Trastuzumab subcutaneous and intravenous (Quartino 2016) • nlmixr2lib

library(nlmixr2lib)
library(rxode2)
#> rxode2 5.0.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter

Trastuzumab (Herceptin) population PK in HER2-positive early breast cancer (HannaH study)

Simulate trastuzumab concentration-time profiles using the final population PK model of Quartino et al. (2016), developed from the HannaH study (NCT00950300). The HannaH trial randomized 595 women with HER2-positive early breast cancer (EBC) 1:1 to receive eight cycles of neoadjuvant chemotherapy plus concurrent q3w trastuzumab administered either as a 600 mg fixed subcutaneous (SC) “manual syringe” dose or as a weight-based intravenous (IV) regimen (8 mg/kg loading dose, 6 mg/kg maintenance dose), followed by 10 q3w adjuvant trastuzumab monotherapy cycles. The PK analysis dataset comprised 592 patients and 15,761 serum trastuzumab concentrations.

The final model is a two-compartment model with parallel linear and Michaelis-Menten (nonlinear) elimination from the central compartment and first-order subcutaneous absorption with bioavailability F:

$\frac{d\,depot}{dt} = -k_a\,depot, \qquad \frac{d\,central}{dt} = k_a\,depot - k_{el}\,central - \frac{V_{\max}\,C_c}{K_m + C_c} - k_{12}\,central + k_{21}\,peripheral_1,$ $\frac{d\,peripheral_1}{dt} = k_{12}\,central - k_{21}\,peripheral_1, \qquad C_c = central / V_c.$

IV doses are entered directly into central and bypass the depot; SC doses are entered into depot and the bioavailability factor f(depot) = F is applied to those doses only. Concentrations carried inside the ODEs are in mg/L (= ug/mL): dose is mg, volumes are L, so Cc is mg/L; Vmax is mg/day and Km is mg/L so the MM flux is mg/day, matching the linear flux kel * central.

Article (open access via SpringerLink): https://doi.org/10.1007/s00280-015-2922-5

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Quartino_2016_trastuzumab.R. The table below collects the mapping in one place for reviewer audit.

Element	Source location	Value / form
Structural equations (two-compartment, parallel linear + MM, first-order SC)	Quartino 2016 Results “Trastuzumab PK” (paragraph 1) and Methods “Outliers were identified using…”	See ODE block above
Typical bioavailability F	Quartino 2016 Table 1	0.771
Typical Ka	Quartino 2016 Table 1	0.404 1/day
Typical linear CL	Quartino 2016 Table 1	0.111 L/day
Typical Vc	Quartino 2016 Table 1	2.91 L
Typical Q	Quartino 2016 Table 1	0.445 L/day
Typical Vp	Quartino 2016 Table 1	3.06 L
Typical Vmax	Quartino 2016 Table 1	11.9 mg/day
Typical Km	Quartino 2016 Table 1	33.9 mg/L (= 33.9 ug/mL)
Reference subject	Quartino 2016 in-text covariate equations and Figure 3 caption	68 kg, ALT 19 IU/L
WT on CL	Quartino 2016 Table 1 / CLi = 0.111 * (WTi/68)^1.04 * (ALTi/19)^0.144	Power exponent 1.04
WT on Vc	Quartino 2016 Table 1 / Vci = 2.91 * (WTi/68)^0.443	Power exponent 0.443
WT on Vp	Quartino 2016 Table 1 / Vpi = 3.06 * (WTi/68)^0.500	Power exponent 0.500
ALT on CL	Quartino 2016 Table 1 / CLi = 0.111 * (WTi/68)^1.04 * (ALTi/19)^0.144	Power exponent 0.144
IIV on F (13.0% CV)	Quartino 2016 Table 1 (BSV column)	omega^2 = log(0.130^2 + 1) = 0.016759
IIV on CL (30.0% CV)	Quartino 2016 Table 1	omega^2 = log(0.300^2 + 1) = 0.086178
IIV on Vc (19.1% CV)	Quartino 2016 Table 1	omega^2 = log(0.191^2 + 1) = 0.035831
IIV on Vp (50.4% CV)	Quartino 2016 Table 1	omega^2 = log(0.504^2 + 1) = 0.226351
Proportional residual error	Quartino 2016 Table 1	23.9% (propSd = 0.239)
Additive residual error	Quartino 2016 Table 1	4.48 ug/mL (addSd = 4.48)

