The mysterious ρ -between or within studies [General Sta­tis­tics]

posted by Astea – Russia, 2018-02-11 18:34 (2313 d 14:09 ago) – Posting: # 18397
Views: 15,773

Dear Detlew!

Thank you very much for the explanation! Now I've got it! (Yes, multitasks harm..)

So, for ρ=0.8 I get now
type1error.2TOST(CV=c(0.3, 0.25), n=122, theta1=c(0.8, 0.9),
                 theta2=c(1.25, 1/0.9), rho=0.8, details=TRUE)
1e+06 simulations. Time consumed (secs)
   user  system elapsed
 979.75   95.18 1115.72
  Intersection null P(Type I Error) theta0 #1 theta0 #2
1      H_A01 n H_Ca        0.048904 0.8000000  0.953047
2      H_A02 n H_Ca        0.049193 1.2500000  1.056122
3      H_Aa n H_C01        0.049620 0.9709781  0.900000
4      H_Aa n H_C02        0.050024 1.0000000  1.111111
5     H_A01 n H_C01        0.024479 0.8000000  0.900000
6     H_A01 n H_C02        0.000000 0.8000000  1.111111
7     H_A02 n H_C01        0.000000 1.2500000  0.900000
8     H_A02 n H_C02        0.024451 1.2500000  1.111111
and inflation at 0.050024

As I understand estimated from several datasets ρ is "between studies" ρ while in Power2TOST we need to use "within studies ρ". But it may be interesting while discussing multicomponent drugs. Especially question may arise for two components, when one of them is HVD while other is not and different approaches or CI limits involved (like telmisartan+amlodipine).
The intermediate question is mentioned situation about parent drug and its metabolite - logically, the correlation for the parameters of parent drug and its metabolite should be stronger than for two different drugs tested on the same population?

Dear Helmut!
Do I understand correctly that in your latest code you exployed all AUC and Cmax individual data for each study in order to estimate "within rho"?

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

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