## Sample size larger than clinical capacity [Power / Sample Size]

Hi Bebac user,

❝ Partially replicated study,…

If possible, avoid the partial replicate design. If you want only three periods (say, you are concerned about a potentially higher drop­out-rate or larger sampled blood volume in a four-period full replicate design), use one of the two-sequence three-period full replicate designs (TRT|RTR or TRR|RTT). Why?
• The sample size will be similar. For a comparison of study costs, see this article.
• Additional to $$\small{CV_\textrm{wR}}$$ you can estimate $$\small{CV_\textrm{wT}}$$.
• Although agencies are only concerned about ‘outliers’ of the reference, here you can assess the test as well. If the study fails and you have less ‘outliers’ after the test than after the reference, you get ammunition for an argument. An example is dasatinib, where the reference is a terrible formulation $$\small{\textsf{(}CV_\textrm{wR}\gg CV_\textrm{wT}}$$, more ‘out­liers’, sub­stan­tial batch-to-batch variability).
• If the study fails but $$\small{CV_\textrm{wT}<CV_\textrm{wR}}$$ (quite often, since pharmaceutical technology improves), you can use this information in planning the next one. The sample size will be smaller than based on the partial replicate, where you have to assume $$\small{CV_\textrm{wT}=CV_\textrm{wR}}$$. See also this article.

Sample size search

 n     power

45   0.7829

48   0.8045

❝ But, I know that I can't use more than 40 volunteers in any BE study

❝ In these cases, what should I do ?

Two options.
1. Perform the study in one of the two-sequence four-period full replicate designs (TRTR|RTRT or TRRT|RTTR or TTRR|RRTT).

library(PowerTOST) sampleN.scABEL(CV = 0.3532, design = "2x2x4", details = FALSE) +++++++++++ scaled (widened) ABEL +++++++++++             Sample size estimation    (simulation based on ANOVA evaluation) --------------------------------------------- Study design: 2x2x4 (4 period full replicate) log-transformed data (multiplicative model) 1e+05 studies for each step simulated. alpha  = 0.05, target power = 0.8 CVw(T) = 0.3532; CVw(R) = 0.3532 True ratio = 0.9 ABE limits / PE constraint = 0.8 ... 1.25 Regulatory settings: EMA Sample size  n     power 34   0.8137

If you are concerned about the inflation of the Type I Error (see this article), adjust the $$\small{\alpha}$$ – which will slightly negatively impact power – or in order to preserve power, increase the sample size after adjustment accordingly.

sampleN.scABEL.ad(CV = 0.3532, design = "2x2x4", details = TRUE) +++++++++++ scaled (widened) ABEL ++++++++++++             Sample size estimation         for iteratively adjusted alpha    (simulations based on ANOVA evaluation) ---------------------------------------------- Study design: 2x2x4 (4 period full replicate) log-transformed data (multiplicative model) 1,000,000 studies in each iteration simulated. Assumed CVwR 0.3532, CVwT 0.3532 Nominal alpha      : 0.05 True ratio         : 0.9000 Target power       : 0.8 Regulatory settings: EMA (ABEL) Switching CVwR     : 0.3 Regulatory constant: 0.76 Expanded limits    : 0.7706 ... 1.2977 Upper scaling cap  : CVwR > 0.5 PE constraints     : 0.8000 ... 1.2500 n  34, nomin. alpha: 0.05000 (power 0.8137), TIE: 0.0652 Sample size search and iteratively adjusting alpha n  34,   adj. alpha: 0.03647 (power 0.7758), rel. impact on power: -4.67% n  38,   adj. alpha: 0.03629 (power 0.8131), TIE: 0.05000 Compared to nominal alpha's sample size increase of 11.8% (~study costs).

Keep in mind that we plan the study for the worst case condition. If reference-scaling for AUC is not acceptable (in many jurisdictions applying ABEL only for Cmax), you may run into trouble (see this article). In your case the maximum $$\small{CV_\textrm{w}}$$ for ABE in a partial replicate design is 24.2%. If it is larger, you would exhaust the clinical capacity and have to opt for #2 anyway.

2. Split the study into groups. I recommend to have one group at the maximum capacity of the clinical site. For the partial replicate design that means 40|8 and for the two-sequence three-period full replicate 40|10. Why don’t use equally sized groups?
• If for any crazy reasons an agency does not allow pooling the data, you still have some power to show BE in the large group. In your case you get 74% power with 40 subjects but only 55% with each of the groups of 24 subjects.
• Furthermore, what would you do – if you are lucky – and one group passes but the other one fails (likely)? Present only the passing one to the agency? I bet that you will be asked for the other one as well. In your case the chance that both groups pass, is 0.552 or just 31%.

In general European agencies are fine with pooling the data and use of the conventional model $$\small{sequence,\,subject(sequence),\,period,\,treatment}\tag{1}$$ I recommend to give a justification in the protocol: Subjects with similar demographics, all randomized at study outset, groups dosed within a limited time interval.
If you are wary (the ‘belt plus suspenders’ approach), pool the data but modify the model taking the group-effects into account, i.e., use $$\small{group,\,sequence,\,subject(group\times sequence),\,period(group),\,group\times sequence,\,treatment}\tag{2}$$ With $$\small{(2)}$$ you have only $$\small{N_\textrm{Groups}-1}$$ degrees of freedom less than in $$\small{(1)}$$ and hence, the loss in power is practically negligible.
What you must not do: Perform a pre-test on the $$\small{group\times treatment}$$ interaction and only if $$\small{p(G\times T)\ge 0.1}$$ use $$\small{(2)}$$. As in any test at level $$\small{\alpha=0.1}$$ you will face a false positive rate of 10%. Then what? Further­more, any pre-test inflates the Type I Error.

Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮
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