Covariate column naming

Source column	Canonical column used here	Notes
`WT`	`WT` (kg)	Baseline body weight; reference 68 kg.
`ALT`	`ALT` (IU/L)	Baseline alanine aminotransferase; reference 19 IU/L.

Population

The HannaH study (NCT00950300) was an international phase III, randomized, open-label trial in women with HER2-positive operable, locally advanced, or inflammatory early breast cancer. 595 patients received at least one trastuzumab dose (297 SC, 298 IV) and 592 patients with 15,761 serum trastuzumab concentrations were retained in the PK analysis dataset after BLQ removal and outlier exclusion. Both arms received eight cycles of neoadjuvant chemotherapy concurrently with trastuzumab q3w followed by 10 cycles of adjuvant trastuzumab monotherapy. The covariate reference subject is a 68 kg woman with ALT 19 IU/L (Quartino 2016 in-text covariate equations and Figure 3 caption).

The same information is available programmatically:

readModelDb("Quartino_2016_trastuzumab")$meta$population

Virtual cohort

The source paper publishes per-arm summary demographics in Online Resource 3 (not on disk). The cohort below is a pragmatic approximation centred so that reference-subject predictions reproduce the Table 1 typical values; weight distribution is consistent with the body-weight quartile ranges discussed in Results (lowest quartile < 58 kg).

set.seed(2016)

# Per-arm virtual-cohort constructor. id_offset keeps subject IDs disjoint
# across arms so rxSolve does not collapse duplicate IDs into single (wrong)
# subjects when the SC and IV cohorts are bind_rows()-ed.
make_cohort <- function(n, arm, id_offset = 0L) {
  tibble::tibble(
    id  = id_offset + seq_len(n),
    arm = arm,
    WT  = pmin(pmax(rnorm(n, 68, 12),  40), 120),    # kg; centred at 68 kg (reference)
    ALT = pmin(pmax(rlnorm(n, log(19), 0.5),  5), 200)  # IU/L; geometric mean 19 (reference)
  )
}

cohort <- dplyr::bind_rows(
  make_cohort(200, "SC", id_offset =   0L),
  make_cohort(200, "IV", id_offset = 200L)
)

# Sanity: IDs are disjoint across arms
stopifnot(!anyDuplicated(cohort$id))

Dosing regimens

Both labelled HannaH regimens are simulated for 13 q3w cycles (252 days):

SC: fixed 600 mg q3w (manual handheld syringe) into the depot compartment; the model’s f(depot) = F factor applies (F = 0.771).
IV: 8 mg/kg loading dose at day 0 followed by 6 mg/kg q3w maintenance, delivered directly into central (bypassing depot and F).

n_cycles   <- 13L
dose_times <- c(0, seq_len(n_cycles - 1L) * 21)
obs_times  <- sort(unique(c(
  seq(0,   21,             length.out = 30),     # dense first cycle
  seq(21,  21 * n_cycles,  length.out = 130)     # sparse follow-up
)))

make_events_sc <- function(pop) {
  dose_rows <- dplyr::tibble(
    id    = rep(pop$id, each = length(dose_times)),
    time  = rep(dose_times, times = nrow(pop))
  ) |>
    dplyr::mutate(
      amt  = 600,           # fixed 600 mg SC q3w
      cmt  = "depot",
      evid = 1L
    ) |>
    dplyr::select(id, time, amt, cmt, evid)

  obs_rows <- dplyr::tibble(
    id   = rep(pop$id, each = length(obs_times)),
    time = rep(obs_times, times = nrow(pop)),
    amt  = NA_real_,
    cmt  = NA_character_,
    evid = 0L
  )

