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Vancomycin (Marques-Minana 2010)

Source: vignettes/articles/MarquesMinana_2010_vancomycin.Rmd
MarquesMinana_2010_vancomycin.Rmd

Model and source

  • Citation: Marques-Minana M-R, Saadeddin A, Peris J-E. Population pharmacokinetic analysis of vancomycin in neonates. A new proposal of initial dosage guideline. Br J Clin Pharmacol. 2010;70(5):713-722. doi:10.1111/j.1365-2125.2010.03736.x
  • Description: One-compartment IV-infusion population PK model for vancomycin in neonates (Marques-Minana 2010). Developed from 70 NICU neonates (postmenstrual age 25.1-48.1 weeks; weight 0.7-3.7 kg). Weight-normalized clearance is linear in postmenstrual age and increased by concomitant amoxicillin-clavulanic acid; weight-normalized volume of distribution is decreased by concomitant spironolactone. Additive interindividual variability on CL and V per the paper’s Step 4 error-model selection; additive residual error.
  • Article: Br J Clin Pharmacol 2010;70(5):713-722

Population

The model was developed from 70 neonates in the neonatal intensive care unit at “Hospital La Fe” (Valencia, Spain), with two serum vancomycin samples per patient drawn around the third dose: a peak 3 h after the 1-h IV infusion completed, and a trough just before the next dose. Postmenstrual age (PMA) ranged 25.1-48.1 weeks (mean 34.6), body weight 0.7-3.7 kg (mean 1.7), gestational age 24-42 weeks (mean 32.2), and postnatal age 4-63 days (mean 16.9); 53% were female (Marques-Minana 2010 Table 2 “Original” group). A separate validation group of 41 neonates with similar demographics (Table 2 “Validation” group) was used to evaluate predictive performance via external mean prediction error and root mean squared prediction error; the validation group did not contribute to model estimation. Race / ethnicity were not tabulated; the cohort is recorded as a single-site Spanish NICU population.

The same information is available programmatically via readModelDb("MarquesMinana_2010_vancomycin")$population.

Source trace

Every numeric value in ini() carries an in-file comment pointing to the Marques-Minana 2010 source location. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (theta1, CL coefficient on PMA*wt) log(1.92e-3) Table 3 theta1 = 1.92e-3 L/h/kg/(week of PMA); 95% CI 1.72e-3, 2.12e-3
lvc (theta3, V_d per kg) log(0.572) Table 3 theta3 = 0.572 L/kg; 95% CI 0.505, 0.639
e_amx_cl (theta2, AMX effect on CL) 0.650 Table 3 theta2 = 0.650; 95% CI 0.391, 0.909
e_spi_vc (theta4, SPI effect on V_d) 0.344 Table 3 theta4 = 0.344; 95% CI 0.242, 0.446
etalcl (35.6% CV additive IIV on CL, applied as cl = exp(lcl)*… + etalcl) 1.616e-3 (L/h)^2 Table 3 w_CL (CV%) = 35.6; converted as SD = 0.356 * typical CL (0.1129 L/h) = 0.0402 L/h, variance = SD^2
etalvc (19.3% CV additive IIV on V_d, applied as vc = exp(lvc)*… + etalvc) 3.522e-2 L^2 Table 3 w_V_d (CV%) = 19.3; converted as SD = 0.193 * typical V (0.9724 L) = 0.1877 L, variance = SD^2
addSd (additive residual SD) 2.69 mg/L Table 3 sigma = 2.69 microgram/mL; 95% CI 0.73, 3.73
One-compartment IV-infusion structure n/a Methods “Pharmacokinetic analysis” Step 1: NONMEM PREDPP ADVAN1 / TRANS2
TVCL = (theta1 * PMA * (1 + theta2 * AMX)) * wt n/a Table 3 footnote
TVV = (theta3 * (1 - theta4 * SPI)) * wt n/a Table 3 footnote
Additive interindividual error model n/a Methods Step 4 / Results paragraph 2: “an additive interindividual error model was selected”
Cohort mean (PMA, weight, GA, PNA) 34.6 wk, 1.7 kg, 32.2 wk, 16.9 d Table 2 “Original (n = 70)” mean row
Target Cmax / Cmin used for dose design 20.5 / 7.5 mg/L Results paragraph 5; Figure 3; Table 5 footnote

Virtual cohort

Original observed data are not publicly available. The cohorts below sample three regimens drawn from Marques-Minana 2010 Table 5 to exercise the model’s PMA term and both covariate effects:

  • typical_q12h – the typical neonate from Results paragraph 5 (PMA = 34.6 weeks, weight = 1.7 kg) dosed 12.5 mg/kg every 12 h with a 1-h infusion (Table 5 PMA = 34 row). This is the cohort whose Cmax / Cmin the paper specifically targeted (Figure 3, Results paragraph 5).
  • typical_amx_q8h – the same typical patient but coadministered amoxicillin-clavulanic acid, dosed 13.0 mg/kg every 8 h (Table 5 PMA = 34 + amoxicillin-clavulanic acid row). Exercises the +65% CL effect with CONMED_AMOXCLAV = 1.
  • typical_spi_q8h – the same typical patient coadministered spironolactone, dosed 8.0 mg/kg every 8 h (Table 5 PMA = 34 + spironolactone row). Exercises the -34% V_d effect with CONMED_SPIRON = 1.

