Graphing Mean PK profile [🇷 for BE/BA]

posted by Helmut Homepage – Vienna, Austria, 2019-04-24 00:23 (1966 d 19:18 ago) – Posting: # 20214
Views: 13,498

Hi roman_max,

❝ recently I received a request from Sponsor to represent mean PK profile in a box-and-whiskers fashion with application of a mean connection line in one graph.


The sponsor should re-consider this idea. Box-plots are nonparametric. For log-normal distributed data (which we likely have) the median is an estimate of the geometric mean. If we want to go this way, the arithmetic mean is not a good idea.

❝ Can anyone share idea (R-code?) how to do it? How a data-set can be organized for this graph?


An idea, yes. I borrowed mittyri’s simulation code. With real data work with the second data.frame.

C <- function(F=1, D, Vd, ka, ke, t) {
  C <- F*D/Vd*(ka/(ka - ke))*(exp(-ke*t) - exp(-ka*t))
  return(C)
}
Nsub     <- 24
D        <- 400
ka       <- 1.39
ka.omega <- 0.1
Vd       <- 1
Vd.omega <- 0.2
CL       <- 0.347
CL.omega <- 0.15
t        <- c(seq(0, 1, 0.25), seq(2,6,1), 8,10,12,16,24)
ke       <- CL/Vd
tmax     <- log((ka/ke)/(ka - ke))
Cmax     <- C(D=D, Vd=Vd, ka=ka, ke=ke, t=tmax)
LLOQ.pct <- 2 # LLOQ = 2% of theoretical Cmax
LLOQ     <- Cmax*LLOQ.pct/100
df1      <- data.frame(t=t)
for (j in 1:Nsub) {
  ka.sub <- ka * exp(rnorm(1, sd = sqrt(ka.omega)))
  Vd.sub <- Vd * exp(rnorm(1, sd = sqrt(Vd.omega)))
  CL.sub <- CL * exp(rnorm(1, sd = sqrt(CL.omega)))
  df1    <- cbind(df1, C(D=D, Vd=Vd.sub, ka=ka.sub, ke=CL.sub/Vd.sub, t=t))
  df1[which(df1[, j+1] < LLOQ), j+1] <- NA
}
names(df1)[2:(Nsub+1)] <- paste0("S.", 1:Nsub)
df2 <- data.frame(t(df1[-1]))
colnames(df2) <- df1[, 1]
names(df2) <- t
print(signif(df2, 3)) # show what we have
plot(x=t, y=rep(0, length(t)), type="n", log="y", xlim=range(t),
     ylim=range(df2, na.rm=TRUE), xlab="time",
     ylab="concentration", las=1)
for (j in seq_along(t)) {
  bx <- boxplot(df2[, j], plot=FALSE)
  if (bx$n > 0) bxp(bx, log="y", boxwex=0.25, at=t[j], axes=FALSE, add=TRUE)
}

Which gave in one run:

      0  0.25 0.5 0.75   1     2     3      4     5      6      8    10    12    16    24
S.1  NA 199.0 304  353 367 295.0 198.0 128.00  82.2  52.60  21.40  8.75    NA    NA    NA
S.2  NA 132.0 218  269 296 278.0 199.0 129.00  79.7  47.90  16.70  5.65    NA    NA    NA
S.3  NA  82.7 121  136 141 126.0 106.0  88.30  73.5  61.30  42.50 29.50 20.50  9.87    NA
S.4  NA 150.0 202  204 184  76.8  24.3   6.91    NA     NA     NA    NA    NA    NA    NA
S.5  NA 102.0 167  206 226 216.0 160.0 110.00  72.6  47.30  19.70  8.16    NA    NA    NA
S.6  NA 132.0 213  260 285 285.0 241.0 197.00 160.0 129.00  84.30 55.10 36.00 15.40    NA
S.7  NA  96.9 157  193 213 216.0 185.0 152.00 124.0 101.00  67.20 44.50 29.50 13.00    NA
S.8  NA  84.1 141  179 203 229.0 213.0 189.00 165.0 143.00 108.00 81.70 61.70 35.20 11.40
S.9  NA 183.0 283  332 349 296.0 211.0 146.00  99.5  67.90  31.50 14.60  6.80    NA    NA
S.10 NA  93.8 150  181 194 166.0 110.0  66.40  38.6  22.10   7.03    NA    NA    NA    NA
S.11 NA 148.0 236  284 304 261.0 176.0 109.00  65.9  39.10  13.60    NA    NA    NA    NA
S.12 NA  95.3 156  193 213 206.0 159.0 114.00  79.8  55.30  26.30 12.50  5.89    NA    NA
S.13 NA  69.3 120  157 182 214.0 197.0 166.00 135.0 108.00  67.40 41.80 25.90  9.91    NA
S.14 NA  73.8 118  144 157 157.0 133.0 109.00  89.2  72.70  48.30 32.10 21.30  9.43    NA
S.15 NA 245.0 383  453 481 419.0 304.0 213.00 147.0 101.00  48.10 22.90 10.90    NA    NA
S.16 NA  97.4 157  192 211 204.0 163.0 124.00  93.4  69.90  39.00 21.80 12.20    NA    NA
S.17 NA  71.9 119  149 167 179.0 160.0 136.00 115.0  96.50  67.90 47.80 33.60 16.60    NA
S.18 NA 133.0 203  232 236 159.0  80.0  35.90  15.1   6.10     NA    NA    NA    NA    NA
S.19 NA 209.0 307  340 338 226.0 127.0  68.00  36.2  19.20   5.39    NA    NA    NA    NA
S.20 NA 156.0 235  266 267 172.0  83.5  36.00  14.6   5.66     NA    NA    NA    NA    NA
S.21 NA 158.0 261  325 360 355.0 274.0 196.00 136.0  92.60  42.50 19.40  8.83    NA    NA
S.22 NA  97.0 163  206 233 248.0 210.0 165.00 127.0  96.30  54.90 31.20 17.70  5.69    NA
S.23 NA 114.0 182  220 240 240.0 208.0 175.00 147.0 123.00  86.70 60.90 42.80 21.20  5.17
S.24 NA 121.0 195  238 261 260.0 216.0 173.00 137.0 109.00  67.90 42.40 26.50 10.40    NA

The bad thing is that you have to use very narrow boxes in order to avoid overlaps (boxwex=0.25).

[image]

In my “bible” that’s called a high ink-to-information ratio* which is bad style. One option would be to draw a thick line instead of the box, a thin line for the whiskers, and smaller points for the outliers, e.g.,

plot(x=t, y=rep(0, length(t)), type="n", log="y", xlim=range(t),
     ylim=range(df2, na.rm=TRUE), xlab="time",
     ylab="concentration", las=1)
for (j in seq_along(t)) {
  bx <- boxplot(df2[, j], plot=FALSE)
  if (bx$n > 0) {
    lines(rep(t[j], 2), c(bx$stats[1, 1], bx$stats[5, 1]))
    lines(rep(t[j], 2), c(bx$stats[2, 1], bx$stats[4, 1]), lwd=3, col="gray50")
    points(t[j], bx$stats[3, 1], pch=3, cex=0.6)
    points(rep(t[j], length(bx$out)), bx$out, pch=1, cex=0.5)
  }
}

[image]

Add a line connecting the medians and you are doomed.

Edit: Hey, Shuanghe – you were much faster!
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