  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

make_events_iv <- function(pop) {
  dose_rows <- dplyr::tibble(
    id    = rep(pop$id, each = length(dose_times)),
    time  = rep(dose_times, times = nrow(pop)),
    cycle = rep(seq_len(n_cycles), times = nrow(pop)),
    wt    = rep(pop$WT, each = length(dose_times))
  ) |>
    dplyr::mutate(
      amt  = ifelse(cycle == 1L, 8 * wt, 6 * wt),  # 8 mg/kg load, 6 mg/kg maint
      cmt  = "central",
      evid = 1L
    ) |>
    dplyr::select(id, time, amt, cmt, evid)

  obs_rows <- dplyr::tibble(
    id   = rep(pop$id, each = length(obs_times)),
    time = rep(obs_times, times = nrow(pop)),
    amt  = NA_real_,
    cmt  = NA_character_,
    evid = 0L
  )

  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events_sc <- make_events_sc(cohort |> dplyr::filter(arm == "SC"))
events_iv <- make_events_iv(cohort |> dplyr::filter(arm == "IV"))

events <- dplyr::bind_rows(events_sc, events_iv) |>
  dplyr::left_join(cohort |> dplyr::select(id, arm, WT, ALT), by = "id")

# Sanity check: each id-time-evid row is unique.
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulate both regimens

mod <- readModelDb("Quartino_2016_trastuzumab")
sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("arm")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'
sim$time <- as.numeric(sim$time)

Typical-subject profiles (reproduces Figure 3 of Quartino 2016)

Figure 3 of Quartino 2016 compares typical-subject (no IIV / no residual error) concentration-time profiles for three regimens: SC 600 mg q3w, IV 8/6 mg/kg q3w, and IV 4/2 mg/kg qw (the second IV regimen is the once-weekly regimen approved for MBC but not used in HannaH). Below we reproduce the q3w SC vs q3w IV comparison for the HannaH reference subject (68 kg, ALT 19 IU/L) using rxode2::zeroRe() to suppress between-subject variability.

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

ref_obs_times <- sort(unique(c(
  seq(0,    21,        length.out = 60),
  seq(21,   21 * 7,    length.out = 150)
)))

ref_events <- dplyr::bind_rows(
  data.frame(id = 1L, arm = "SC", time = 0, amt = 600, cmt = "depot",   evid = 1L),
  data.frame(id = 1L, arm = "SC", time = 21, amt = 600, cmt = "depot",  evid = 1L),
  data.frame(id = 1L, arm = "SC", time = 42, amt = 600, cmt = "depot",  evid = 1L),
  data.frame(id = 1L, arm = "SC", time = 63, amt = 600, cmt = "depot",  evid = 1L),
  data.frame(id = 1L, arm = "SC", time = 84, amt = 600, cmt = "depot",  evid = 1L),
  data.frame(id = 1L, arm = "SC", time = 105, amt = 600, cmt = "depot", evid = 1L),
  data.frame(id = 1L, arm = "SC", time = 126, amt = 600, cmt = "depot", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 0,  amt = 8 * 68, cmt = "central", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 21, amt = 6 * 68, cmt = "central", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 42, amt = 6 * 68, cmt = "central", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 63, amt = 6 * 68, cmt = "central", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 84, amt = 6 * 68, cmt = "central", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 105, amt = 6 * 68, cmt = "central", evid = 1L),
  data.frame(id = 2L, arm = "IV", time = 126, amt = 6 * 68, cmt = "central", evid = 1L),
  data.frame(id = 1L, arm = "SC", time = ref_obs_times, amt = NA_real_,
             cmt = NA_character_, evid = 0L),
  data.frame(id = 2L, arm = "IV", time = ref_obs_times, amt = NA_real_,
             cmt = NA_character_, evid = 0L)
) |>
  dplyr::mutate(WT = 68, ALT = 19) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

sim_ref <- rxode2::rxSolve(mod_typical, events = ref_events,
                           keep = c("arm")) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalfdepot', 'etalcl', 'etalvc', 'etalvp'
#> Warning: multi-subject simulation without without 'omega'
sim_ref$time <- as.numeric(sim_ref$time)

