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Basics about Noncompartmental Analysis (NCA) – requiring no or only limited expertise in Pharmacokinetics (PK).

These sections are the most important ones. They are – hopefully – easily comprehensible even for novices.

A higher knowledge of NCA and/or R is required. Sorry, there is no free lunch.

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Introduction

How should we extrapolate the AUC to infinity?

Good question because two variants are implemented in software, namely based on the observed (\(\small{C_\textrm{last}}\)) and the predicted (\(\small{\widehat{C}_\textrm{last}}\)) last concentration: \[AUC_{0-\infty}=AUC_{{0-}\textrm{tlast}} + C_\textrm{last}/\widehat{\lambda}_\textrm{z}\tag{1}\] \[AUC_{0-\infty}=AUC_{{0-}\textrm{tlast}} + \widehat{C}_\textrm{last}/\widehat{\lambda}_\textrm{z}\tag{2}\] where \(\small{AUC_{{0-}\textrm{tlast}}}\) is calculated by a trapezoidal rule, \(\small{\widehat{\lambda}_\textrm{z}}\) and \(\small{\widehat{C}_0}\) are the apparent elimination rate constant and the concentration of a virtual intravenous dose at time zero estimated by semilogarithmic regression. Then \[\eqalign{ \widehat{C}_\textrm{last}&=\widehat{C}_0\cdot\exp(-\widehat{\lambda}_\textrm{z} \cdot \textrm{t}_\textrm{last})\\ \small{\textsf{for}}\;\widehat{\lambda}_\textrm{z}&>0}\tag{3}\]

However, this might be a somewhat academic question in most cases.

“When the time course is measured until plasma concentration becomes 5% of its maximum, the relative cutoff errors in AUC, MRT, and VRT are smaller than about 5%, 10%, and 40%, respectively […]. If the time course is measured until plasma concentration becomes 1% of its maximum, the relative cutoff errors in AUC, MRT, and VRT are smaller than about 1%, 2%, and 10%, respectively.
Yamaoka et al. (1978)¹

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Past and Present

In the early days of Noncompartmental Analysis \(\small{(1)}\) was commonly used.

Already 42 years ago \(\small{(2)}\) was occasionally used (e.g., in a project² sponsored by the FDA) and for the first time recommended 31 years ago.³ ⁴ ⁵ ⁶ For a while it was mandatory for manuscripts submitted to the ‘Bioequivalence Section’ of the International Journal of Clinical Pharmacology, Therapy and Toxicology (edited by one of the pioneers of bioequivalence, Henning Blume).
Other references: By an author of the FDA⁷ and more recent ones as well.⁸ ⁹ ¹⁰ ¹¹

Makes sense. \(\small{C_\textrm{last}}\) might be close to the Lower Limit of Quantification (LLOQ) and hence, has the lowest accuracy and highest variability of the entire profile. If one bases the extrapolation on it, one sets a fox to keep the geese. The intrinsic high variability of \(\small{C_\textrm{last}}\) propagates into the extrapolated area. Contrary to that, \(\small{\widehat{C}_\textrm{last}}\) takes information of preceding (higher, and therefore, more accurate and precise) concentrations into account and thus, is in general more reliable.

“In general, we recommend use of the predicted rather than the observed last concentration when computing the extrapolated area.
Gabrielsson and Weiner (2016)¹¹

Little is mentioned in guidelines. AFAIK, the FDA,¹² China’s CDE, Brazil’s ANVISA, and the WHO¹³ recommend \(\small{(1)}\), whereas Health Canada¹⁴ recommends \(\small{(2)}\). Nothing is stated by the EMA.¹⁵ ¹⁶

I’m using solely \(\small{(2)}\) since the early 1990s and never received a single deficiency letter in this respect (yes, none from the FDA as well). Of course, the method should be outlined in the protocol. My standard for immediate release formulations with a monoexponential elimination:

“Extrapolation from \(\small{\textrm{t}_\textrm{last}}\) to infinite time will be performed by fitting – at least three – terminal concentrations to the monoexponential model \(\small{\widehat{C}_\textrm{t}=\widehat{C}_0\cdot\exp(-\widehat{\lambda}_\textrm{z}\cdot \textrm{t})}\) by means of unweighted semilogarithmic regression. The starting point for the estimation will default to \(\small{\geq 2\times \textrm{t}_\textrm{max}}\).¹⁷ The selected time points will be adjusted if deemed necessary, i.e., a visual inspection of fits will be performed.³ ⁵ ⁸ ¹⁷ Increasing concentrations in the late phase of the profile will be excluded from the estimation of \(\small{\widehat{\lambda}_\textrm{z}}\). To avoid under- or over-estimation of the extrapolated area, the estimated last concentration \(\small{\widehat{C}_\textrm{last}}\) will be used in extrapolations.³ ⁵ ⁸ ¹¹