The PAGE column carries the canonical postmenstrual age in months (PAGE = PMA_weeks / 4.35); the model model() block converts back to weeks internally.

set.seed(20100913)

n_sub <- 60L

make_cohort <- function(label, pma_wk, wt_kg, amx, spi,
                        dose_mg_kg, tau_h, id_offset) {
  ids         <- id_offset + seq_len(n_sub)
  dose_amt_mg <- dose_mg_kg * wt_kg
  infusion_h  <- 1
  n_doses     <- 14  # 7 days of dosing at q12h, ~5 days at q8h -- both reach steady state given t1/2 ~ 6 h
  dose_times  <- seq(0, by = tau_h, length.out = n_doses)

  dose_rows <- tidyr::expand_grid(id = ids, time = dose_times) |>
    dplyr::mutate(
      evid             = 1L,
      amt              = dose_amt_mg,
      cmt              = "central",
      rate             = dose_amt_mg / infusion_h,
      cohort           = label,
      WT               = wt_kg,
      PAGE             = pma_wk / 4.35,
      CONMED_AMOXCLAV  = amx,
      CONMED_SPIRON    = spi
    )

  # Coarse buildup grid + dense final-interval grid for Cmax / Cmin resolution.
  last_dose_t <- max(dose_times)
  obs_times <- sort(unique(c(
    seq(0, infusion_h * 2,            by = 0.25),
    seq(0, last_dose_t,               by = 1),
    seq(last_dose_t, last_dose_t + tau_h, by = 0.1)
  )))
  obs_rows <- tidyr::expand_grid(id = ids, time = obs_times) |>
    dplyr::mutate(
      evid             = 0L,
      amt              = 0,
      cmt              = NA_character_,
      rate             = 0,
      cohort           = label,
      WT               = wt_kg,
      PAGE             = pma_wk / 4.35,
      CONMED_AMOXCLAV  = amx,
      CONMED_SPIRON    = spi
    )

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

events <- dplyr::bind_rows(
  make_cohort("typical_q12h",     pma_wk = 34.6, wt_kg = 1.7,
              amx = 0, spi = 0, dose_mg_kg = 12.5, tau_h = 12, id_offset =    0L),
  make_cohort("typical_amx_q8h",  pma_wk = 34.6, wt_kg = 1.7,
              amx = 1, spi = 0, dose_mg_kg = 13.0, tau_h =  8, id_offset = 1000L),
  make_cohort("typical_spi_q8h",  pma_wk = 34.6, wt_kg = 1.7,
              amx = 0, spi = 1, dose_mg_kg =  8.0, tau_h =  8, id_offset = 2000L)
)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("MarquesMinana_2010_vancomycin")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("cohort", "WT", "PAGE", "CONMED_AMOXCLAV", "CONMED_SPIRON")
) |> as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

For the Figure 3 typical-value replication and the dose-design tables in Marques-Minana 2010 Table 5 / Results paragraph 5, also simulate with the random effects forced to zero. We use the params = c(etalcl = 0, etalvc = 0) override (rather than rxode2::zeroRe()) because for this model’s additive-IIV encoding the two approaches diverge after a prior stochastic rxSolve on mod: zeroRe() modifies the model’s ini() omega entries but the already-cached compiled-solver state on mod keeps drawing the original etas, so subsequent typical-value calls inherit the same between-subject variability as the stochastic run. Setting the eta parameters directly via params = bypasses the cached omega entirely and produces the typical-value trajectory the paper’s Figure 3 / Table 5 design targets are stated against.

sim_typical <- rxode2::rxSolve(
  mod,
  events = events,
  params = c(etalcl = 0, etalvc = 0),
  keep   = c("cohort", "WT", "PAGE", "CONMED_AMOXCLAV", "CONMED_SPIRON")
) |> as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 3 – typical concentration-time profile, PMA = 34.6 wk, 12.5 mg/kg q12h

Marques-Minana 2010 Figure 3 shows the simulated concentration-time profile for a typical individual in the cohort (PMA = 34.6 weeks, weight = 1.7 kg) dosed at 12.5 mg/kg every 12 h with a 1-h IV infusion, alongside the 90% prediction interval and the time-of-Cmax and time-of-Cmin sampling points. The Results paragraph 5 reports predicted Cmin near 7.5 mg/L and Cmax not exceeding 20.5 mg/L for this regimen.

