## Loss in power [Regulatives / Guidelines]

Hi mittyri and all,

R-code to estimate the loss in power (two groups of equal size). Example for my simulations above and assuming that we will get a significant Group-by-Treatment interaction at the level of the test.

library(PowerTOST) CV          <- 0.3 theta0      <- 1 targetpower <- 0.8 p.level     <- 0.1 res         <- sampleN.TOST(CV=CV, theta0=theta0, targetpower=targetpower,                             print=FALSE) N           <- res[["Sample size"]] if (N >= 12) { # at least minimum sample size acc. to GLs?   pwr.mod3pooled <- res[["Achieved power"]] } else {   N <- 12   pwr.mod3pooled <- power.TOST(CV=CV, theta0=theta0, n=N) } pwr.mod2       <- suppressMessages(power.TOST(CV=CV, theta0=theta0,                                               n=N-1)*(1-p.level)) pwr.mod3groups <- power.TOST(CV=CV, theta0=theta0, n=N/2)*p.level pwr.mod2and3   <- pwr.mod2+pwr.mod3groups cat(sprintf("CV %5.3f%%, theta0 %.4f, targetpower %.2f%%    : sample size %i",             100*CV, theta0, 100*targetpower, N),     "\nLevel of the G\u00D7T test (model 1)                  :",       sprintf("% 6.4f", p.level),      "\nPower of studies evaluated by model 2 (pooled)   :",       sprintf("%5.2f%%", 100*pwr.mod2),     "\nPower of studies evaluated by model 3 (groups)   :",       sprintf("%5.2f%%", 100*pwr.mod3groups),     "\nModel 2 (pooled) and 3 (groups) combined         :",       sprintf("%5.2f%%", 100*pwr.mod2and3),     "\nPower of studies evaluated by model 3 (pooled)   :",       sprintf("%5.2f%%", 100*pwr.mod3pooled),     "\nLoss in power if simple model 3 cannot be applied:",       sprintf("%5.2f%%", 100*(pwr.mod3pooled-pwr.mod2and3)), "\n")

Gives

CV 30.000%, theta0 1.0000, targetpower 80.00%    : sample size 32 Level of the G×T test (model 1)                  :  0.1000 Power of studies evaluated by model 2 (pooled)   : 71.80% Power of studies evaluated by model 3 (groups)   :  3.25% Model 2 (pooled) and 3 (groups) combined         : 75.05% Power of studies evaluated by model 3 (pooled)   : 81.52% Loss in power if simple model 3 cannot be applied:  6.47%

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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