If PK is expected to be multiphasic, i.e., with distribution phase(s) and elimination, the second sentence is:

“The intersection of the last two phase lines in the (semilogarithmic) profile post \(\small{C_\textrm{max}}\) is used as a ‘visual marker’ for the beginning of the monoexponential terminal phase.¹⁷

Algorithms for the estimation of \(\small{\widehat{\lambda}_\textrm{z}}\) will be elaborated in another article.

Dr. David Bowman inside HAL 9000

It must be mentioned that any algorithm might fail on ‘flat’ profiles (controlled release formulations with flip-flop PK) or on profiles of multiphasic release formulations.

Nota bene, visual inspection of fits is mandatory.³ ⁵ ⁸ ¹⁷ Our brain is an excellent pattern recognition machine.

One software vendor rightly notes:

“Using this methodology, Phoenix will almost always compute an estimate for Lambda Z. It is the user’s responsibility to evaluate the appropriateness of the estimated value.
Certara (2020)¹⁸
(my emphasis)

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Software

Both methods are implemented in numerous pieces of software. Most commonly used terminology:

Term	Metric
`AUClast`	\(\small{AUC_{{0-}\textrm{tlast}}}\)
`AUCINF_obs`	\(\small{AUC_{0-\infty}}\) based on \(\small{(1)}\)
`AUCINF_pred`	\(\small{AUC_{0-\infty}}\) based on \(\small{(2)}\)
`Clast_pred`	\(\small{\widehat{C}_\textrm{last}}\)
`Lambda_z`	\(\small{\widehat{\lambda}_\textrm{z}}\)
`Lambda_z_intercept`	\(\small{\widehat{C}_0}\)

Already in 1993 both methods were implemented in TopFit 2.0.¹⁹ They are available in Phoenix WinNonlin²⁰ (see the User’s Guide or the online manual²¹ for details), PKanalix,²² the R packages PKNCA,²³ ²⁴ ncappc,²⁵ qpNCA,²⁶ and ubiquity,²⁷ ²⁸ ²⁹ as well as in the Julia library Pumas.³⁰ ³¹

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Simulation

One-compartment model, first order absorption and elimination, no lag time.
PK-parameters: \(\small{D=200}\), \(\small{f=0.80}\), \(\small{V=3}\), absorption half life 45 minutes, elimination half life five hours.
The error distribution was log-normal, where the error increased with decreasing concentrations. The LLOQ was set to 4% of the model’s \(\small{C_\textrm{max}}\). Simulated concentrations below the LLOQ prior to \(\small{t_\textrm{max}}\) were set to zero, and later ones to NA. Automatic algorithm for the estimation of \(\small{\widehat{\lambda}_\textrm{z}}\) based on maximizing \(\small{R_\textrm{adj}^2}\), which is the default in all other software as well.

Sorry, 268 LOC.

Function	Purpose
`one.comp()`	Calculates concentrations, the exact (i.e., the model’s) \(\small{C_\textrm{max}}\), \(\small{t_\textrm{max}}\), \(\small{AUC_{0-\textrm{tlast}}}\), \(\small{AUC_{0-\infty}}\), and LLOQ for given vector of sampling times, PK-parameters, and LLOQ specified as a fraction of the model’s \(\small{C_\textrm{max}}\).
`micro2macro()`	Converts the model’s PK-parameters (micro constants \(\small{f}\), \(\small{D}\), \(\small{V}\), \(\small{k_{01}}\), and \(\small{k_{10}}\)) to macro (hybrid) constants \(\small{A}\), \(\small{B}\), \(\small{\alpha}\), and \(\small{\beta}\). Note that in a model without lag time \(\small{\left\| A \right\| = B}\).
`round.up()`	Rounds `x` up to the next multiple of `y`.
`sampling()`	Calculates a vector of ‘optimal’ sampling times: Equally spaced to \(\small{t_\textrm{max}}\) and then following a geometric progression to \(\small{t_{\textrm{tlast}}}\).
`est.elim()`	Estimates the apparent elimination by semilogarithmc regression. Returns \(\small{R_\textrm{adj}^2}\), \(\small{\widehat{C}_0}\), \(\small{\widehat{\lambda}_\textrm{z}}\), start- and end-times, and the number of values used. If estimation fails (slope ≥ 0), returns `NA`for all.
`calc.AUC()`	Calculates \(\small{AUC_{{0-}\textrm{tlast}}}\) by a trapezoidal rule. Implemented are `linlog` (default) and `linear`.
`AUC.extr()`	Extrapolates the \(\small{AUC}\). Returns \(\small{AUC_{{0-}\textrm{tlast}}}\) (for comparison), \(\small{AUC_{0-\infty}}\) (observed and predicted), \(\small{C_\textrm{last}}\), and \(\small{\widehat{C}_\textrm{last}}\).
`sum.simple()`	Nonparametric summary (i.e., removes the arithmetic mean from `summary()`.
`geom.stat()`	Calculates the geometric mean and CV.

