VSL
☆

India,
2017-01-31 06:47

Posting: # 16998
Views: 8,345

## Replicate designs [Design Issues]

Dear All,
Could you please explain the following points?
1. Is there any thumb rule (apart from %CV more than 30), when to use three way against four way cross over design?
2. As we know, four way design reduces the sample size compared to three way designs, is there any additional advantage which four way design give (in terms of overall outcome of the study)?
3. Even though variability is less than 30%, we perform three or four ways cross over study, would it enhances chance of passing the study (i.e forced BE) compared to simple two way design?
VSL

Edit: Subject line changed (was: Higher order cross over designs). [Helmut]
Helmut
★★★

Vienna, Austria,
2017-01-31 12:42

@ VSL
Posting: # 17000
Views: 7,924

## Replicate designs: Pros & Cons

Hi VSL,

your terminology is unfortunate. Generally x-way (x: 2, 3, 4…) refers to the number of treatments (or formulations). The common 2×2×2 (for simplicity aka 2×2, TR|RT, AB|BA) refers to two treatments, two sequen­ces, two periods. If we have more than one treatment we talk about a ”higher order crossover”. Examples: 3×3 and 4×4 Latin Squares or a 3×6×3 Williams’s design.
In none of these designs any of the treatments is replicated.

» 1. Is there any thumb rule (apart from %CV more than 30), when to use three way against four way cross over design?

IMHO, only if the sample volume is limited, a three-period replicate is the better choice. In a four-period replicate the chance of dropouts is higher than in three-period replicates. However, the loss of power is overrated by many.

» 2. […] four way design reduces the sample size compared to three way designs,

Correct. But to get the same power the number of treatments (and hence, the number of biosamples mainly driving the study costs) is similar. Sample sizes (n) and number of treatments (t) for GMR 0.9, target power 80%:

```           FDA’s RSABE       2×2×4   2×2×3   2×3×3 CV%   n  t    n  t    n  t   30  32 128  46 138  45 135  40  24  96  38 114  33  99  50  22  88  34 102  30  90  60  24  96  36 108  33  99            EMA’s ABEL       2×2×4   2×2×3   2×3×3 CV%   n  t    n  t    n  t  30  34 136  50 150  54 162  40  30 120  46 138  42 126  50  28 112  42 126  39 117  60  32 128  48 144  48 144```

In all cases (independent from the scaling method) the four-period full replicate requires the least number of treatments – which is both ethically and economically preferable.

» […] is there any additional advantage which four way design give

You’ll get CVwT additionally to CVwR (which is required for reference-scaling). More about that at the end of the post. Nice to know and required for the FDA’s RSABE for NTIDs.

» (in terms of overall outcome of the study)?

If you mean the chance of passing BE, no.

» 3. Even though variability is less than 30%, we perform three or four ways cross over study, would it enhances chance of passing the study (i.e forced BE) compared to simple two way design?

Generally not. The sample size is not directly accessible, only power. The sample sample size is iteratively altered until at least the target power is reached. Example:

```library(PowerTOST) # sample size and expected power for ABE design <- c("2x2x2", "2x2x4", "2x2x3", "2x3x3") CV     <- seq(0.15, 0.3, 0.05) theta0 <- 0.95 # expected T/R-ratio target <- 0.90 # target power res    <- matrix(nrow=length(CV), ncol=2*length(design)+1,                  byrow=FALSE, dimnames=NULL) colnames(res) <- c("CV%", paste0(rep(design, each=2), c(": n", ": pwr"))) for (j in seq_along(CV)) {   res[j, 1] <- 100*CV[j]   for (k in seq_along(design)) {     x <- sampleN.TOST(CV=CV[j], theta0=theta0, targetpower=target,                       design=design[k], details=FALSE, print=FALSE)     res[j, k*2] <- x[["Sample size"]]     res[j, k*2+1] <- signif(100*x[["Achieved power"]], 4)   } } print(as.data.frame(res), row.names=FALSE)```

