Bioequivalence and Bioavailability Forum

CV point estimate outside CI [General Sta­tis­tics]

posted by d_labes  – Berlin, Germany, 2012-12-05 13:13 (4939 d 13:18 ago) – Posting: # 9672
Views: 11,642

Dear All!

Sometimes it may be desirable to calculate the confidence interval for a coefficient of variation. See this thread.

PowerTOST therefore contains a function CVCL() to do this. Helmut, in a personal communication, pointed out a peculiarity of the confidence intervals if one uses some rather unusual values for alpha, the probability of error:

R-code (new defined CVCL() in an upcoming version of PowerTOST):
CVCL <- function(CV, df, side=c("upper", "lower", "2-sided"), alpha=0.05)
{
  ssintra <- log(1.0 + CV^2)*df
  side    <- match.arg(side)
 
  limits <- switch(EXPR=side,
      upper= c(0, ssintra/qchisq(alpha,df)),
      lower= c(ssintra/qchisq(1-alpha,df), Inf),
      # 2-sided
      c(ssintra/qchisq(1-alpha/2,df), ssintra/qchisq(alpha/2,df)))
  limits <-(sqrt(exp(limits)-1))
  names(limits) <- c("lower CL", "upper CL")
  return(limits)
}

alphas <- c(0,0.001,0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.5545, 0.6, 0.7,
            0.8, 0.9, 0.95, 0.99, 1)
data.frame(alpha=alphas, t(sapply(FUN=CVCL, X=alphas, CV=0.3, df=12, side="upper")))

Have a look at the output
(lower limit of course always zero for a upper one-sided CI):
    alpha lower.CL   upper.CL
   0.0000        0       Inf
   0.0010        0   0.7715381
   0.0100        0   0.5795936
   0.0500        0   0.4677793
   0.1000        0   0.4222230
   0.2000        0   0.3763370
   0.3000        0   0.3482476
   0.4000        0   0.3269586
   0.5000        0   0.3089950
   0.5545        0   0.2999708
   0.6000        0   0.2926612
   0.7000        0   0.2767673
   0.8000        0   0.2599767
   0.9000        0   0.2394445
   0.9500        0   0.2245282
   0.9900        0   0.2005828
   1.0000        0   0.0000000

Above alpha ~0.5545 the confidence interval does not cover the point estimate. This is astonishing to me and fascinating, because in my belief the point estimate was always bracketed by a confidence interval.

Is this correct? Or is there a hidden bug? The latter I can't imagine because the calculation is simple enough.

Complete thread:

• CV point estimate outside CId_labes 2012-12-05 12:13 
  • What the heck? Helmut 2012-12-05 18:41
    • Code validated d_labes 2012-12-06 09:21
      • PE outside its CI?! Helmut 2012-12-06 11:14
        • PE outside its CI?! Jack 2012-12-06 13:20
          • PE outside its CI?! Helmut 2012-12-07 15:51
        • PE outside its CI! d_labes 2012-12-06 15:04
          • PE outside its CI! Helmut 2012-12-07 15:40
            • PE outside its CI! ElMaestro 2012-12-07 22:40
              • CV of log-normal data d_labes 2012-12-09 16:20
            • Two-sided brain d_labes 2012-12-10 08:25
              • Operationally equivalent… Helmut 2012-12-11 14:54
            • Austrian logic? ElMaestro 2012-12-11 15:41
              • Fuzzy logic Helmut 2012-12-11 16:12