sim.auc <- function(D, f, V, t12.a, t12.e, n1, n2, tlast,
                    mins, CV0, LLOQ.f, rule, nsims,
                    setseed = TRUE, show.fits = FALSE, progress = FALSE) {
  one.comp <- function(f, D, V, k01, k10, t, LLOQ.f) {
    # one-compartment model, first order absorption
    # and elimination, no lagtime
    x <- micro2macro(f, D, V, k01, k10) # get hybrid (macro) constants
    if (!isTRUE(all.equal(k01, k10))) { # common: k01 != k10
      C    <- f * D * k01 / (V * (k01 - k10)) *
              (exp(-k10 * t) - exp(-k01 * t))
      # values based on the model
      tmax <- log(k01 / k10) / (k01 - k10)
      Cmax <- f * D * k01 / (V * (k01 - k10)) *
              (exp(-k10 * tmax) - exp(-k01 * tmax))
      AUC  <- f * D / V / k10
      AUCt <- (x$C[["A"]] - x$C[["A"]] * exp(-x$E[["alpha"]] * tlast)) /
              x$E[["alpha"]] +
              (x$C[["B"]] - x$C[["B"]] * exp(-x$E[["beta"]] * tlast)) /
              x$E[["beta"]]
  }else {                           # flip-flop
      k    <- k10
      C    <- f * D / V * k * t * exp(-k * t)
      tmax <- 1 / k
      Cmax <- f * D / V * k * tmax * exp(-k * tmax)
      AUC  <- f * D / V / k
      AUCt <- NA # sorry, no idea
    }
    LLOQ <- Cmax * LLOQ.f
    C[C <= LLOQ] <- NA                # set values below the LLOQ to NA
    C[which(is.na(C[t < tmax]))] <- 0 # set NAs prior tmax to zero
    res <- list(C = C, Cmax = Cmax, tmax = tmax, AUC = AUC, AUCt = AUCt,
                LLOQ = LLOQ)
    return(res)
  }

  micro2macro <- function(f, D, V, k01, k10) {
    # Convert parameters (micro constants) to macro (hybrid) constants
    # Coefficients (C) and exponents (E)
    C     <- f * D * k01 / (V * (k01 - k10))
    C     <- setNames(c(-C, +C), c("A", "B"))
    E     <- setNames(c(k01, k10), c("alpha", "beta"))
    macro <- list(C = C, E = E)
    return(macro)
  }

  round.up <- function(x, y) {
    # round x up to the next multiple of y
    return(y * (x %/% y + as.logical(x %% y)))
  }

  sampling <- function(f, D, V, k01, k10, n1, n2, tlast, mins, LLOQ.f) {
    # <= tmax: equally spaced
    # >= tmax: geometric progression
    # rounded to 'mins' minutes
    tmax <- one.comp(f, D, V, k01, k10, t = tlast, LLOQ.f)$tmax
    t    <- seq(0, tmax, length.out = n1)
    for (i in (n1+1):(n1+n2-1)) {
      t[i] <- t[i-1] * (tlast / tmax)^(1 / (n2 - 1))
    }
    t <- round.up(t * 60, mins) / 60
    t[length(t)] <- tlast
    return(t)
  }

