.80963512
10    RT    10.14185204   9     TR    9.607803079
12    RT    10.15300387   11    TR    9.288176863
13    RT    9.234133361   14    TR    10.09032121
16    RT    9.6316848     17    TR    9.594284762
18    RT    9.933736262   20    TR    9.591241713
19    RT    10.13849011   22    TR    10.15347438
21    RT    9.254534945   24    TR    9.978455637
23    RT    10.26022747   25    TR    9.979773551
28    RT    10.46726026   27    TR    9.865065177
29    RT    10.69775349   30    TR    10.14016787
31    RT    10.79830095   32    TR    9.793933869
33    RT    9.443833778   34    TR    9.951208574
36    RT    10.43203552   35    TR    8.986816373
38    RT    10.00525728   37    TR    10.28299786
40    RT    10.17148289   39    TR    9.742132651
42    RT    9.604308711   41    TR    10.01563264

period 2      lnauc         
subj  seq   r             subj  seq   t
2     TR    9.689028928   1   RT    10.05836031
3     TR    8.541183313   4     RT    9.840464576
6     TR    8.929588497   5     RT    10.17625787
7     TR    9.78535555    8     RT    10.59544292
9     TR    9.859390879   10    RT    9.781956608
11    TR    10.12780881   12    RT    10.61589893
14    TR    9.948133331   13    RT    9.377874464
17    TR    9.883167747   16    RT    9.989570382
20    TR    9.682245193   18    RT    10.11575538
22    TR    9.913510257   19    RT    10.01053274
24    TR    9.982305249   21    RT    10.35609722
25    TR    9.827957054   23    RT    10.24275972
27    TR    10.13028259   28    RT    10.47511429
30    TR    10.19712472   29    RT    10.55732173
32    TR    10.09170793   31    RT    10.60293417
34    TR    10.22557906   33    RT    9.621163434
35    TR    9.004169836   36    RT    10.08396733
37    TR    10.22878581   38    RT    10.02238122
39    TR    9.725128774   40    RT    10.4355172
41    TR    9.793740653   42    RT    9.646916863


Thanks & Regards
Helmut
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Vienna, Austria,
2019-07-27 23:53

@ Datacollector
Posting: # 20456
Views: 991
 

 

Hi Datacollector,

looks familiar. :-D

Since we are in the same boat and out of curiosity: p-values of the sequence effect were given by the CRO and also by the BfArM with 0.0077 (AUC) and 0.0252 (Cmax).
Recalculated in Phoenix WinNonlin 8.1 and R 3.6.1 (function lm() of stats):

PK metric  p (period)  p (sequence)
  AUC        0.0321      2.42·10–5
  Cmax       0.0358      2.36·10–5

What‽


Extending what I wrote at the end of this post (not for you – as an obvious initiate – but the archive). Let’s assume that the two groups randomized to sequences TR and RT differ (by chance) in their body weights. Might happen cause we don’t stratify in a crossover for anything. Both T and R have a relative BA of 1. Hence, T/R should be 100%. I assumed that the response with a body weight of 70 would be exactly 1. Due to different volumes of distribution the response will be higher in the group with low BW and vice versa. Two cases (the responses are the means of groups):
  1. No period effects:
    group  BW  sequence  period  treatment  per. effect  response
      1    75     TR       1         T          1.00      0.933
      1    75     TR       2         R          1.00      0.933
      2    50     RT       1         R          1.00      1.400
      2    50     RT       2         T          1.00      1.400
    crossover
      T   = √0.933 × 1.400 = 1.143
      R   = √0.933 × 1.400 = 1.143
      T/R = 100% (unbiased)
    period 1
      T   = 0.933
      R   = 1.400
      T/R =  67% (bias –33%)
    period 2
      T   = 1.400
      R   = 0.933
      T/R = 150% (bias +50%)


  2. Extremely unequal period effects:
    group  BW  sequence  period  treatment  per. effect  response
      1    75     TR       1         T          1.25      1.167
      1    75     TR       2         R          1.25      1.167
      2    50     RT       1         R          0.50      0.700
      2    50     RT       2         T          0.50      0.700
    crossover
      T   = √1.167 × 0.700 = 0.904
      R   = √1.167 × 0.700 = 0.904
      T/R = 100% (unbiased)
    period 1
      T   = 1.167
      R   = 0.700
      T/R = 167% (bias +67%)
    period 2
      T   = 0.700
      R   = 1.167
      T/R =  60% (bias –40%)
Apart from Freeman’s theoretical stuff this shows clearly that is futile to analyze periods of a crossover separately. Given, such different body weights are unlikely. However, try it with a smaller difference. Estimates will always be biased.
One might be tempted to be prepared for the worst (i.e., bizarre deficiency letters) and aim at a stratified randomization keeping body weights as close as possible. But where will it end? Having a single slow metabolizer in one group and none in the other could already be the killer. Doesn’t make any sense.

