## 'CVcap' [Power / Sample Size]

❝ what do mean about `'CVcap' = 0.2142`

If the CV_{wR} >21.42% the additional criterion “must pass 80–125%” becomes increasingly important and power drops.

It’s not explicitly stated in the FDA’s guidances (therefore, we give it in quotes) but can be easily derived with a little algebra. In a nutshell: Limits are scaled based on \(\small{CV_\text{wR}}\) with the FDA’s regulatory constant \(\small{\theta_0}\) in the first place. But for any \(\small{CV_\text{wR}>21.42\%}\) that would result in

*implied limits*\(\small{\left\{L,U\right\}}\), which are wider than 80.00 – 125.00%. That’s not we want for an NTID.$$\eqalign{

\Delta&=1/0.9\approx 1.11111\\

\sigma_\text{w0}&=0.10\\

\theta_0&=\frac{\log_e\Delta}{\sigma_\text{w0}}\approx1.053595\\

s_\text{wR}&=\sqrt{\log_e(CV_\text{wR}^2+1)}\\

\left\{L,U\right\}&=100\exp(\mp\theta_0\cdot s_\text{wR})

}$$Practically the limits are scaled indeed, but if the study would have passed,

*additionally*inclusion within the conventional 80.00 – 125.00% limits is assessed as well.

That’s numerically the same as if scaling would be ‘capped’ at \(\small{CV_\text{wR}=21.42\%}\).

If algebra is not your thing, try this:

`fun <- function(x) {`

Delta <- 1.11111 # aproximate; only the FDA knows why

sigma.0 <- 0.10

theta.0 <- log(Delta) / sigma.0

swR <- sqrt(log(x^2 + 1))

# the implied upper limit which is ≈1.25

U <- exp(theta.0 * swR)

return(U - 1.25)

}

CVcap <- uniroot(fun, interval = c(0.01, 0.3),

extendInt = "upX")$root # numerically find the CV where U ≈1.25

cat(sprintf("\'CVcap\' = %.4g\n", CVcap))

'CVcap' = 0.2142

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- Sample size calculation for NTI molecules narra1813 2019-08-10 09:21 [Power / Sample Size]
- PowerTOST: sampleN.NTIDFDA() Helmut 2019-08-10 11:23
- PowerTOST: sampleN.NTIDFDA() Mahmoud 2024-02-06 11:45
- 'CVcap'Helmut 2024-02-06 13:51
- sampleN.NTIDFDA(), power.NTIDFDA, pa.NTIDFDA are deprecated d_labes 2024-02-26 10:54

- 'CVcap'Helmut 2024-02-06 13:51

- PowerTOST: sampleN.NTIDFDA() Mahmoud 2024-02-06 11:45

- PowerTOST: sampleN.NTIDFDA() Helmut 2019-08-10 11:23