Power<50% [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2024-03-01 15:44 (79 d 18:26 ago) – Posting: # 23888
Views: 767

Hi BEQool,

❝ Why do we pass the study if the power is below 50%?

Let’s dive deeper into you example:

library(PowerTOST)
n   <- sampleN.scABEL(CV = 1.1, theta0 = 0.95, design = "2x2x3",
                      details = FALSE, print = FALSE)[["Sample size"]]
n   <- seq(n, 36, -2)
res <- data.frame(n = n, lower = NA_real_, upper = NA_real_, power = NA_real_)
for (j in seq_along(n)) {
  res[j, 2:3] <- CI.BE(CV = 1.1, pe = 0.95, n = n[j], design = "2x2x3")
  res[j, 4]   <- power.scABEL(CV = 1.1, theta0 = 0.95, n = n[j], design = "2x2x3")
}
print(signif(res, 4), row.names = FALSE)

  n  lower upper  power
 88 0.7838 1.151 0.8080
 86 0.7821 1.154 0.7974
 84 0.7803 1.157 0.7866
 82 0.7784 1.159 0.7750
 80 0.7764 1.162 0.7626
 78 0.7744 1.165 0.7503
 76 0.7723 1.169 0.7360
 74 0.7701 1.172 0.7226
 72 0.7679 1.175 0.7070
 70 0.7655 1.179 0.6911
 68 0.7631 1.183 0.6743
 66 0.7606 1.187 0.6567
 64 0.7579 1.191 0.6373
 62 0.7551 1.195 0.6180
 60 0.7522 1.200 0.5972
 58 0.7492 1.205 0.5745
 56 0.7460 1.210 0.5504
 54 0.7426 1.215 0.5267
 52 0.7391 1.221 0.5008
 50 0.7353 1.227 0.4733
 48 0.7314 1.234 0.4453
 46 0.7272 1.241 0.4134
 44 0.7227 1.249 0.3816
 42 0.7180 1.257 0.3490
 40 0.7129 1.266 0.3122
 38 0.7075 1.276 0.2751
 36 0.7016 1.286 0.2372

Strange. I have to think about it… :ponder:
CI.BE() gives us the realized results (i.e., the values observed in a particular study), whereas power.scABEL() the results of 105 simulations. Both the CV and PE are skewed to the right and, therefore, I would expect that simulated power is lower than assessing whether a particular study passes. However, such a large discrepancy is surprising for me.

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