sweiner
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2020-06-30 01:07
(114 d 01:43 ago)

Posting: # 21612
Views: 2,327
 

 higher order crossover methodology [General Sta­tis­tics]

Hi,
In a 5-way BE crossover trial, is there a methodology available that allows one to analyze 3 out of 5 sequences for BE in an interim fashion, and contingent upon results complete the remaining 2 sequences and analyze all 5 sequences at the conclusion?
Could you please provide references on this subject.

Thanks,
Sveta


Edit: Category changed; see also this post #1[Helmut]
Helmut
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Vienna, Austria,
2020-06-30 12:19
(113 d 14:31 ago)

@ sweiner
Posting: # 21615
Views: 1,734
 

 All dosed subjects have to be analyzed

Hi Sveta,

» In a 5-way BE crossover trial, is there a methodology available that allows one to analyze 3 out of 5 sequences for BE in an interim fashion, and contingent upon results complete the remaining 2 sequences and analyze all 5 sequences at the conclusion?

Once you dosed subjects (i.e., in all 5 sequences), you have to analyze them. Anything else is not ethical. Along these lines the EMA’s BE-GL, section Subject accountability:

Ideally, all treated subjects should be included in the statistical analysis. […]
The data from all treated subjects should be treated equally. It is not acceptable to have a protocol which specifies that ‘spare’ subjects will be included in the analysis only if needed as replacements for other subjects who have been excluded. It should be planned that all treated subjects should be included in the analysis, even if there are no drop-outs.

(my emphasis)

Even if your protocol would be accepted by the IEC/IRB and agency (I hope not), your approach might lead to an inflated type I error (if you fail with 3 sequences and continue with the other 2) because at the end you will use 60% of the data twice. Calls for some kind of α-adjustment (narrower CI) due to multiplicity issues.

» Could you please provide references on this subject.

IMHO, nothing published – and for a reason. Don’t even think about the ‘magic’ α 0.0294. In short: Forget it.

Dif-tor heh smusma 🖖
Helmut Schütz
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sweiner
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2020-06-30 17:08
(113 d 09:42 ago)

@ Helmut
Posting: # 21621
Views: 1,674
 

 All dosed subjects have to be analyzed

Thanks Helmut! This is very helpful.


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
Relaxation
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Germany,
2020-06-30 14:10
(113 d 12:40 ago)

@ sweiner
Posting: # 21618
Views: 1,703
 

 higher order crossover methodology

Dear Sveta.

Nothing to add to the answer already given.
I just want to ask, whether you may want to give some more background information on the situation.
Because I really was not able to think of a scenario, where considering only a part of the population based on the sequences could provide a benefit (unless its a sneaky two-stage, but then as said: nothing to add to the answer given).
Likely just a case of limited imaginative power on my side :ponder:.

Best regards,

Steven.
sweiner
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2020-06-30 17:10
(113 d 09:41 ago)

@ Relaxation
Posting: # 21622
Views: 1,668
 

 higher order crossover methodology

» I just want to ask, whether you may want to give some more background information on the situation.
» Because I really was not able to think of a scenario, where considering only a part of the population based on the sequences could provide a benefit […]

Dear Steven, thanks for the feedback!
Here the first part of the 5-way crossover analysis (Part A- 3x3 analysis) would be under fasted conditions (Tablet formulation #1 vs. Tablet formulation #2 vs. Capsule formulation), and if BE is shown for either Tablet formulation vs. Capsule formulation, same subjects would complete in a 2x2 fashion under fed conditions (Tablet #1 or #2 [depending on BE result] vs. Capsule). In the final analysis, once all 5 sequences complete all 5 periods, fasted state vs. fed state to be compared for BE.


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
ElMaestro
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Belgium?,
2020-06-30 18:17
(113 d 08:34 ago)

@ sweiner
Posting: # 21623
Views: 1,675
 

 higher order crossover methodology

Ah,

it is all coming together now.

Thanks sweiner,
this is a great question.:-)

» In a 5-way BE crossover trial, is there a methodology available that allows one to analyze 3 out of 5 sequences for BE in an interim fashion, and contingent upon results complete the remaining 2 sequences and analyze all 5 sequences at the conclusion?

