## tmax (DR & multiphasic) [Regulatives / Guidelines]

Dear all,

another goody. Lines 811–814

The IR GL states:

another goody. Lines 811–814

[…] A formal statistical evaluation of t_{max} is not required. However, there should be no apparent difference in median t_{max} and its range between test and reference product.

^{1}The IR GL states:

However, […] there should be no apparent difference in median t_{max} and its variability between test and reference product.

*variability*of the median might be in the EMA’s opinion (without applying nonparametric statistics this generally ended up in more or less eloquent ). Now I’m enlightened. It is the*range*! Splendid idea! A statistical parameter with a breakdown point^{2}of zero. Not even a dyed-in-the-wool nonparametrician on the maximum allowed dose of Schützenafil^{®}would*ever*compare data based on their ranges.*Maybe*the IQR performs better?^{3}- Upon their own risk German-speakers might follow this link for additional information.

- The breakdown point of an estimator is defined as the number of incorrect values which will not lead to a biased result.
- The arithmetic mean has a breakdown point of 1: Imagine an (even infinitely large) set of identical values (say 1). Now change a
*single*original value to \(\small{\infty}\). The arithmetic mean of the new set is \(\small{\infty}\).

\(x_1=1,x_2=1,\ldots, x_{i=n}=1\rightarrow \bar{x}=\frac{1}{n}\sum_{i=1}^{i=n}x_i=1\)

\(x_1=1,x_2=1,\ldots, x_{i=n}=\infty\rightarrow \bar{x}=\frac{1}{n}\sum_{i=1}^{i=n}x_i=\infty \; \small{\square}\)

- The median has a breakdown point of 50%. You would need to change 50% of values to ∞ in order to contaminate the median. Therefore, the median is a robust estimator of location.

- Unfortunately the range performs just as bad as the arithmetic mean. Only two values of the entire data set (min & max) are used. Everything else is ignored. Imagine two (if you like very large) ranked sets:

`R {1, …, 1, 2} median 1, range 1`

→ apparent difference

T1 {1, …, 1, 3} median 1, range 2

Or more weird:

`T2 {1, …, 1, 1} median 1, range 0`

→ superior?

- The arithmetic mean has a breakdown point of 1: Imagine an (even infinitely large) set of identical values (say 1). Now change a
- Duno. Try:

`t <- c(0.5, 0.67, 0.83, 1, 1.33, 1.67, 2)`

p <- c(0.025, 0.1, 0.15, 0.45, 0.15, 0.1, 0.025)

n <- 24

set.seed(1234567)

R <- sample(t, size=n, replace=TRUE, prob=p)

T <- sample(t, size=n, replace=TRUE, prob=p)

med <- c(median(R), median(T))

rng <- c(range(R), range(T))

iqr <- c(IQR(R), IQR(T))

f <- "%s%3.2f%s%3.2f%s%+3.2f%s"

op <- par(no.readonly = TRUE)

par(family="mono")

boxplot(R, T, range = 0, names = c("R", "T"), ylim = c(0, max(t)), las = 1)

legend("bottomright", box.lwd = 0, box.col = "white", legend = paste(

sprintf(f, " Medians: R=", med[1], ", T=", med[2],

" (\u2206=", med[2]-med[1], ")"), "\n",

sprintf(f, "Ranges : R=", rng[1], ", T=", rng[2],

" (\u2206=", rng[2]-rng[1], ")"), "\n",

sprintf(f, "IQRs : R=", iqr[1], ", T=", iqr[2],

" (\u2206=", iqr[2]-iqr[1], ")"), "\n"), cex = 0.9,

title = "Statistics of Tmax")

points(x = jitter(rep(1, n), 10), R)

points(x = jitter(rep(2, n), 5), T)

box()

par <- op

BTW, what’s*“no apparent difference”*?

—

Helmut Schütz

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

Science Quotes

*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:

- Draft EMA MR formulations GL published! Ohlbe 2013-03-15 12:10 [Regulatives / Guidelines]
- Housekeeping suggestions Helmut 2013-03-15 13:28
- Scaling for pAUCs Helmut 2013-03-15 14:19
- Draft EMA MR formulations GL published! ioanam 2013-03-30 17:54
- Topicals → 1995 NfG Helmut 2013-03-30 22:51
- Topicals, generic ElMaestro 2013-03-31 19:26
- Topicals, generic ioanam 2013-04-01 07:51
- Topicals, generic The Outlaw Torn 2013-04-01 08:03

- Topicals, generic ioanam 2013-04-01 07:51

- Clarity on waiving multiple dose study Tina 2013-05-15 14:19
- Hey, it is just a draft! Helmut 2013-05-17 18:49
- Critical review of García-Arieta et al. (2012) Helmut 2013-06-29 19:44

- Hey, it is just a draft! Helmut 2013-05-17 18:49
- SD vs. MD, partial AUCs Helmut 2013-06-21 19:24
- SD vs. MD, partial AUCs Shuanghe 2013-06-25 17:22
- SD vs. MD, partial AUCs Helmut 2013-06-25 19:15
- SD vs. MD, partial AUCs Shuanghe 2013-06-27 11:07
- pAUCs, alternative metrics, alcohol Helmut 2013-06-27 14:38

- SD vs. MD, partial AUCs Shuanghe 2013-06-27 11:07

- SD vs. MD, partial AUCs Helmut 2013-06-25 19:15

- SD vs. MD, partial AUCs Shuanghe 2013-06-25 17:22
- tmax (DR & multiphasic)Helmut 2013-06-22 01:15
- Presentations of the EUFEPS meeting Helmut 2013-07-15 15:50
- ⧫ Deadline approaching ⧫ Helmut 2013-08-16 16:41
- Download comment form Helmut 2013-08-26 11:28

- Food effect Compliance 2013-08-26 12:04
- Food effect Dr_Dan 2013-08-26 16:48

- Variability (MR vs. IR) Helmut 2013-09-12 15:23