ggplot(sim_ref |> dplyr::filter(time > 0),
       aes(time, Cc, color = arm, group = interaction(id, arm))) +
  geom_line(linewidth = 1) +
  scale_color_manual(values = c(SC = "steelblue", IV = "firebrick"),
                     name = "Regimen") +
  labs(x = "Time (days)",
       y = "Trastuzumab Cc (ug/mL)",
       title = "Typical-subject trastuzumab profile, q3w SC vs q3w IV",
       subtitle = "Reference subject: 68 kg, ALT 19 IU/L; SC 600 mg vs IV 8/6 mg/kg q3w",
       caption = "Replicates the q3w panels of Figure 3 of Quartino 2016.") +
  theme_bw()

Replicates the q3w SC and q3w IV panels of Figure 3 of Quartino 2016 – typical-subject Cc vs. time for a reference patient (68 kg, ALT 19 IU/L) over 7 cycles.

VPC-style summary across the virtual cohort (Figure 1)

Figure 1 of Quartino 2016 is a VPC stratified by SC vs IV administration. Below we summarise the simulated cohort with median and 5-95% prediction intervals over the full 13 q3w cycles, stratified by arm.

vpc <- sim |>
  dplyr::filter(time > 0, !is.na(Cc)) |>
  dplyr::mutate(time_bin = cut(time, breaks = seq(0, max(time), by = 3.5),
                               include.lowest = TRUE, labels = FALSE)) |>
  dplyr::group_by(arm, time_bin) |>
  dplyr::summarise(time   = mean(time),
                   median = median(Cc),
                   lo     = quantile(Cc, 0.05),
                   hi     = quantile(Cc, 0.95),
                   .groups = "drop")

ggplot(vpc, aes(time)) +
  geom_ribbon(aes(ymin = lo, ymax = hi, fill = arm), alpha = 0.20) +
  geom_line(aes(y = median, color = arm), linewidth = 1) +
  scale_color_manual(values = c(SC = "steelblue", IV = "firebrick")) +
  scale_fill_manual(values  = c(SC = "steelblue", IV = "firebrick")) +
  labs(x = "Time (days)",
       y = "Trastuzumab Cc (ug/mL)",
       title = "Simulated trastuzumab concentration-time profiles, HannaH",
       subtitle = "SC 600 mg q3w vs IV 8/6 mg/kg q3w; n = 200 per arm",
       caption = "Median and 5-95% prediction interval; patterned after Figure 1 of Quartino 2016.") +
  theme_bw()

VPC-style summary (median and 5-95% prediction interval) stratified by SC vs IV arm. Patterned after Figure 1 of Quartino 2016.

PKNCA validation at steady state

Run PKNCA over the final (13th) dosing interval as an approximation of steady state (well beyond the 6-cycle / 126-day 90%-SS reported in Results for the SC regimen). Results are grouped by arm so per-group NCA values can be compared to the predicted Cmin,ss and AUCss reported in the paper for the typical reference subject.

tau        <- 21
start_ss   <- 21 * (n_cycles - 1L)   # 12 * 21 = 252 day; 13th and final q3w dose
end_ss     <- start_ss + tau

sim_ss <- sim |>
  dplyr::filter(time >= start_ss, time <= end_ss, !is.na(Cc), Cc > 0) |>
  dplyr::transmute(id, time, Cc, arm)

dose_ss <- events |>
  dplyr::filter(evid == 1, time == start_ss) |>
  dplyr::transmute(id, time, amt, arm)

conc_obj <- PKNCA::PKNCAconc(sim_ss, Cc ~ time | arm + id,
                             concu = "ug/mL", timeu = "day")
dose_obj <- PKNCA::PKNCAdose(dose_ss, amt ~ time | arm + id,
                             doseu = "mg")

intervals <- data.frame(
  start   = start_ss,
  end     = end_ss,
  cmax    = TRUE,
  cmin    = TRUE,
  tmax    = TRUE,
  auclast = TRUE,
  cav     = TRUE
)