Should give:

``` CV% 2x2x2: n 2x2x2: pwr 2x2x4: n 2x2x4: pwr 2x2x3: n 2x2x3: pwr 2x3x3: n 2x3x3: pwr   15       16      92.60        8      93.29       12      93.36       12      93.36   20       26      91.76       12      90.15       18      90.18       18      90.18   25       38      90.89       20      92.43       28      90.76       30      92.44   30       52      90.20       26      90.43       40      91.09       39      90.44```

In conventional (unscaled) ABE the sample sizes for the 4-period full replicate designs are ~½ of the 2×2×2 and the ones for the 3-period replicates ~¾ of the 2×2×2.

The number of periods in replicate designs is not so important.
You have to decide whether you use one of the full replicates (two sequences; four periods: 2×2×4 or RTRT|TRTR, three periods: 2×2×3 or RTR|TRT) or the partial replicate (three sequences; three periods: 2×3×3 or RRT|RTR|TRR). The later is a lousy design (since T is not repeated and the FDA’s model is over-specified). In the worst case the study is done and the optimizer fails to converge (independent from the software). Then you are in bad situation. Lots of money spent, no result at all… Please avoid it; don’t follow guidelines blindly.

If you opt for one of the full replicates (which I hope) you should perform the pilot study in a full replicate design as well. In many cases the variability of T is lower than the one of R – which will lead to a lower sample size for the pivotal study. If the pilot study was performed in the partial replicate you have to assume that CVwT = CWwR. Examples for GMR 0.90, target power 80%, 4-period full replicate:
• CVwT = CVwR = 50%
• FDA’s RSABE
```library(PowerTOST) sampleN.RSABE(CV=0.50, theta0=0.9, targetpower=0.8, design="2x2x4",               details=FALSE, print=FALSE)[["Sample size"]] # [1] 22```
• EMA’s ABEL
```sampleN.scABEL(CV=0.50, theta0=0.9, targetpower=0.8, design="2x2x4",               details=FALSE, print=FALSE)[["Sample size"]] # [1] 28```
• CVwT = 35%, CVwR = 50%
• FDA’s RSABE
```sampleN.RSABE(CV=c(0.35, 0.50), theta0=0.9, targetpower=0.8, design="2x2x4",               details=FALSE, print=FALSE)[["Sample size"]] # [1] 18```
• EMA’s ABEL
```sampleN.scABEL(CV=c(0.35, 0.50), theta0=0.9, targetpower=0.8, design="2x2x4",               details=FALSE, print=FALSE)[["Sample size"]] # [1] 22```
In other words, if you “know” that T shows a lower intra-subject variability than R you’ll get a reward in terms of the required sample size (same scaling based on CVwR but narrower CI based on CVw pooled from CVwT and CVwR). Try this code for the EMA’s ABEL:

```library(PowerTOST) CVwT <- 0.35 # CV of T CVwR <- 0.50 # CV of R PE   <- 0.9 # pooled CV used for the calculation of the CI CVw  <- mse2CV(mean(c(CV2mse(CVwT), CV2mse(CVwR)))) # scaled BE limits AR   <- 100*scABEL(CV=CVwR, regulator="EMA") # 90% CI assuming CVwT = CVwR n1   <- sampleN.scABEL(CV=CVwR, theta0=PE, targetpower=0.8, design="2x2x4",                        details=FALSE, print=FALSE)[["Sample size"]] CI1  <- round(100*CI.BE(pe=PE, CV=CVw, n=n1, design="2x2x4"), 2) if (CI1[["lower"]] >= AR[["lower"]] & CI1[["upper"]] <= AR[["upper"]] &     PE >= 0.8 & PE <= 1.25) {   concl1 <- paste("(passes BE with", n1, "subjects)") } else {   concl1 <- paste("(fails BE with", n1, "subjects)") } # 90% CI with CVwT < CVwR n2   <- sampleN.scABEL(CV=c(CVwT, CVwR), theta0=PE, targetpower=0.8, design="2x2x4",                        details=FALSE, print=FALSE)[["Sample size"]] CI2  <- round(100*CI.BE(pe=PE, CV=CVw, n=n2, design="2x2x4"), 2) if (CI2[["lower"]] >= AR[["lower"]] & CI2[["upper"]] <= AR[["upper"]] &     PE >= 0.8 & PE <= 1.25) {   concl2 <- paste("(passes BE with", n2, "subjects)") } else {   concl2 <- paste("(fails BE with", n2, "subjects)") } cat(sprintf("\nCVwT = %.2f%%, CVwR = %.2f%%, CVw = %.2f%%",             100*CVwT, 100*CVwR, 100*CVw),     "\nAR    :", sprintf("%.2f - %.2f%%", AR[["lower"]], AR[["upper"]]),     "\n90% CI:", sprintf("%.2f - %.2f%%", CI1[["lower"]], CI1[["upper"]]),     concl1,     "\n90% CI:", sprintf("%.2f - %.2f%%", CI2[["lower"]], CI2[["upper"]]),     concl2, "\n")```

