Posting: # 16998
Could you please explain the following points?
Many Thanks in advance
Edit: Subject line changed (was: Higher order cross over designs). [Helmut]
Posting: # 17000
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%:
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:
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:
You should get:
All the best,
The quality of responses received is directly proportional to the quality of the question asked. ☼
Posting: # 17002
Thanks Helmut for your elaborate explanation.