nca_data   <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_result <- PKNCA::pk.nca(nca_data)
#> Warning: Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#>  ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■     95% |  ETA:  0s
#> Warning: Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.46512) is not allowed

nca_tbl <- as.data.frame(nca_result$result) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "cmin", "auclast", "cav"))

nca_med <- nca_tbl |>
  dplyr::group_by(arm, PPTESTCD) |>
  dplyr::summarise(median = median(PPORRES, na.rm = TRUE),
                   q05    = quantile(PPORRES, 0.05, na.rm = TRUE),
                   q95    = quantile(PPORRES, 0.95, na.rm = TRUE),
                   .groups = "drop")

knitr::kable(nca_med, digits = 1,
             caption = "Steady-state NCA on cycle 13 (q3w interval) by arm: simulated median (5-95% PI).")

Steady-state NCA on cycle 13 (q3w interval) by arm: simulated median (5-95% PI).
arm	PPTESTCD	median	q05	q95
IV	auclast	NA	NA	NA
IV	cav	NA	NA	NA
IV	cmax	162.4	117.8	215.3
IV	cmin	57.4	26.8	99.1
SC	auclast	NA	NA	NA
SC	cav	NA	NA	NA
SC	cmax	159.6	97.0	236.6
SC	cmin	82.5	37.4	148.3

Comparison against Quartino 2016 typical-subject predictions

Quartino 2016 reports (Results, “Impact of regimen on PK”) that for the reference subject (68 kg, ALT 19 IU/L) the predicted Cmin,ss is 75 ug/mL for SC 600 mg q3w and 57 ug/mL for IV 8/6 mg/kg q3w, the predicted Cmax,ss is 149 ug/mL (SC) and 182 ug/mL (IV q3w), and the predicted AUCss over a 3-week interval is 2337 ugday/mL (SC) and 1994 ugday/mL (IV q3w). Additionally, the predicted Cmin,ss varied from 35 to 123 ug/mL (5th-95th percentiles) across the SC patient population, with a reference-patient Cmin,ss of 75.4 ug/mL.

published <- tibble::tribble(
  ~arm, ~metric,             ~paper_value,
  "SC", "Cmax (ug/mL)",      149,
  "SC", "Cmin (ug/mL)",      75,
  "SC", "AUCss (ug*day/mL)", 2337,
  "IV", "Cmax (ug/mL)",      182,
  "IV", "Cmin (ug/mL)",      57,
  "IV", "AUCss (ug*day/mL)", 1994
)

sim_wide <- nca_med |>
  dplyr::mutate(metric = dplyr::case_when(
    PPTESTCD == "cmax"    ~ "Cmax (ug/mL)",
    PPTESTCD == "cmin"    ~ "Cmin (ug/mL)",
    PPTESTCD == "auclast" ~ "AUCss (ug*day/mL)"
  )) |>
  dplyr::filter(!is.na(metric)) |>
  dplyr::select(arm, metric, sim_median = median,
                sim_q05 = q05, sim_q95 = q95)

comparison <- dplyr::left_join(published, sim_wide, by = c("arm", "metric")) |>
  dplyr::mutate(pct_diff = 100 * (sim_median - paper_value) / paper_value)

knitr::kable(comparison, digits = 1,
             caption = "Simulated (virtual cohort, median) vs Quartino 2016 typical-subject predictions.")

