## Power of two stage design [Power / Sample Size]

Dear Pjs,

» Currently i am cross verifying power value with the published paper of the potvin for two stage. They had calculated power with modification of Hauschke et al. For example if i take N=12, CV=40% and ratio 95% power by method C is reported to be 0.7505. For the same parameters power by FARTSSIE is -24.19%.

This is a fundamental misunderstanding.
What you try to do is, if I understand you correctly, to obtain the power of a two stage design.
This is not possible in FARTSSIE and also not in the R package PowerTOST.

The framework of TSDs is so complicated that no algebraic solution for obtaining power is available. What you have to do is to use simulations, like the ones described in the Potvin paper.

Have a look into the R add-on package Power2Stage. With the function power.2stage() you are able to verify the type 1 error and the power reported in the Potvin paper.

Example:
library(Power2Stage) # power at true ratio=0.95 power.2stage(alpha=c(0.0294, 0.0294), method="C", CV=0.4, n1=12, GMR=0.95, theta0=0.95)
gives
TSD with 2x2 crossover Method C: alpha0 = 0.05, alpha (s1/s2) = 0.0294 0.0294 Target power in power monitoring and sample size est. = 0.8 Power calculation via non-central t approx. CV1 and GMR = 0.95 in sample size est. used No futility criterion BE acceptance range = 0.8 ... 1.25 CV = 0.4; n(stage 1) = 12; GMR= 0.95 1e+05 sims at theta0 = 0.95 (p(BE) = 'power'). p(BE)    = 0.75058 p(BE) s1 = 0.00986 Studies in stage 2 = 98.95% Distribution of n(total) - mean (range) = 78.9 (12 ... 302) - percentiles  5% 50% 95%  32  74 142 

# empirical type 1 error power.2stage(alpha=c(0.0294, 0.0294), method="C", CV=0.4, n1=12, GMR=0.95, theta0=1.25)
gives
TSD with 2x2 crossover Method C: alpha0 = 0.05, alpha (s1/s2) = 0.0294 0.0294 Target power in power monitoring and sample size est. = 0.8 Power calculation via non-central t approx. CV1 and GMR = 0.95 in sample size est. used No futility criterion BE acceptance range = 0.8 ... 1.25 CV = 0.4; n(stage 1) = 12; GMR= 0.95 1e+06 sims at theta0 = 1.25 (p(BE) = TIE 'alpha'). p(BE)    = 0.034468 p(BE) s1 = 0.003881 Studies in stage 2 = 99.5% Distribution of n(total) - mean (range) = 79.1 (12 ... 360) - percentiles  5% 50% 95%  32  74 142 

BTW: If you aim to work exactly like Potvin et al. you have to set the argument pmethod="shifted" in the function calls. This calculates power in the power monitoring step of the two stage schemes via a somewhat crude approximation and was used in the Potvin paper for speed reasons only.

Nevertheless you will not obtain exacly the same numbers due to the unknown auxillary conditions for the simulations like e.g. the seed of the random number genarator or its type.

BTW2: The negative power from FARTSSIE is of course nonsense and results from an approximation for the power calculation. The exact power for a fixed (1-stage) design with your settings is
library(PowerTOST) power.TOST(CV=0.4, n=12) [1] 0.02843316

Regards,

Detlew