Loss of power etc. [Design Issues]

posted by zizou – Plzeň, Czech Republic, 2016-03-28 01:44 (3239 d 06:52 ago) – Posting: # 16146
Views: 23,991

(edited on 2016-03-28 11:31)

Dear Helmut,

Thanks for additions to my comment.

❝ 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).


My bad habit to use the terms acc. to guidelines (EMA 1401).
4.1.3 Subjects
Number of subjects
The number of subjects to be included in the study should be based on an appropriate sample size calculation. The number of evaluable subjects in a bioequivalence study should not be less than 12.

Neverthless sample size estimation is correct.

❝ Which country’s? I don’t hope a European one.


Personally I don't know, so that information can be misrepresented somehow. Nevertheless recently I was asked about response to insufficient sample size in performed study which demonstrated BE. It was study in 2x2 crossover design, no drop outs, sample size estimation performed and discussed in protocol. Only CV and GMR gone really much worse than expected.
(I don't know if response that sample size was estimated as described in protocol etc. with some references on literature intra-subject CV was enough.)
If we assumed the study results for another study, double sample size would be required for 80% power.

About post-hoc power as not important if the study demonstrated bioequivalence, I am still not so convinced (little bit yes).
When null hypothesis is false (formulations are BE) and we failed to reject bioinequivalence (probability beta = type II error = producer's risk) is for example 50%.
One of two studies will fail by chance?
With such under powered study there will be low reproducibility of results (by the other (supporting) studies)? ... Ok. When we double sample size it should be more reproducible, but with GMR in 80-125 it could be only about sample size.
If someone got luck to win with power 50% or 33% ... it should be still no problem for regulatory or is there a problem that if someone want to remake the whole study (don't know why) it would be hard acc. to needed luck.

(I am just thinking and writing.)

It is non sense when I got the idea to forget the power/producer's risk at all and design the study only for getting the 90% CI in 0.8000-1.2500.
(Once I was asked for sample size estimation with comment that study will be performed on 36 subjects. :D Fortunally it was Ok., maybe sponsor had made some own estimations, but it looked like impossible after first reading of such command x).)

Without required power (not good statistical practice - I am just only playing with the numbers when I am using algebra for LL (Lower Limit of 90% CI) below):

Assumpitons: 24 subjects, GMR 0.95-1.05, CV below 35.7%. If all mentioned assumptions remain in valid then BE will be demonstrated.

# the worst border case:
GMR=.95
CV=.357
n1=12
n2=12
alpha=.05
LL=exp(log(GMR)-sqrt(log(CV^2+1)/2*(1/n1+1/n2))*qt(1-alpha,n1+n2-2))
LL
# [1] 0.800133 # luck with power 35%

 # When I will think about not so good GMR (0.9), better CV 30% (not HVDs), and n=36:
GMR=.9
CV=.3
n1=18
n2=18
alpha=.05
LL=exp(log(GMR)-sqrt(log(CV^2+1)/2*(1/n1+1/n2))*qt(1-alpha,n1+n2-2))
LL
# [1] 0.8006268 # luck with power 51%


Remember, with no power comes no responsibility.

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