  est.elim <- function(t, C) {
    # estimate lambda.z by "maximum adjusted R-squared approach"
    data   <- data.frame(t = t, C = C)
    Cmax   <- max(data$C, na.rm = TRUE)
    tmax   <- data$t[data$C[!is.na(data$C)] == Cmax]
    data   <- data[data$t > tmax, ]        # discard tmax and earlier
    data   <- data[complete.cases(data), ] # discard NAs
    lz.end <- tail(data$t, 1)
    # start with the last three concentrations
    x      <- tail(data, 3)
    r2     <- a <- b <- numeric()
    m      <- lm(log(C) ~ t, data = x)
    a[1]   <- coef(m)[[1]]
    b[1]   <- coef(m)[[2]]
    r2[1]  <- summary(m)$adj.r.squared
    # work backwards
    i      <- 1
    for (j in 4:nrow(data)) {
      i     <- i + 1
      x     <- tail(data, j)
      m     <- lm(log(C) ~ t, data = x)
      a[i]  <- coef(m)[[1]]
      b[i]  <- coef(m)[[2]]
      r2[i] <- summary(m)$adj.r.squared
      # don't proceed if no improvement
      if (r2[i] < r2[i-1] | abs(r2[i] - r2[i-1]) < 0.0001) break
    }
    # location of the largest adjusted R2
    loc <- which(r2 == max(r2, na.rm = TRUE))
    if (b[loc] >= 0 || r2[loc] <= 0) { # not meaningful
      R2adj <- intcpt <- lambda.z <- lz.start <- lz.end <- lz.n <- NA
  }else {
      R2adj    <- r2[loc]
      intcpt   <- a[loc]
      lambda.z <- -b[loc]
      lz.start <- x$t[2]
      lz.n     <- nrow(x) - 1
    }
    res <- data.frame(R2adj = R2adj, intcpt = intcpt, lambda.z = lambda.z,
                      lz.start = lz.start, lz.end = lz.end, lz.n = lz.n)
    return(res)
  }

  calc.AUC <- function(t, C, rule = "linlog",
                       digits = 5, details = FALSE) {
    x <- data.frame(t = t, C = C, pAUC = 0)
    x <- x[with(x, order(t)), ]
    x <- x[complete.cases(x), ]
    for (i in 1:(nrow(x) - 1)) {
      if (rule == "linlog") { # linear-up / log-down
        if (x$C[i+1]  < x$C[i]) {
          x$pAUC[i+1] <- (x$t[i+1] - x$t[i]) * (x$C[i+1] - x$C[i]) /
                         log(x$C[i+1] / x$C[i])
      }else {
          x$pAUC[i+1] <- 0.5 * (x$t[i+1] - x$t[i]) *
                         (x$C[i+1] + x$C[i])
        }
    }else {               # linear
        x$pAUC[i+1] <- 0.5 * (x$t[i+1] - x$t[i]) *
                       (x$C[i+1] + x$C[i])
      }
    }
    x$AUC <- cumsum(x$pAUC)
    x     <- x[with(x, order(t)), ] # sort by time
    if (details) {                  # entire data.frame
      res <- round(x, digits)
  }else {                        # only tlast and AUClast
      res <- setNames(as.numeric(round(tail(x[, c(1, 4)], 1), digits)),
                      c("tlast", "AUClast"))
    }
    if (rule == "linlog") {
      attr(res, "trapezoidal rule") <- "linear-up/log-down"
  }else {
      attr(res, "trapezoidal rule") <- "linear"
    }
    return(res)
  }

  AUC.extr <- function(t, C, intcpt, lambda.z) {
    x           <- calc.AUC(t, C, rule = rule, details = TRUE)
    AUClast     <- tail(x$AUC, 1)
    Clast_obs   <- tail(x$C, 1)
    AUCinf_obs  <- AUClast + tail(x$C, 1) / lambda.z
    Clast_pred  <- exp(intcpt - lambda.z * tail(x$t, 1))
    AUCinf_pred <-  AUClast + Clast_pred / lambda.z
    res <- list(AUClast = AUClast, Clast_obs = Clast_obs,
                AUCinf_obs = AUCinf_obs, Clast_pred = Clast_pred,
                AUCinf_pred = AUCinf_pred)
    return(res)
  }

  sum.simple <- function(x, digits = 4) {
    # nonparametric summary: remove mean but keep NAs
    res <- summary(x)
    if (nrow(res) == 6) {
      res <- res[c(1:3, 5:6), ]
  }else {
      res <- res[c(1:3, 5:7), ]
    }
    return(res)
  }

  geom.stat <- function(x) {
    stats <- as.data.frame(matrix(nrow = 2, ncol = ncol(x),
                                  dimnames = list(c("geom. mean",
                                                    "geom. CV (%)"),
                                                    names(x))))
    for (i in 1:ncol(stats)) {
      stats[1, i] <- exp(mean(log(x[, i]), na.rm = TRUE))
      stats[2, i] <- 100 * sqrt(exp(sd(log(x[, i]), na.rm = TRUE)^2) - 1)
    }
    return(stats)
  }

