Bioequivalence and Bioavailability Forum • Loss of power etc.

Loss of power etc. [Design Issues]

posted by Helmut – Vienna, Austria, 2016-03-26 15:46 (3283 d 08:01 ago) – Posting: # 16142
Views: 24,457

Hi zizou,

❝ Personally I don't like the option of replacing of subjects. But some sponsors require that. […]

You gave nice examples! I think that part of the job of CROs is to educate their customers. The potential loss of power caused by dropouts is overrated by many. A handy educational tool (plots for dummies!) comes with the functions pa.ABE() and pa.scABE() in PowerTOST.

❝ For example 26 subjects are needed for 80% power. Expected drop-out rate xx%. Sample size 32. When number of subjects for BE evaluation is lower than 26 subjects, additional subjects will be treated.

Is it really worth the trouble it may cause in the analysis?

library(PowerTOST) pi <- 0.80 theta0 <- 0.95 CV <- 0.24 do.rate <- 0.15 worst <- 4 # lower than desired n0 <- sampleN.TOST(CV=CV, theta0=theta0, targetpower=pi, design="2x2x2", print=FALSE)[["Sample size"]] n1 <- ceiling(n0/(1-do.rate)/2)*2 # adjust and round up to even n <- n1:(n0-worst) pw <- vector() for(j in seq_along(n)) { pw[j] <- suppressMessages(power.TOST(CV=CV, theta0=theta0, n=n[j])) cat(sprintf("%i %.2f%%%s", n[j], 100*pw[j], "\n")) } plot(n, pw, ylim=c(min(pw), 1), las=1, xlab="sample size", ylab="expected power") abline(h=pi) abline(v=c(n0, n1), lty=3) text(n, pw, round(100*pw, 1), cex=0.8, pos=3) 32 88.17% 31 87.14% 30 86.09% 29 84.88% 28 83.65% 27 82.22% 26 80.77% 25 79.07% 24 77.35% 23 75.32% 22 73.27%

If your expected droput-rate was 15% and you end up just with 25 subjects, the expected (!) power will be 79.1% – if (if‼) your assumptions about the CV and the T/R-ratio will hold true…

A common practice (especially in designs with more than two periods) is to dose “stand-ins” as soon as possible. Say you drop below your desired sample size after the second period, you start dosing them in period 3. Generally the data are naïvely pooled …

period subject 1 2 3 4 1 – x • • • • x+1 – y • • • •

… ignoring the true structure which is:

period subject 1 2 3 4 5 6 1 – x • • • • x+1 – y • • • •

Treating such a mess correctly could be demanding. Even if “stand-ins” are dosed after completing all periods of the “regulars”, at the end we have twice as many periods than planned in the original design.

❝ ❝ What if we do get significant group term? […]

❝ You can calculate post-hoc power (sometimes required by regulatory when sample size was calculated with assumptions "GMR in 0.95-1.05 and intra-subject CV x%" and true GMR was outside the expected interval or intra-subject CV was higher than expected.

Which country’s? I don’t hope a European one. Regulators (and sponsors as well) should learn that the sample size estimation (based on a priori power) is based on assumptions. Nothing more, nothing less (hence, the term “sample size calculation” should be avoided). BTW, we don’t know the true GMR. It lies with 90% probability somewhere within the 90% CI around the PE. It is a bizarre idea to relate the PE to the assumed T/R-ratio. Even if the CV is higher than expected and the PE more deviating from 1 than expected and the study passes (though with less than desired power) the only thing we can conclude is that our assumptions were wrong. Who cares? The job of regulators is to be concerned about the consumer risk (α), which is maintained in passing studies by definition. Only the producer’s risk (β) was higher than desired. As ElMaestro once wrote “Being lucky is not a crime”.
Imagine: You visit a casino once in your life to play roulette and place a single bet of € 1,000 on the magic number 24. The ball spins and at the end drops into the 24-pocket of the wheel. Instead of paying out € 35,000 the croupier tells you with a smirk on his face: “Congratulations, but since this achievement was highly improbable we don’t pay you anything. Thank you very much, see you next time.”

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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Complete thread:

Study conduct in groups Smitha 2015-02-02 04:21 [Design Issues]
- Study conduct in groups ElMaestro 2015-02-02 08:21
- Study conduct in groups Helmut 2015-02-02 13:08
  - Study conduct in groups Smitha 2015-02-04 04:30
    - Study conduct in groups Helmut 2015-02-04 12:57
      - Study conduct in groups felipeberlinski 2015-02-04 22:36
        
        Study conduct in groups ElMaestro 2015-02-04 23:58
        Significant ≠ relevant Helmut 2015-02-05 00:49
        
        Significant ≠ relevant Astea 2016-03-24 20:10
        
        Significant ≠ relevant ElMaestro 2016-03-24 23:12
        Significant ≠ relevant zizou 2016-03-25 21:41
        
        Loss of power etc.Helmut 2016-03-26 14:46
        
        Loss of power etc. Astea 2016-03-27 21:18
        Loss of power etc. zizou 2016-03-27 23:44
        
        Combined power? Helmut 2016-03-28 14:29
        Loss of power etc. Astea 2016-03-28 23:57
        
        Loss of power etc. ElMaestro 2016-03-29 00:16
        Mystery Helmut 2016-03-29 17:28
        
        Back to the Future Astea 2016-03-29 21:57
        
        Back to the Future ElMaestro 2016-03-29 23:11
        
        Using lectures != Reading them mittyri 2016-03-30 00:17
        
        Recycling Helmut 2016-03-30 00:42
        
        Recycling Astea 2016-03-30 12:23
        
        Recycling Beholder 2016-03-30 13:00