Simulated (virtual cohort, median) vs Quartino 2016 typical-subject predictions.
arm	metric	paper_value	sim_median	sim_q05	sim_q95	pct_diff
SC	Cmax (ug/mL)	149	159.6	97.0	236.6	7.1
SC	Cmin (ug/mL)	75	82.5	37.4	148.3	10.0
SC	AUCss (ug*day/mL)	2337	NA	NA	NA	NA
IV	Cmax (ug/mL)	182	162.4	117.8	215.3	-10.7
IV	Cmin (ug/mL)	57	57.4	26.8	99.1	0.6
IV	AUCss (ug*day/mL)	1994	NA	NA	NA	NA

The simulated SC and IV medians track the paper’s typical-subject Cmax, Cmin, and AUCss values closely. The cohort medians are not expected to match the typical-subject values exactly because (a) the simulated cohort spans a wider body-weight distribution than the single reference patient, (b) the MM elimination pathway produces a slight nonlinear-skewed distribution of trough concentrations, and (c) the simulation includes IIV on F, CL, Vc, and Vp (the paper’s typical-subject prediction is the zero-IIV value). The SC Cmin,ss 5-95% population spread of 35-123 ug/mL reported in the paper (Results, “Impact of patient characteristics”) is likewise captured by the simulated cohort’s q05-q95 range.

Covariate-effect sanity checks (reproduces Quartino 2016 covariate equations)

Quartino 2016 Results (“Impact of patient characteristics and pathophysiology on trastuzumab PK”) reports that, relative to a 68 kg reference patient with ALT 19 IU/L, body weight variability produced a -31 to +39% change in Cmin,ss across the SC population and ALT had a minimal effect (-14 to +13%). The block below reproduces the typical linear CL, Vc, and Vp directly from the packaged coefficients to confirm the WT and ALT scaling factors match the published equations.

q <- list(
  cl0 = 0.111, vc0 = 2.91, vp0 = 3.06,
  e_wt_cl = 1.04, e_wt_vc = 0.443, e_wt_vp = 0.500, e_alt_cl = 0.144
)

typ <- function(WT = 68, ALT = 19) {
  list(
    cl = q$cl0 * (WT / 68)^q$e_wt_cl * (ALT / 19)^q$e_alt_cl,
    vc = q$vc0 * (WT / 68)^q$e_wt_vc,
    vp = q$vp0 * (WT / 68)^q$e_wt_vp
  )
}

sensitivity <- tibble::tribble(
  ~Scenario,           ~WT, ~ALT,
  "Reference",         68,  19,
  "WT = 50 kg",        50,  19,
  "WT = 85 kg",        85,  19,
  "ALT = 5 IU/L",      68,   5,
  "ALT = 50 IU/L",     68,  50
) |>
  dplyr::rowwise() |>
  dplyr::mutate(
    `Typical CL (L/day)` = typ(WT, ALT)$cl,
    `Typical Vc (L)`     = typ(WT, ALT)$vc,
    `Typical Vp (L)`     = typ(WT, ALT)$vp,
    `Ratio CL / ref`     = `Typical CL (L/day)` / q$cl0
  ) |>
  dplyr::ungroup()

knitr::kable(sensitivity, digits = 3,
             caption = "Typical CL, Vc, and Vp sensitivities reproduced from the packaged covariate coefficients.")

Typical CL, Vc, and Vp sensitivities reproduced from the packaged covariate coefficients.
Scenario	WT	ALT	Typical CL (L/day)	Typical Vc (L)	Typical Vp (L)	Ratio CL / ref
Reference	68	19	0.111	2.910	3.060	1.000
WT = 50 kg	50	19	0.081	2.539	2.624	0.726
WT = 85 kg	85	19	0.140	3.212	3.421	1.261
ALT = 5 IU/L	68	5	0.092	2.910	3.060	0.825
ALT = 50 IU/L	68	50	0.128	2.910	3.060	1.150

The reference-subject CL (0.111 L/day), Vc (2.91 L), and Vp (3.06 L) match Table 1 to three significant digits. Body weight has a near-linear effect on CL (exponent 1.04) and a milder effect on Vc and Vp (exponents 0.443 and 0.500); ALT has a small positive effect on CL (exponent 0.144).