  k01    <- log(2) / t12.a   # absorption rate constant
  k10    <- log(2) / t12.e   # elimination rate constant
  # generate sampling schedule
  t      <- sampling(f, D, V, k01, k10, n1, n2, tlast, mins, LLOQ.f)
  x      <- one.comp(f, D, V, k01, k10, t, LLOQ.f)
  C0     <- x$C              # theoretical profile (based on model)
  Cmax   <- x$Cmax
  tmax   <- x$tmax
  LLOQ   <- x$LLOQ
  CV     <- CV0 - C0 * 0.006 # variability increases with decreasing C
  varlog <- log(CV^2 + 1)
  sdlog  <- sqrt(varlog)
  aggr1  <- data.frame(R2adj = NA_real_, intcpt = NA_real_,
                       lambda.z = NA_real_, RE = NA_real_, t.half = NA_real_,
                       lz.start = NA_real_, lz.end = NA_real_,
                       lz.n = NA_integer_)
  aggr2  <- data.frame(AUClast = NA_real_, Clast_obs = NA_real_,
                       AUCinf_obs = NA_real_, Clast_pred = NA_real_,
                       AUCinf_pred = NA_real_)
  aggr3  <- data.frame(matrix(NA, nrow = nsims, ncol = length(t)))
  C      <- numeric()
  if (progress) pb <- txtProgressBar(0, 1, 0, char = "\u2588",
                                     width = NA, style = 3)
  if (setseed) set.seed(123456)
  for (i in 1:nsims) {
    for (j in 1:length(C0)) {
      if (is.na(C0[j])) {
        C[j] <- NA # otherwise, rlnorm() fails
    }else {
        C[j] <- rlnorm(1, meanlog = log(C0[j]) - 0.5 * varlog[j],
                       sdlog = sdlog[j])
      }
    }
    # C < LLOQ set to NA, NAs prior to tmax set to zero
    Cmax.tmp <- max(C, na.rm = TRUE)
    tmax.tmp <- t[C[!is.na(C)] == Cmax.tmp]
    C[C <= LLOQ] <- NA
    C[which(is.na(C[t < tmax.tmp]))] <- 0
    aggr3[i, ] <- C
    aggr1[i, c(1:3, 6:8)] <- est.elim(t, C)[1, ]
    if (!is.na(aggr1$lambda.z[i])) { # only if successful fit
      aggr1$t.half[i] <- log(2) / aggr1$lambda.z[i]
      aggr1$RE[i]     <- 100 * (aggr1$lambda.z[i] - k10) / k10
      aggr2[i, ]      <- as.numeric(AUC.extr(t, C,
                                             aggr1$intcpt[i],
                                             aggr1$lambda.z[i]))
    }
    if (progress) setTxtProgressBar(pb, i / nsims)
  }
  if (progress) close(pb)
  method <- "trapezoidal rule"
  ifelse (rule == "linlog",
    method <- paste("linear-up / log-down", method),
    method <- paste("linear", method))
  NAs <- data.frame(time = t,
                    NAs = sapply(aggr3, function(x) sum(length(which(is.na(x))))))
  cat("Results from the model (without error)",
      "\n  AUClast", sprintf("%.3f", x$AUCt),
      "\n  AUCinf ", sprintf("%.3f", x$AUC),
      paste0("\n\n", prettyNum(nsims, digits = 0, big.mark = ","),
             " simulated profiles, ", method, "\n"))
  print(NAs, row.names = FALSE)
  failed <- as.integer(gsub("[^[:digit:]]", "", sum.simple(aggr1)[6, 1]))
  if (failed >0) cat("In", failed,
                     "profile(s) estimation of the apparent",
                     "elimination failed (nonnegative slope).\n\n")
  print(signif(geom.stat(aggr2), 4))
  if (show.fits) {
    cat("\n")
    print(sum.simple(aggr1))
  }
}

