Bioequivalence and Bioavailability Forum • Martin‽

Martin‽ [🇷 for BE/BA]

posted by Helmut – Vienna, Austria, 2013-07-28 04:01 (3922 d 10:39 ago) – Posting: # 11081
Views: 46,835

Hi ElMaestro & Martin,

❝ Sorry to embark on archaelogy.

Great. Comes handy for some TSD sim’s I’m currently running!

meang <- function(z) { exp(mean(log(na.omit(z)))) }

mu <- 1

CV <- 0.3

set.seed(20130728)

n  <- 1e7

x  <- rlnorm(n=n, meanlog=log(mu)-0.5*log(1+CV^2), sdlog=sqrt(log(CV^2+1)))

y  <- rlnorm(n=n, meanlog=log(mu), sdlog=sqrt(log(CV^2+1)))

res<- matrix(nrow=2, ncol=6)

colnames(res) <- c("a. mean", "%RE a. mean", "CV", "%RE CV",

                   "g. mean", "%RE g. mean")

rownames(res) <- c("Par. 1 (x)", "Par. 2 (y)")

split.screen(c(2, 1))

  screen(1)

    hist(log(x), freq=F, xlim=c(-1, 1), las=1, breaks="fd",

         col="bisque", border=NA, font.main=1, cex.main=1,

         main=expression(meanlog==log[e](mu)-0.5%*%log[e](1+italic(CV)^2)),

         xlab=expression("log("*italic(x)*")"))

    abline(v=log(meang(x)), lwd=2, col="red")

  screen(2)

    hist(log(y), freq=F, xlim=c(-1, 1), las=1, breaks="fd",

         col="bisque", border=NA, font.main=1, cex.main=1,

         main=expression(meanlog==log[e](mu)),

         xlab=expression("log("*italic(x)*")"))

    abline(v=log(meang(y)), lwd=2, col="green")

close.screen(all=TRUE)

res[1, 1] <- mean(x)

res[1, 2] <- 100*(mean(x)-mu)/mu

res[1, 3] <- sd(x)/mean(x)

res[1, 4] <- 100*(sd(x)/mean(x)-CV)/CV

res[1, 5] <- meang(x)

res[1, 6] <- 100*(meang(x)-mu)/mu

res[2, 1] <- mean(y)

res[2, 2] <- 100*(mean(y)-mu)/mu

res[2, 3] <- sd(y)/mean(y)

res[2, 4] <- 100*(sd(y)/mean(y)-CV)/CV

res[2, 5] <- meang(y)

res[2, 6] <-100*(meang(y)-mu)/mu

round(res, 5)

           a. mean %RE a. mean      CV   %RE CV g. mean %RE g. mean

Par. 1 (x) 1.00008     0.00773 0.29994 -0.01999 0.95792    -4.20770

Par. 2 (y) 1.04414     4.41438 0.29992 -0.02725 1.00011     0.01147

Or alternatively:

boxplot(log(x), log(y), ylab="log(x, y)",

        names=c("Par. 1", "Par. 2"), las=1)

abline(h=0, lty=3)

Sometimes

drives my nuts. Modified from help(rlnorm):
The log normal distribution has density $$\small{f(x)=\frac{1}{\sqrt{2\pi}\sigma x}\exp (-\frac{(\log_{e}x - \mu)^2}{2 \sigma^2})}$$ where $\small{\mu}$ and $\small{\sigma}$ are the mean and standard deviation of the logarithm. The mean is $\small{E(X) = \exp(\mu + \frac{1}{2}\sigma^2)}$, the median is $\small{med(X) = \exp(\mu)}$, and the variance $\small{Var(X) = \exp(2\mu+\sigma^2)\exp(\sigma^2-1)}$ and hence the coefficient of variation is $\small{\sqrt{\exp(\sigma^2)-1}}$ […].

How I love the word “hence”.

Note that the maximum is located at $\small{mode(X)=\exp(\mu-\sigma^2)}$.

—
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:

Parallel bears meeting at random in infinity d_labes 2010-04-22 11:43 [🇷 for BE/BA]
- Parallel bears meeting at random in infinity ElMaestro 2010-04-22 12:53
  - Parallel groups in bear - CIs d_labes 2010-04-22 14:00
    - Parallel groups in bear - CIs ElMaestro 2010-04-22 21:47
      - Parallel groups in bear - CIs d_labes 2010-04-23 09:09
    - Parallel groups in bear - CIs yjlee168 2010-04-25 23:29
- Parallel bears meeting at random in infinity yjlee168 2010-04-22 23:09
  - Modelling Parallel bears d_labes 2010-04-23 09:12
    - Modelling Parallel bears yjlee168 2010-04-23 21:14
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        Validating vs. WinNonlin... yjlee168 2010-04-24 19:36
        Validating vs. WinNonlin... yjlee168 2010-04-26 00:09
        
        Validating vs. WinNonlin... Helmut 2010-04-26 01:29
        
        WNL in replicate BE yjlee168 2010-04-26 08:59
        
        WNL in replicate BE Helmut 2010-04-26 16:15
      - Modelling Parallel bears yjlee168 2010-04-25 19:34
        
        Modelling Parallel bears ElMaestro 2010-04-25 20:40
        Dataset Helmut 2010-04-25 22:38
        
        Dataset yjlee168 2010-04-25 22:44
        
        Dataset Helmut 2010-04-26 01:13
        
        Dataset yjlee168 2010-04-26 08:16
        
        NCA → Statistical analysis for parallel study Helmut 2010-04-26 13:12
        
        NCA → Statistical analysis for parallel study yjlee168 2010-04-26 18:43
        
        dilemma yjlee168 2010-04-26 08:41
        Equal variances d_labes 2010-04-26 09:04
        
        Equal variances yjlee168 2010-04-26 09:22
        
        GLM = Equal variances d_labes 2010-04-26 13:29
        
        GLM = Equal variances Helmut 2010-04-26 14:45
        
        I'm a believer d_labes 2010-04-26 15:58
        
        I'm a believer Helmut 2010-04-26 16:31
        
        Equal variances Helmut 2010-04-26 12:55
        
        gls() for unequal variances? d_labes 2010-04-26 16:36
        
        gls() for unequal variances? Helmut 2010-04-26 17:00
        Sims Helmut 2010-04-27 01:36
        
        Sandwich - Simsalabim d_labes 2010-04-28 10:58
        
        Sandwich - Simsalabim Helmut 2010-04-28 14:19
        parametrization of R function rlnorm martin 2010-05-02 18:22
        
        Mean of log-normal d_labes 2010-05-03 16:22
        parametrization of R function rlnorm ElMaestro 2013-07-26 21:42
        
        Martin‽Helmut 2013-07-28 02:01