Wrong formula for CV [Regulatives / Guidelines]

posted by Helmut Homepage – Vienna, Austria, 2022-03-20 16:57 (57 d 03:41 ago) – Posting: # 22849
Views: 463

Hi Shatha,
$$\small{CV_\textrm{intra}=100\sqrt{MSE}}\tag{1}$$$$\small{CV_\textrm{intra}=100\sqrt{\exp(MSE)-1}}\tag{2}$$
\(\small{(1)}\) was given in Health Canadas’ guidances of 1992 and 1996. \(\small{(1)}\) is only approximate for relatively small variances. The bias is always negative and hence, when used in sample size estimations misleading (studies will be underpowered).

library(PowerTOST)
CV        <- seq(0.05, 0.5, 0.05)
mse       <- CV2mse(CV)
CV.appr   <- sqrt(CV2mse(CV))
bias      <- sprintf("%+.2f%%", 100 * (CV.appr - CV) / CV)
# sample size for T/R-ratio 0.95, at least 80% power
res       <- data.frame(CV = CV, CV.appr = CV.appr, bias = bias,
                        n = NA_integer_, power = NA_real_,
                        n.appr = NA_integer_, power.appr = NA_real_)
for (j in seq_along(CV)) {
  res$n[j]      <- sampleN.TOST(CV = CV[j], print = FALSE)[["Sample size"]]
  res$n.appr[j] <- sampleN.TOST(CV = CV.appr[j], print = FALSE)[["Sample size"]]
  # minimum acc. to GLs
  if (res$n[j] < 12)      res$n[j]      <- 12
  if (res$n.appr[j] < 12) res$n.appr[j] <- 12
  res$power[j]      <- round(power.TOST(CV = CV[j], n = res$n[j]), 5)
  res$power.appr[j] <- round(power.TOST(CV = CV[j], n = res$n.appr[j]), 5)
}
CV.appr   <- round(CV.appr, 5)
print(res, row.names = FALSE)

   CV    CV.appr   bias  n   power n.appr power.appr
 0.05 0.04996879 -0.06% 12 1.00000     12    1.00000
 0.10 0.09975135 -0.25% 12 0.98835     12    0.98835
 0.15 0.14916638 -0.56% 12 0.83052     12    0.83052
 0.20 0.19804220 -0.98% 20 0.83468     20    0.83468
 0.25 0.24622068 -1.51% 28 0.80744     28    0.80744
 0.30 0.29356038 -2.15% 40 0.81585     38    0.79533
 0.35 0.33993873 -2.87% 52 0.80747     50    0.79168
 0.40 0.38525317 -3.69% 66 0.80525     62    0.77978
 0.45 0.42942138 -4.57% 82 0.80691     76    0.77602
 0.50 0.47238073 -5.52% 98 0.80322     88    0.75845


It took Health Canada until 2018 to give the correct \(\small{(2)}\). Never trust in guidances. ;-)

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