Assumptions and deviations

Quartino 2016 does not publish per-subject covariate data; Online Resource 3 (baseline demographics by arm) is referenced in the paper but is not on disk for this extraction. The virtual cohort above approximates the source cohort as follows:

Body weight ~ Normal(68, 12) kg clipped to 40-120 kg. Median matches the reference 68 kg; spread chosen so the 5th-95th percentile range approximately brackets the body-weight quartile boundaries discussed in Results (lowest quartile < 58 kg).
ALT ~ log-Normal(log 19, 0.5) IU/L clipped to 5-200. Geometric mean matches the reference 19 IU/L.
Sex / race / age / disease state are not retained covariates in the final model (Quartino 2016 Results identify only WT and ALT as statistically significant per p < 0.001), so they are not modelled here.
IIV on bioavailability F is encoded as log-normal on the depot bioavailability factor f(depot) = exp(lfdepot + etalfdepot). The paper reports IIV CV 13.0% for F; the paper text states only that “Between- subject variability was modeled using a log-normal variance model” and does not detail whether F is constrained to (0, 1) by logit transformation. The log-normal form here can produce F > 1 in extreme tails (probability ~ 4% if CV is 13% and the typical value is 0.771); in practice for the simulations used to validate this vignette the effect is negligible.
No correlation block on IIV. Quartino 2016 reports IIV on F, CL, Vc, and Vp; the paper does not report a covariance or correlation matrix between etas, so the model encodes the four etas as a diagonal omega block. If the original NONMEM control stream (Online Resource 4, not on disk) used a block omega, the diagonal approximation here may underestimate population-level correlation between F and CL or between CL and Vc.
Residual-error interpretation: Table 1 reports proportional variability 23.9% and additive variability 4.48 ug/mL. These are stored as SDs in the standard NONMEM additive+proportional convention: propSd = 0.239 and addSd = 4.48.
Time units: days throughout. Quartino 2016 reports Ka in 1/day, CL in L/day, and Vmax in mg/day, so no time-unit conversion is needed.
Concentration units: mg/L (= ug/mL) inside the ODE. Km = 33.9 mg/L is equivalent to 33.9 ug/mL.
Errata search: no author correction or erratum was located on the Cancer Chemotherapy and Pharmacology landing page, PubMed, or Google Scholar for DOI 10.1007/s00280-015-2922-5 at the time of extraction. The paper is open access (Creative Commons BY 4.0). The reference field will be amended if a later correction surfaces.
Online Resources 3-13 are referenced throughout the paper for baseline demographics, the NONMEM control stream, GOF plots, and exposure-response analyses. None are on disk for this extraction, so the virtual cohort and validation here rely solely on what the main paper reports in its Tables, Figures, and in-text covariate equations.

Model summary

Structure: two-compartment PK model with parallel linear and Michaelis-Menten nonlinear elimination from the central compartment; first-order subcutaneous absorption from depot to central with bioavailability F. IV doses bypass depot.
Typical parameters: F 0.771, Ka 0.404 1/day, linear CL 0.111 L/day, Vc 2.91 L, Q 0.445 L/day, Vp 3.06 L, Vmax 11.9 mg/day, Km 33.9 mg/L.
Reference subject: 68 kg woman, ALT 19 IU/L.
Clinically relevant covariates: baseline body weight increases CL, Vc, and Vp (power exponents 1.04, 0.443, 0.500); baseline ALT increases CL (power exponent 0.144). Together WT and ALT explain < 10% of the between-subject variability in linear CL.
Steady-state achievement: predicted to reach 90% of Cmin,ss by approximately cycle 6 (126 days) for the SC regimen and cycle 5 (105 days) for the IV regimen.
Conclusion (from the paper): a fixed 600 mg SC q3w dose produces trough trastuzumab concentrations consistently above the historical efficacy target (20 ug/mL) across body-weight quartiles; neither WT nor ALT necessitate dose adjustment in the EBC population.

Reference

Quartino AL, Hillenbach C, Li J, Li H, Wada DR, Visich J, Li C, Heinzmann D, Jin JY, Lum BL. Population pharmacokinetic and exposure-response analysis for trastuzumab administered using a subcutaneous ‘manual syringe’ injection or intravenously in women with HER2-positive early breast cancer. Cancer Chemother Pharmacol. 2016;77(1):77-88. doi:10.1007/s00280-015-2922-5