## helter-skelter [RSABE / ABEL]

Hi Mikalai,

» I am gonna describe two bad scenarios.
»
» The first one, we assume that the CV of a drug is around 35%, so we are ready for the worst inflation TIE in our ABEL trial with 4-periods. Thus, we decided to increase our sample size to 42 subjects to compensate for the adjusted TIE and then added the 15% dropout rate that resulted in 49 subjects in our full sample size. We have done our trial. We have got the CV around 32% and big inflation TIE, but we passed because of safety measures.

I cannot reproduce your numbers. Given. Though you could state in the SAP which adjusted α you expect (and that you increased the sample size accordingly), you have to state as well that you will adjust α based on the outcome of the study (observed CVwR, actual sample size).
The TIE depends not only on CVwR but – to a minor extent – the sample size as well.

  CV    alpha  n      TIE 0.35 0.050000 34 0.065566θ0 0.90, 80% power, naïve ABEL: inflated TIE
0.35 0.036100 38 0.050000 ← larger sample size for adjusted α
0.35 0.036100 44 0.050145 ← compensate for 15% dropouts, inflated TIE!
0.35 0.035972 44 0.050000 ← requires more adjustment

If the CVwR is higher than expected, open a bottle of Champagne; more scaling, less adjustment necessary and you gain power. You are right that you have to adjust more if the CVwR moves towards 30% but the loss in power in this example (35% → 32%) is negligible.

  CV    alpha  n do (%)      TIE alpha.ad TIE.ad   power 0.32 0.035972 44   0.00 0.071249 0.033167   0.05 0.83263 0.32 0.035972 43   2.63 0.070963 0.033393   0.05 0.82458 0.32 0.035972 42   5.26 0.070994 0.033460   0.05 0.81875 0.32 0.035972 41   7.89 0.071328 0.033307   0.05 0.80961 0.32 0.035972 40  10.53 0.071046 0.033356   0.05 0.80196 0.32 0.035972 39  13.16 0.070948 0.033430   0.05 0.79346 0.32 0.035972 38  15.79 0.071003 0.033342   0.05 0.78409

58 lines of R-code upon request.

» The second is a bit worse. We assume that the CV of a drug is around 40-42%. We decided to recruit 40 subjects - with full compensation - to conduct a 4 periods ABEL trial. Then have suddenly got the CV 32% and massive inflation TIE. We failed the trail because of the lack of power.

Shit happens.

library(PowerTOST) CV.exp <- 0.40 n.adj  <- sampleN.scABEL.ad(CV = CV.exp, design="2x2x4",                             print = FALSE)[["Sample size"]] n.act  <- seq(40, n.adj, -1) CV.act <- 0.32 res    <- data.frame(n = n.act, alpha = NA, power = NA) for (j in seq_along(n.act)) {   x           <- scABEL.ad(CV = CV.act, design="2x2x4",                            n = n.act[j], theta0 = 0.90,                            print = FALSE)   res[j, 2:3] <- as.numeric(unlist(x)[c(15, 17)]) } print(res, row.names = FALSE)

 n    alpha   power 40 0.033355 0.80195 39 0.033430 0.79346 38 0.033342 0.78409 37 0.033587 0.77602 36 0.033399 0.76411 35 0.033224 0.75303 34 0.033527 0.74509 33 0.033422 0.73438 32 0.033414 0.72151

» We did the second trial with 49 subjects and passed.

No dropouts this time? Risky; in such a case I would power the second study more.

» There are a couple of questions.
» Are these scenarios are plausible?

The first one is common, though in my studies I try to educate my clients that this “increase the sample size based on anticipated dropout rate” is a waste of money. Try the function pa.scABE() of PowerTOST to see why.

» How frequent can they be?

No idea about the second one. I know just one case where the sponsor doubled the sample size…

» Could three-periods trials reduce the number of subjects?

On the contrary, my dear Dr Watson! The power of study depends on the number of treatments. Compared to a 2×2×2 you get similar power with ~½ of the sample size in a 4-period and ~¾ of the sample size in a 3-period replicate or, if you prefer, you need ~50% more subjects in a 3-period than in a 4-period replicate.

ABE   CV 2x2x2 2x2x4 2x2x3  4/2  3/2 0.30    40    20    30 0.50 0.75 0.35    52    26    38 0.50 0.73 0.40    66    34    50 0.52 0.76 0.45    82    42    62 0.51 0.76 0.50    98    50    74 0.51 0.76 0.55   116    58    86 0.50 0.74 0.60   134    68   100 0.51 0.75 ABEL   CV 2x2x4 2x2x3  3/4 0.30    34    50 1.47 0.35    34    50 1.47 0.40    30    46 1.53 0.45    28    42 1.50 0.50    28    42 1.50 0.55    30    44 1.47 0.60    32    48 1.50 ABEL (adjusted)   CV 2x2x4 2x2x3  3/4 0.30    42    66 1.57 0.35    38    58 1.53 0.40    32    50 1.56 0.45    28    42 1.50 0.50    28    42 1.50 0.55    30    44 1.47 0.60    32    48 1.50

Study costs are similar (since mainly driven by bioanalytics). However, the more periods, the more likely subjects drop out. One the other hand, the 3-period replicate requires more adjustment than the 4-period replicate.

% sample size penalty of adjusted ABEL   CV 2x2x4 2x2x3 0.30 23.53 32.00 0.35 11.76 16.00 0.40  6.67  8.70 0.45   –     –  0.50   –     –  0.55   –     –  0.60   –     –  

» In Belarus, if you decided to conduct a crossover ABE trial in multiple groups and decided to drop the group factor and its interaction from the statistical model (3rd method of FDA) then you have to prove …

We cannot prove anything in science. Proofs belong to the realms of logic and mathematics.

» … the groups are from the same population. You should statistically compare the demographics of groups. And you can only drop the group factor if there are no statistical differences between groups …

That’s an extremely stupid approach. At which level will you test? 0.05, 0.10? What about false positives? BTW, any pre-test inflates the TIE and a post hoc test is nonsense.* We discussed that ad nauseam! Explore those.
Don’t dive into such muddy waters. Include the group term in the model (i.e., specify the FDA’s Model II taking into account that groups were tested on different dates) but without a pre-test. The loss in power is very, very low compared to the pooled Model III. See the end of Example 1.

• Writing a paper about that is on my TODO-list since May 2017…

Dif-tor heh smusma 🖖
Helmut Schütz

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