You should get:

```CVwT = 35.00%, CVwR = 50.00%, CVw = 42.96% AR    : 69.84 - 143.19% 90% CI: 79.07 - 102.44% (passes BE with 28 subjects) 90% CI: 77.74 - 104.20% (passes BE with 22 subjects)```

Cheers,
Helmut Schütz

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VSL
☆

India,
2017-01-31 14:03

@ Helmut
Posting: # 17002
Views: 7,599

## Replicate designs: Pros & Cons

Thanks Helmut for your elaborate explanation.
Balaji
☆

India,
2017-03-04 11:19

@ Helmut
Posting: # 17131
Views: 6,940

## Replicate designs: Pros & Cons

Hello Helmut,

Thanks for your clarification on the semi replicate and replicate designs.
However could you please elaborate on the below . .

» In the worst case the study is done and the optimizer fails to converge (independent from the software)

- What do you meanly optimiser fails to converge ? When does this happen ?

Helmut
★★★

Vienna, Austria,
2017-03-06 11:40

@ Balaji
Posting: # 17137
Views: 7,059

## Partial replicate design & ABE for the FDA

Hi Balaji,

» However could you please elaborate on the below . .
»
» » In the worst case the study is done and the optimizer fails to converge (independent from the software)
»
» - What do you meanly optimiser fails to converge ?

As I wrote above:

» » » » […] the partial replicate is a lousy design (since T is not repeated and the FDA’s model is over-specified).

My wording was not precise. The partial replicate design is not lousy per se – only model recommended by the FDA’s to evaluate if. The model attempts to estimate the intra-subject variability of T which is not uniquely contained in the data. Do you remember our conversation about intra-subject variability in a parallel design? Similar story.

» When does this happen ?

If one is not allowed to scale (swR <0.0294) and use the FDA’s mixed-effects model for ABE with the `FA0(2)` specification of the covariance structure according to the guidance. Such a situation is not uncommon: RSABE possible for Cmax but not for AUC.
1. If one is lucky the software only throws a warning:
`Convergence criteria met but final hessian is not positive definite.` (SAS)
```Newton's algorithm converged with modified Hessian. Output is suspect. Model may be over-specified. A simpler model could be tried.``` (Phoenix/WinNonlin)
However, the estimated s²wT is nonsense. This is just annoying (the agency is not interested in the variability of the test product and one doesn’t have to report it). The PE and its 90% CI is still correct.
2. In certain cases the optimizers fails to converge. See John’s data set of AUCinf. In Phoenix/WinNonlin the same warning as above but in SAS:
```WARNING: Did not converge. WARNING: Output 'Estimates' was not created.```
This is terrible because one gets no result for ABE at all. Study done, statistician blamed for it…
It is impossible to know beforehand whether one will end up with #1 or #2; search the forum for details. Ways out:
• State in the protocol that you will deviate from the guidance and use `FA0(1)` instead.
• Stick to the code given in the guidance but use one of the fully replicated designs (RTRT|TRTR, RTTR|TRRT, RTR|TRT, or RTT|TRR) instead. IMHO, much better.
Furthermore, 4-period replicate designs require less treatments than 3-period replicates (see above). Unless one runs into problems with the total blood volume I don’t see any reason for performing 3-period replicate studies.
Note that these problems are apparent only with the FDA’s model for ABE. The fixed-effects model preferred by the EMA does not have any issues.

I asked numerous times here and in Certara’s Extranet why one wants to use a partial replicate design – and never received an answer.
May I ask: Why do you want to use it?

Cheers,
Helmut Schütz

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nobody
nothing

2017-03-06 13:47

@ Helmut
Posting: # 17139
Views: 6,872

## Partial replicate design & ABE for the FDA

» I asked numerous times here and in Certara’s Extranet why one wants to use a partial replicate design – and never received an answer.

One guy told me: I'm not going to determine any parameter that is

a - not asked for by authorities
b - might put my product (now or in the furture...) in a bad light compared to reference

In the very beginning of this scaling discussion someone stated (regarding replicate for Reference): "Why should I characterize the REFERENCE product? This should f**ing do the originator!" No joke...

Kindest regards, nobody
Helmut
★★★

Vienna, Austria,
2017-03-06 14:00

@ nobody
Posting: # 17140
Views: 6,871

## Partial replicate design & ABE for the FDA

Hi nobody,

» One guy told me: I'm not going to determine any parameter that is
»
» a - not asked for by authorities

Good advice. I have given up reporting anything (even in an exploratory manner) which is not requested.

» b - might put my product (now or in the furture...) in a bad light compared to reference

I know which side you are on. Honestly, when it comes to variability in many cases generics perform better than the originator products. Pharmaceutical technology improves and the originator doesn’t want to change “the winning team” knowing that a major variation would require a BE-study.

» In the very beginning of this scaling discussion someone stated (regarding replicate for Reference): "Why should I characterize the REFERENCE product? This should f**ing do the originator!" No joke...

Les Benet at the BioInternational ’94 in Munich. You’ve been there…

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
nobody
nothing

2017-03-06 14:18

@ Helmut
Posting: # 17141
Views: 6,883

## Partial replicate design & ABE for the FDA

» Les Benet at the BioInternational ’94 in Munich. You’ve been there…

Nice location, btw. (you still have the list of participants? ***glotz***)

...but even some 10 years ago (and later) from time to time this sentiment came up from Schlipsträgers...

Re. Test better than Ref: But you can't know in advance and if you have a look at some of the "companies" nowadays "developing" generics your "gut feeling"/experience from the past might be subjected to some change (as so many things nowadays...)

Kindest regards, nobody
Helmut
★★★

Vienna, Austria,
2017-03-06 17:49

@ nobody
Posting: # 17142
Views: 6,922

## Partial replicate design & ABE for the FDA

» Nice location, btw.

Yep.

» (you still have the list of participants? ***glotz***)

Can’t remember whether one existed. I only have the list of organizers and speakers.

» Re. Test better than Ref: But you can't know in advance …

Only an educated guess from a pilot.

» … and if you have a look at some of the "companies" nowadays "developing" generics your "gut feeling"/experience from the past might be subjected to some change (as so many things nowadays...)

All too true.

Cheers,
Helmut Schütz

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