Cheers,
Helmut Schütz
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mittyri
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Russia,
2019-07-28 15:19

@ Helmut
Posting: # 20457
Views: 914
 

 Sequence effect Vs Subject effect?

Hi Helmut,

» Since we are in the same boat and out of curiosity: p-values of the sequence effect were given by the CRO and also by the BfArM with 0.0077 (AUC) and 0.0252 (Cmax).
» Recalculated in Phoenix WinNonlin 8.1 and R 3.6.1 (function lm() of stats):
»

PK metric  p (period)  p (sequence)
»   AUC        0.0321      2.42·10–5
»   Cmax       0.0358      2.36·10–5

What‽

which one sequence effect are you referring to?

Kind regards,
Mittyri
Helmut
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2019-07-28 15:59

@ mittyri
Posting: # 20458
Views: 904
 

 Sequence effect Vs Subject effect?

Hi Mittyri,

» which one sequence effect are you referring to?

Are you trying to confuse me? The crappy nested model (sorry, my Capt’n), all effects fixed. AUC only.

PHX/WNL
Hypothesis       Numer_DF Denom_DF      SS   MS     F_stat  P_value
sequence                1       38  2.9315 2.93152 49.0660 2.423E-08
sequence*subject       38       38 14.0771 0.37045  6.2004 7.174E-08
treatment               1       38  0.0190 0.01903  0.3185 0.57580
period                  1       38  0.2959 0.29594  4.9532 0.03205
Error                               2.2704 0.05975


R
                 Df  Sum Sq Mean Sq F value    Pr(>F)
sequence          1  2.9315 2.93152 49.0660 2.423e-08 ***
sequence:subject 38 14.0771 0.37045  6.2004 7.171e-08 ***
treatment         1  0.0190 0.01903  0.3185   0.57580
period            1  0.2959 0.29594  4.9532   0.03205 *
Residuals        38  2.2704 0.05975

Cheers,
Helmut Schütz
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mittyri
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Russia,
2019-07-28 16:20

@ Helmut
Posting: # 20459
Views: 907
 

 Sequence effect Vs Subject effect?

Hi Helmut,

Sorry for confusion
I meant to divide the MS of the sequence effect by the MS of subject(sequence), not by the MS of the residual error (same manner you did in famous Rscript published). F is about 7.9, sorry R is not available at the moment to check p value

Kind regards,
Mittyri
Helmut
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Vienna, Austria,
2019-07-28 16:36

@ mittyri
Posting: # 20460
Views: 898
 

 Oops!

Hi Mittyri,

» I meant to divide the MS of the sequence effect by the MS of subject(sequence), not by the MS of the residual error

Oops, how stupid!

Analysis of Variance Table

Response: log(AUC)
                 Df Sum Sq Mean Sq F value   Pr(>F)   
sequence          1  2.932  2.9315  49.066 2.42e-08 ***

period            1  0.296  0.2959   4.953   0.0321 * 
treatment         1  0.019  0.0190   0.319   0.5758   
sequence:subject 38 14.077  0.3704   6.200 7.17e-08 ***
Residuals        38  2.270  0.0597                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Between subjects
          Df  Sum Sq Mean Sq F value    Pr(>F)   
sequence   1  2.9315 2.93150  7.9134 0.0077255 **

Residuals 38 14.0770 0.37045                     
Error: Within subjects
          Df  Sum Sq  Mean Sq F value  Pr(>F) 
period     1 0.29594 0.295940  4.9532 0.03205 *
treatment  1 0.01903 0.019032  0.3185 0.57580 
Residuals 38 2.27040 0.059746                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Analysis of Variance Table

Response: log(Cmax)
                 Df Sum Sq Mean Sq F value   Pr(>F)   
sequence          1  1.821  1.8205  23.193 2.36e-05 ***

period            1  0.372  0.3718   4.737   0.0358 * 
treatment         1  0.005  0.0049   0.063   0.8033   
sequence:subject 38 12.731  0.3350   4.268 9.78e-06 ***
Residuals        38  2.983  0.0785                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Between subjects
          Df  Sum Sq Mean Sq F value   Pr(>F) 
sequence   1  1.8205 1.82050  5.4341 0.025152 *

Residuals 38 12.7310 0.33501                   
Error: Within subjects
          Df  Sum Sq Mean Sq F value Pr(>F) 
period     1 0.37182 0.37182  4.7370 0.0358 *
treatment  1 0.00494 0.00494  0.0629 0.8033 
Residuals 38 2.98270 0.07849                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


THX! I stand corrected.

Cheers,
Helmut Schütz
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