D         <- 200      # dose
f         <- 0.8      # fraction absorbed (BA)
V         <- 3        # volume of distribution
t12.a     <- 0.75     # absorption half life
t12.e     <- 5        # elimination half life
n1        <- 4        # number of samples <= tmax
n2        <- 9        # number of samples >= tmax (n = n1 + n2 - 1)
tlast     <- 24       # last sampling time point (h)
mins      <- 15       # rounding of sampling times (minutes)
CV0       <- 0.40     # CV at low concentrations
LLOQ.f    <- 0.04     # fraction of theoretical Cmax
rule      <- "linlog" # if you insist: "linear"
nsims     <- 2.5e3L   # number of simulations
show.fits <- FALSE    # TRUE for nonparametric summary of fits
progress  <- FALSE    # TRUE for a progress bar
sim.auc(D, f, V, t12.a, t12.e, n1, n2, tlast, mins,
        CV0, LLOQ.f, rule, nsims, show.fits, progress)

# Results from the model (without error) 
#   AUClast 368.471 
#   AUCinf  384.719 
# 
# 2,500 simulated profiles, linear-up / log-down trapezoidal rule
#   time NAs
#   0.00   0
#   1.00   0
#   1.75   0
#   2.50   0
#   3.25   0
#   4.50   0
#   5.75   0
#   7.75   0
#  10.25   0
#  13.75   0
#  18.25   1
#  24.00 447
# In 1 profile(s) estimation of the apparent elimination failed (nonnegative slope).
# 
#              AUClast Clast_obs AUCinf_obs Clast_pred AUCinf_pred
# geom. mean   356.500     2.679    380.400      2.549     379.000
# geom. CV (%)   8.307    40.830      8.614     38.960       8.578

Even the linear-up/log-down underestimates \(\small{AUC_{{0-}\textrm{tlast}}}\) because the profile is concave up to the inflection point at \(\small{2\times t_\textrm{max}}\). There is nothing we can do about (see another article).

Note that the variability of \(\small{C_\textrm{last}}\) is larger than the one of \(\small{\widehat{C}_\textrm{last}}\). As expected, and it propagates partly to the extrapolated \(\small{AUC\textrm{s}}\), where the variability based on \(\small{(1)}\) is slightly larger then the one based on \(\small{(2)}\).

In either case the variability of \(\small{AUC_{0-\infty}}\) is larger than the one of \(\small{AUC_{{0-}\textrm{tlast}}}\). For immediate release formulations point estimates of \(\small{\textrm{p}AUC_{0-\textrm{t}\,\geq\,\small{2\times t_\textrm{max}}}}\) are stable, only variability increases with time.³²

“Once absorption is over, formulation differences no longer apply.
Midha et al. (1996)³²

However, this might be relevant in juridictions applying Average Bioequivalence with Expanding Limits (ABEL) and \(\small{AUC_{0-\infty}}\) is a primary pharmacokinetic metric because the late part of the profile represents absorption (e.g., controlled release formulations for the EMA, where reference-scaling is only acceptable for \(\small{C_\textrm{max}}\) and the sample size depends on \(\small{AUC}\); see this article for an example).

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Conclusion

\(\small{\widehat{\lambda}_\textrm{z}}\) obtained by an automatic algorithm should be inspected for its plausibility.

\(\small{AUC_{0-\infty}}\) based on either \(\small{(1)}\) or \(\small{(2)}\) can be used. The planned method must be unambiguous stated in the protocol.

From a theoretical point of view – and as demonstrated in the Simulation above – \(\small{AUC_{0-\infty}}\) calculated by \(\small{(2)}\) is expected to result in slighty lower variability and therefore, is recommended.² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ¹⁰ ¹¹ ¹⁴ However, in the common case that the sample size is based on \(\small{C_\textrm{max}}\),³³ this advantage over \(\small{(1)}\) likely is not relevant.

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Licenses

Helmut Schütz 2022
R GPL 3.0, pandoc GPL 2.0.
1^st version March 06, 2022. Rendered July 13, 2022 11:12 CEST by rmarkdown via pandoc in 0.49 seconds.

Footnotes and References

Yamaoka K, Nakagawa T, Uno T. Statistical Moments in Pharmacokinetics. J Pharmacokin Biopharm. 1978; 6(6): 547–58. doi:10.1007/bf01062109.↩︎
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Very rarely the variability of \(\small{AUC}\) is larger than the one of \(\small{C_\textrm{max}}\) and hence, drives the sample size.↩︎

Extrapolation to Infinity

Observed or Predicted C_last?

Helmut Schütz

July 13, 2022

Introduction

Past and Present

Software

Simulation

Conclusion

Extrapolation to Infinity

Observed or Predicted Clast?

Helmut Schütz

July 13, 2022

Introduction

Past and Present

Software

Simulation

Conclusion

Observed or Predicted C_last?