Bioequivalence and Bioavailability Forum

ISR (Rocci et al. 2007) [🇷 for BE/BA]

posted by Helmut  – Vienna, Austria, 2013-04-24 21:31 (4417 d 13:27 ago) – Posting: # 10491
Views: 4,478

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



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! 
Helmut Schütz


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• ISR (Rocci et al. 2007)Helmut 2013-04-24 19:31 [🇷 for BE/BA]