Helmut
★★★

Vienna, Austria,
2016-12-25 01:49
(1598 d 05:37 ago)

Posting: # 16876
Views: 2,962

## Inflation of the TIE with Xu’s ‘Method F’? [Two-Stage / GS Designs]

Dear all,

I’m confused. Xu et al. (doi:10.1002/pst.1721) claim that for a range of CV 10–30% and n1 12–? and design constraints (α0 0.05, α1 0.0248, α1 0.0364, maximum total sample size 42, stopping for futility in the first stage if the (1–2α1) CI is entirely outside 0.9492–1/0.9492) the maximum Type I Error (assessed at a true GMR 0.80) is 0.050. So far, so good. But:

library(Power2Stage)
power.2stage.fC(method="C", alpha0=0.05, alpha=c(0.0248, 0.0364),
CV=0.2, n1=12, GMR=0.95, theta0=0.8, max.n=42,
fCrit="CI", fClower=0.9492, targetpower=0.8,
pmethod="shifted", nsims=1e6)

TSD with 2x2 crossover
Method C: alpha0 = 0.05, alpha (s1/s2) = 0.0248 0.0364
Interim power monitoring step included
Target power in power monitoring and sample size est. = 0.8
Power calculation via shifted central t approx.
CV1 and GMR = 0.95 in sample size est. used
Maximum sample size max.n = 42
Futility criterion 90% CI outside 0.9492 ... 1.053519
BE acceptance range = 0.8 ... 1.25

CV = 0.2; n(stage 1) = 12; GMR= 0.95

1e+06 sims at theta0 = 0.8 (p(BE)='alpha').
p(BE)    = 0.053425
p(BE) s1 = 0.032461
Studies in stage 2 = 32.75%

Distribution of n(total)
- mean (range) = 16.7 (12 ... 42)
- percentiles
5% 50% 95%
12  12  34

What? Am I missing sumfink?

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
d_labes
★★★

Berlin, Germany,
2016-12-27 11:09
(1595 d 20:18 ago)

@ Helmut
Posting: # 16881
Views: 2,458

## Inflation of the TIE with Xu’s ‘Method F’?

Dear Helmut,

» I’m confused. Xu et al. (doi:10.1002/pst.1721) claim that for a range of CV 10–30% and n1 12–? and design constraints (α0 0.05, α1 0.0248, α1 0.0364, maximum total sample size 42, stopping for futility in the first stage if the (1–2α1) CI is entirely outside 0.9492–1/0.9492) the maximum Type I Error (assessed at a true GMR 0.80) is 0.050. ... But:
»

library(Power2Stage)
» power.2stage.fC(method="C", alpha0=0.05, alpha=c(0.0248, 0.0364),
»                 CV=0.2, n1=12, GMR=0.95, theta0=0.8, max.n=42,
»                 fCrit="CI", fClower=0.9492, targetpower=0.8,
»                 pmethod="shifted", nsims=1e6)
» ...
»
» 1e+06 sims at theta0 = 0.8 (p(BE)='alpha').
» p(BE)    = 0.053425
» ...
»

What? Am I missing sumfink?

IMHO no. Another claim of the authors not fulfilled was already reported some times ago here. Not every claim contains gold .
Ask our Ol'Captain to forget his task to get a "philosophical" understanding of SD and fire up his Compiler instead to verify this ominous Power2Stage::power.2stage.fC().

But ... Do the authors really claim that n1=12 and CV=0.2 together with the other TSD characteristics do not lead to an alpha-inflation?
If I remeber the paper correctly they have an "optimized" n1=18 in their method F. Optimized w.r.t. (quote from the paper) "An optimal design is defined as the design that has at least 80% power and at most 5% overall type I error rate for all ISCV values within the specified ISCV range and achieves the smallest cost function value described ...".
That does not necessarily mean that all designs they had choosen from during optimization had a TIE <=0.05 itself.
Another quote: "Unacceptable designs (my explanation: TIE>0.05, power<80%) were assigned an extremely high cost value in order to keep the search within the acceptable region of the design space."

Regards,

Detlew
ElMaestro
★★★

Denmark,
2016-12-27 11:43
(1595 d 19:43 ago)

@ d_labes
Posting: # 16882
Views: 2,258

## Inflation of the TIE with Xu’s ‘Method F’?

Hi detleffff and all,

» Ask our Ol'Captain to forget his task to get a "philosophical" understanding of SD and fire up his Compiler instead to verify this ominous Power2Stage::power.2stage.fC().

Oh, my philosophystical meanderings are all about SE's. At least today.
Anyways, happy to learn that I am now being given a chance to serve in the role of arbiter, oracle and a scientific equivalent of Kim Jong-un.

I will be happy to give it a try, but please have some patience with me, I have not done any C programming for the past 6 months due to various technological challenges such as a a 256GB m.2 SSD that died a sudden but very painful dead, in combination with an external backup drive that worked beautifully until I actually tried to read data from it .

Pass or fail!
ElMaestro