One or two-tailed? [General Sta­tis­tics]

posted by Astea – Russia, 2015-02-05 02:20 (3748 d 21:16 ago) – Posting: # 14375
Views: 9,909

Dear statisticians! sorry for forcing in this branch... This tails makes me feel blue.

My question is the following: comparing formulas from Chow S.-C., Wang H. On Sample Size Calculation in Bioequivalence Trials, Journal of Pharmacokinetics and Pharmacodynamics, Vol. 28, No. 2, 2001 (2), p.161 and Chow S.C., Shao J., Wang H., Sample size calculations in clinical research. Marcel Dekker, New York, NY, 2003 on p.260 I see that
- in the book the authors restricts themselves with the formula concerning beta/2
- in the example they use values z_alpha=1.96 and z_beta/2=0.84 for alpha =0.05 and beta =80%, theta0=1 and CV=0.4 and get totally 42 subjects.

I'm trying to evaluate formulas (2) p.161 from Chow S.-C., Wang H. On Sample Size Calculation in Bioequivalence Trials, Journal of Pharmacokinetics and Pharmacodynamics, Vol. 28, No. 2, 2001 (note that there is an excess square for \delta).
For sample size calculation in standard 2x2 crossover design we use for the first iteration the following values: alpha=0.05, beta=80%

z_alpha=1.64 and z_beta/2=1,28 for the case when mu_T=mu_R (theta0=1) and
z_alpha=1,64 and z_beta/2=0,84 otherwise
(in Excel I am tapping TINV(0,1,10000); TINV(0,2,10000) and TINV(0,4,10000) respectively)
(10000 is just a big-big number, I'm not sure Excel knows "infinity").
For CV=0.4 and theta0=0.95 after five iterations I got 66 subjects. Both PowerTost and bear give the same result. And all seemed to be good but why then in Chow S.C., Shao J., Wang H., Sample size calculations in clinical research. Marcel Dekker, New York, NY, 2003 on p.260 in the example they use values z_alpha=1.96 and z_beta/2=0.84 for alpha =0.05 and beta =80%? Suspect I read the book inattentively and in depends on the CI (90% or 95%), but the question remains: how many "tails" for alpha and beta do we have to use in BE studies?

"Being in minority, even a minority of one, did not make you mad"

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