Should read: "In a 5-way BE crossover trial, is there a methodology available that allows one to analyze 3 out of 5 periods for BE in an interim fashion, and contingent upon results complete the remaining 2 periods and analyze all 5 periods at the conclusion?"

This is an interesting idea, one that has not been explored much yet in the public domain; I think a few other sponsors have used it.
It is definitely doable as a single protocol. It is in fact what other companies / sponsors are achieving with two separate studies. Just do it, I think it may not require much operational adjustment or statistical fiddling, unless you can say you will switch to another formulation and re-start another 5-period trial once the first formulation fails after 3 periods.

A great post, in my opinion.

I could be wrong, but...

Best regards,
ElMaestro

No, of course you do not need to audit your CRO if it was inspected in 1968 by the agency of Crabongostan.
Helmut
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2020-07-01 11:14
(112 d 15:36 ago)

@ ElMaestro
Posting: # 21630
Views: 1,650
 

 Fed (IBD) → fasting

Hi ElMaestro & Sveta,

» Should read: "In a 5-way BE crossover trial, is there a methodology available that allows one to analyze 3 out of 5 periods for BE in an interim fashion, and contingent upon results complete the remaining 2 periods and analyze all 5 periods at the conclusion?"
»
» It is definitely doable as a single protocol. […] I think it may not require much operational adjustment or statistical fiddling, …
[image]
@ElMaestro: Operational – no. Statistical – likely yes.
The current regulatory thinking expressed at numerous conferences (nothing published) is that one still has to adjust α because in the first part one gets two chances to demonstrate BE (see this presentation, slide 23). I belonged to the first church (90% CI) for decades though now I’m a convert. I would not try to find an ‘optimal’ 1 adjusted α.

I regolatori stanno bene con [image] Signor Bonferroni.

@Sveta: For most drugs it is more difficult to demonstrate BE in fed state (true food-drug interaction, higher variability) than in fasted state. Consider to switch your approach (fed followed by fast­ed). I haven’t seen a single case where the fed study passed and the fasted one failed, but a lot of cases the other way ’round – which required reformulation. Unfortunately many companies start with the fasted study (hey, that’s standard) only to be hit in fed state.
I recommend also to evaluate the first part according to the “Two at a Time” principle (two separate ana­lyses 2 as Incomplete Block Designs, i.e., T1 vs R and T2 vs R) and not “All at Once” (by one – pooled – ANOVA). 3 For details and references see the vignette of PowerTOST.
Note that the EMA’s BE-GL states:

In studies with more than two treatment arms (e.g. […] a four period study including test and reference in fed and fasted states), the analysis for each comparison should be conducted excluding the data from the treatments that are not relevant for the comparison in question.

(my emphasis)


  1. One would have to formalize the decision process in the selection of T1 or T2: GMR closer to one; if similar, the one with lower variability, etc. IMHO, not worth the efforts, since the average gain in sample sizes even for an optimistic α 0.0304 over Bonferroni’s 0.025 is just ~5%. Add the given reluctance of assessors towards simulation-based methods…

  2. Since you will have only two treatments in each analysis, estimate the sample size for a 2×2×2 design and not for 3×3 Latin Squares. Requires sometimes slightly higher sample sizes.
    library(PowerTOST)
    CV     <- seq(0.15, 0.3, 0.01) # Intra-subject CV
    theta0 <- 0.95                  # Assumed T/R-ratio
    target <- 0.80                  # Target (desired) power
    alpha0 <- 0.05                  # Nominal level
    k      <- 2                     # Number of tests
    alpha  <- alpha0/k              # Bonferroni-adjustment
    res    <- data.frame(CV = CV,
                         design.3 = "3x3",   n.3 = NA, power.3 = NA,
                         design.2 = "2x2x2", n.2 = NA, power.2 = NA)
    for (j in 1:nrow(res)) {
      res[j, 3:4] <- signif(sampleN.TOST(alpha = alpha, CV = res$CV[j], theta0 = theta0,
                                         targetpower = target, design = res$design.3[j],
                                         details = FALSE,  print = FALSE)[7:8], 3)
      res[j, 6:7] <- signif(sampleN.TOST(alpha = alpha, CV = res$CV[j], theta0 = theta0,
                                         targetpower = target, design = res$design.2[j],
                                         details = FALSE,  print = FALSE)[7:8], 3)
    }
    res$change <- sprintf("%+4.2f", 100*(res[, 6] - res[, 3])/res[, 3])
    res$change[res$change == "+0.00"] <- "±0.00"
    names(res)[2:6] <- rep(c("design", "n", "power"), 2)
    txt    <- paste0("Assumed \u03B8 ", theta0, ", target (desired) power ", target)
    if (alpha != 0.05) {
      txt <- paste0(txt, ", adjusted \u03B1 ", alpha, " (", 100*(1-2*alpha), "% CI), ")
    } else {
      txt <- paste0(txt, ", \u03B1 0.05 (conventional 90% CI), ")
    }
    txt    <- paste0(txt, "TIE \u2264", signif(1-(1-alpha)^k, 5), "\n")
    cat(txt); print(res, row.names = FALSE)


