Dear all,
in case someone else is suffering…
#################################################################
# Mario L. Rocci, Jr., Viswanath Devanarayan, David B. Haughey, #
# and Paula Jardieu #
# Confirmatory Reanalysis of Incurred Bioanalytical Samples #
# AAPS J 9(3), E336–43 (2007) #
#################################################################
ISR1 <- function(c1, c2, main, unit)
{
Pct.diff<- 100*(c2-c1)/((c1+c2)/2)
Pos.d <- length(Pct.diff[Pct.diff>0])
Zero.d <- length(Pct.diff[Pct.diff==0])
Neg.d <- length(Pct.diff[Pct.diff<0])
diff.r <- log10(c2) - log10(c1) # Step 1
Ratio <- 10^(diff.r) # sample ratios
mean <- mean(diff.r) # global mean
sd <- sd(diff.r) # global SD
n <- length(diff.r) # No of samples
geo.mean<- sqrt(c1*c2) # Step 2
MR <- 10^(mean) # Step 3
sig <- c(-1, +1) # helper to compute +/-
RL <- 10^(mean+sig*2*sd/sqrt(n)) # Ratio limits (lo/hi)
Bias <- "– no" # Bias (default: no)
if (max(RL)<1) Bias <- "– negative"
if (min(RL)>1) Bias <- "– positive"
ifelse (Bias == "– no", # Bias statement
Bias.state <- "(ratio 1 within limits).",
Bias.state <- "(ratio 1 outside limits).")
LA <- 10^(mean+sig*sd) # Step 4
Comp <- length(Ratio[Ratio >= LA[1] # No of ratios within limits
& Ratio <= LA[2]])
Comp.pct<- Comp/n # Pct of included samples
ifelse (Comp.pct >= 2/3, # Assessment
Pass <- "– passed LA (\u22652/3).",
Pass <- "– failed LA (<2/3).")
Abs.diff <- abs(Pct.diff) # absolute % differences
y <- length(Abs.diff[Abs.diff > 20])/n
# Fraction of samples
# with > 20% deviation
ifelse (y <= 2/3, # FDA/EMA Assessement
Reg <- "– passed", Reg <- "– failed") # 2/3 within ±20%
split.screen(c(2, 1))
screen(1)
#####################
# Difference plot #
#####################
yscale <- max(abs(Pct.diff))
if (yscale < 20) yscale <- 20
plot(geo.mean, Pct.diff, ylim=c(-yscale, yscale), las=1, log="x", pch=16,
main=paste0(main," ISR: Difference plot"),
xlab="", ylab="% Measurement difference")
abline(h=0, lty="dotted") # 0%
lines(range(geo.mean), rep(mean(Pct.diff), 2),
lwd=2, col="blue") # Mean difference
lines(range(geo.mean), rep(-20, 2), # ±20% (Regulatory limits)
lwd=2, col="red")
lines(range(geo.mean), rep(20, 2), lwd=2, col="red")
screen(2)
#####################
# Bland-Altman plot #
#####################
yscale <- max(max(Ratio), 1/min(Ratio))
if (yscale < 1.25) yscale <- 1.25
plot(geo.mean, Ratio, las=1, ylim=(c(1/yscale, yscale)), log="xy", pch=16,
main=paste0(main," ISR: Bland-Altman plot"),
xlab=paste0("Geometric mean ", unit), ylab="Measurement ratio")
abline(h=1, lty="dotted") # Ratio 1
lines(range(geo.mean), rep(MR, 2), # Mean ratio
lwd=2, col="blue")
lines(range(geo.mean), rep(RL[1], 2), # Ratio limits
lwd=2, col="darkgreen")
lines(range(geo.mean), rep(RL[2], 2), lwd=2, col="darkgreen")
lines(range(geo.mean), rep(LA[1], 2), # Limits of agreement
lwd=2, col="red")
lines(range(geo.mean), rep(LA[2], 2), lwd=2, col="red")
close.screen(all=TRUE)
###########
# Results #
###########
cat("\n", sprintf("%s%s %i %s", main, ":", n, "repeated samples\n"),
sprintf("%s%i%s%i%s%i%s", "\u2206: ",
Neg.d, " negative, ", Zero.d, " zero, ", Pos.d, " positive"), "\n",
sprintf("%s%.2f%%", "Maximum |\u2206|: ",max(Abs.diff)), "\n")
if (y == 0) {
cat(" No samples")
} else {
cat(sprintf(" %.2f%% %s", 100*y, "of samples"))
}
cat(" showed >20% |\u2206|", Reg, "regulatory criterion (\u22652/3 within ±20%).\n\n")
cat(" Mean ratio (2nd/1st analyses):", sprintf("%.2f%%", 100*MR), "\n",
"Ratio limits:", sprintf("%.2f%%", 100*RL),
Bias, "bias of repeats", Bias.state, "\n",
"Limits of agreement:", sprintf("%.2f%%", 100*LA), "\n")
if (Comp.pct == 0) cat(" No samples")
if (Comp.pct == 1) cat(" All samples")
if (Comp.pct > 0 | Comp.pct <1) {
cat(sprintf(" %.2f%% %s", 100*Comp.pct, "of samples showed "))
}
cat("ratios within LsA", Pass, "\n\n")
}
Gives with …
# Example 1
Reported <- c(478, 107, 826, 108, 248, 696, 141, 194, 548, 676,
636, 635, 244, 527, 139, 107, 664, 187, 690, 187)
Repeated <- c(406, 107, 718, 109, 250, 674, 135, 179, 564, 598,
676, 624, 240, 579, 117, 99.3, 583, 176, 610, 190)
ISR1(Reported, Repeated, "Expl.1, LC/MS-MS", "(ng/mL)")
Expl.1, LC/MS-MS: 20 repeated samples
∆: 13 negative, 1 zero, 6 positive
Maximum |∆|: 17.19%
No samples showed >20% |∆| – passed regulatory criterion (≥2/3 within ±20%).
Mean ratio (2nd/1st analyses): 95.31%
Ratio limits: 92.12% 98.61% – negative bias of repeats (ratio 1 outside limits).
Limits of agreement: 88.33% 102.85%
65.00% of samples showed ratios within LsA – failed LA (<2/3).
… and
![[image]](img/uploaded/image166.png)
Don’t blame the messenger. 
Rocci ML, Devanarayan V, Haughey DB, Jardieu P. Confirmatory Reanalysis of Incurred Bioanalytical Samples. AAPS J. 2007;9(3):Article 40. online —
Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png)
Helmut Schütz
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Ing. Helmut Schütz