libaiyi ★ China, 20180523 10:40 (2250 d 04:12 ago) Posting: # 18801 Views: 5,367 

Hi, all I want to ask about power calculation. In BE, Cmax, AUCt, and AUCinf are all needed for power consideration. And the power for each one need to be bigger than overall power for the accumulation of power. But AUCinf and AUCt are highly correlated, so could I decrease the individual power and only consider about AUCt and Cmax for the power setting? Thanks in advance. 
Helmut ★★★ Vienna, Austria, 20180523 12:40 (2250 d 02:12 ago) @ libaiyi Posting: # 18802 Views: 4,524 

Hi libaiyi, ❝ I want to ask about power calculation. In BE, Cmax, AUCt, and AUCinf are all needed for power consideration. […] But AUCinf and AUCt are highly correlated, AUC and C_{max} are (highly?) correlated as well. ❝ […] so could I […] only consider about AUCt and Cmax for the power setting? If you think about sample size estimation I would go a step further and consider only the PK metric with the highest variability, which generally* is the one of C_{max} (see [msg]this thread[/msg], linked other posts, and references). You could use function power.2TOST() of the Rpackage PowerTOST to explore various correlations (ρ). This issue is a little bit academic because ρ is rarely known.
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
libaiyi ★ China, 20180524 12:02 (2249 d 02:50 ago) @ Helmut Posting: # 18811 Views: 4,417 

❝ You could use function ❝ ❝
Hi Helmut, Thank you for the reply. I am afraid that I did not state clearly. I still want to clarify do you mean that for the estimation of sample size, the power need to be calculated as: Overall power = (power of AUC0 * power of AUCinf * power of Cmax) like 0.8=（0.92*0.92*0.92） And it could not be simplified as Overall power = (power of AUC0 * power of Cmax) to decrease power needed of each for the lack of ρ? Thanks again. 
Helmut ★★★ Vienna, Austria, 20180524 14:54 (2248 d 23:58 ago) @ libaiyi Posting: # 18812 Views: 4,438 

Hi libaiyi, ❝ And it could not be simplified as Overall power = (power of AUC0 * power of Cmax) to decrease power needed of each for the lack of ρ? For two tests, it could. Try this (conventional BElimits, T/Rratio 0.95, target power 0.8, 2×2×2 crossover):
If ρ=1, power ~ the one by TOST of the PK metric with the higher CV. Implicitly people assume a perfect correlation when estimating the sample size based on the PK metric with the higher CV. If ρ=0, power ~ p_{TOST1} × p_{TOST2}. 证明完毕 _{} Similar for three tests (e.g., for the FDA). Let’s assume the CV of AUC_{0–∞} with 0.22 to be a little bit larger than the one of AUC_{0–t} with 0.2. Then we would get p_{TOST1} × p_{TOST2} × p_{TOST3} = 0.8158×0.9848×0.9660 = 0.7762. Since likely the correlation is high (esp. between AUC_{0–t} and AUC_{0–∞}), a relative drop in power from the desired 0.8 by less than 3% doesn’t worry me. In practice (high correlation) the loss will be negligible. Another example. Since CV1 scratches the limit of HVD(P)s, it might be a good idea to be more cautious and assume a T/R of 0.90 (and – if you are courageous – assume a nicer one of AUC at 0.925). Let’s try a 4period full replicate design:
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
libaiyi ★ China, 20180530 05:24 (2243 d 09:28 ago) @ Helmut Posting: # 18827 Views: 4,148 

Thank you so much for the answer! I understand now. 