    Peanuts:
    Assumed θ 0.95, target (desired) power 0.8, adjusted α 0.025 (95% CI), TIE ≤0.049375
       CV design  n power design  n power change
     0.15    3x3 15 0.857  2x2x2 16 0.855  +6.67
     0.16    3x3 15 0.808  2x2x2 16 0.806  +6.67
     0.17    3x3 18 0.839  2x2x2 18 0.813  ±0.00
     0.18    3x3 21 0.858  2x2x2 20 0.816  -4.76
     0.19    3x3 21 0.817  2x2x2 22 0.817  +4.76
     0.20    3x3 24 0.833  2x2x2 24 0.815  ±0.00
     0.21    3x3 27 0.844  2x2x2 26 0.812  -3.70
     0.22    3x3 27 0.808  2x2x2 28 0.808  +3.70
     0.23    3x3 30 0.817  2x2x2 30 0.802  ±0.00
     0.24    3x3 33 0.824  2x2x2 34 0.823  +3.03
     0.25    3x3 36 0.828  2x2x2 36 0.816  ±0.00
     0.26    3x3 39 0.830  2x2x2 38 0.808  -2.56
     0.27    3x3 39 0.801  2x2x2 40 0.801  +2.56
     0.28    3x3 42 0.803  2x2x2 44 0.813  +4.76
     0.29    3x3 45 0.805  2x2x2 46 0.805  +2.22
     0.30    3x3 48 0.805  2x2x2 50 0.814  +4.17


  3. In the ANOVA you get only one – pooled – residual variance. Apart from problems with potentially biased estimates and inflated TIE, you could base your decision only on the T/R-ratios. If they are similar, which one will you select? Flip a coin? In the IBD-analyses you get two variance estimates, which in such a case would be helpful.

Dif-tor heh smusma 🖖
Helmut Schütz
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sweiner
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2020-07-07 03:00
(106 d 23:50 ago)

@ Helmut
Posting: # 21654
Views: 1,346
 

 Fed (IBD) → fasting

Helmut, thank you very much for the reply related to the adjustment of alpha, testing of fed vs. fasted, as well as the detailed sample size discussion with R code provided.

Can you please also provide feedback on one more scenario:
6-way crossover, with the following treatments A) tablet formulation #1 fasted, B) tablet formulation #2 fasted, C) capsule formulation fasted, D) tablet formulation #1 fed, E) tablet formulation #2 fed, F) capsule formulation fed.

Is there an approach that can be used to test only the first 3 treatments (all fasted) in an interim fashion, and contingent upon the results continue to test the final 3 treatments (all fed)? We are assuming a typical Latin Square such as:

A B C D E F
B C D E F A
C D E F A B
D E F A B C
E F A B C D
F A B C D E

To allow the proposed interim analysis (all fasted), is it possible to execute only the first necessary part of the Latin Square, such as:

A B C x x x
B C x x x A
C x x x A B
x x x A B C
x x A B C x
x A B C x x

With completion of the remaining parts (all fed) after the interim analysis:

x x x D E F
x x D E F x
x D E F x x
D E F x x x
x x A B C x
F x x x D E


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5! [Ohlbe]
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