The replication below shows the final steady-state dosing interval with the typical-value line overlaid on the inter-individual 90% interval (5th-95th percentiles) computed from the stochastic simulation. Vertical guides mark the peak sampling time (1-h infusion end + 3 h delay = 4 h post-dose) and the trough sampling time (just before the next dose).

ss_window_start <- max(events$time[events$evid == 1 & events$cohort == "typical_q12h"])
tau_h           <- 12
ss_window_end   <- ss_window_start + tau_h

stochastic_ribbon <- sim |>
  dplyr::filter(cohort == "typical_q12h",
                time >= ss_window_start,
                time <= ss_window_end) |>
  dplyr::mutate(time_in_tau = time - ss_window_start) |>
  dplyr::group_by(time_in_tau) |>
  dplyr::summarise(
    q05 = quantile(Cc, 0.05, na.rm = TRUE),
    q50 = quantile(Cc, 0.50, na.rm = TRUE),
    q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

typical_line <- sim_typical |>
  dplyr::filter(cohort == "typical_q12h",
                time >= ss_window_start,
                time <= ss_window_end) |>
  dplyr::mutate(time_in_tau = time - ss_window_start)

ggplot() +
  geom_ribbon(data = stochastic_ribbon,
              aes(x = time_in_tau, ymin = q05, ymax = q95),
              alpha = 0.20, fill = "steelblue") +
  geom_line(data = typical_line,
            aes(x = time_in_tau, y = Cc),
            colour = "steelblue", linewidth = 0.9) +
  geom_vline(xintercept = 4,    linetype = "dashed", colour = "grey50") +
  geom_vline(xintercept = tau_h, linetype = "dashed", colour = "grey50") +
  geom_hline(yintercept = 7.5,  linetype = "dotted", colour = "grey30") +
  geom_hline(yintercept = 20.0, linetype = "dotted", colour = "grey30") +
  labs(
    x       = "Time within steady-state dosing interval (h)",
    y       = "Vancomycin concentration (mg/L)",
    title   = "Figure 3 replication",
    caption = paste(
      "Typical 1.7-kg neonate, PMA = 34.6 wk, 12.5 mg/kg q12h IV (1 h infusion).",
      "Ribbon = 90% inter-individual interval (5th-95th).",
      "Vertical dashes mark Cmax-sampling time (4 h post-dose) and Cmin time (12 h).",
      "Horizontal dots = paper's Cmin / Cmax targets (7.5 / 20 mg/L).",
      sep = "\n"
    )
  )

Covariate-effect overlay – typical q12h vs. typical + AMX q8h vs. typical + SPI q8h

The Marques-Minana 2010 dosing recommendation in Table 5 keeps the trough near 7.5 mg/L and the peak below 20 mg/L across all three regimens by adjusting both the dose and the interval to absorb the covariate effects (amoxicillin-clavulanic acid raises CL, requiring shorter intervals; spironolactone shrinks V_d, requiring a smaller dose to avoid Cmax overshoot). The panel below overlays the typical steady-state profile for each cohort across one dosing interval, so the model’s reproduction of that nomogram can be inspected at a glance.

cohort_tau <- c(typical_q12h = 12, typical_amx_q8h = 8, typical_spi_q8h = 8)

typ_overlay <- sim_typical |>
  dplyr::group_by(cohort) |>
  dplyr::mutate(
    last_dose_t = max(events$time[events$evid == 1 & events$cohort == dplyr::first(cohort)])
  ) |>
  dplyr::ungroup() |>
  dplyr::filter(time >= last_dose_t,
                time <= last_dose_t + cohort_tau[cohort]) |>
  dplyr::mutate(time_in_tau = time - last_dose_t)

ggplot(typ_overlay, aes(time_in_tau, Cc, colour = cohort)) +
  geom_line(linewidth = 0.9) +
  geom_hline(yintercept = 7.5,  linetype = "dotted", colour = "grey30") +
  geom_hline(yintercept = 20.0, linetype = "dotted", colour = "grey30") +
  scale_colour_manual(
    values = c(typical_q12h    = "steelblue",
               typical_amx_q8h = "firebrick",
               typical_spi_q8h = "darkgreen")
  ) +
  labs(
    x       = "Time within steady-state dosing interval (h)",
    y       = "Vancomycin concentration (mg/L)",
    colour  = "Cohort (Table 5)",
    title   = "Typical-individual steady-state profiles across Table 5 regimens",
    caption = "Horizontal dots = paper's Cmin / Cmax targets (7.5 / 20 mg/L)."
  )

PKNCA validation

The block below computes per-cohort steady-state Cmax, Tmax, Cmin, and average concentration over the final dosing interval. The PKNCA formula is grouped by cohort + id so per-regimen NCA values are emitted directly. The expected targets from Marques-Minana 2010 Results paragraph 5 are a peak below 20 mg/L and a trough near 7.5 mg/L for each cohort (the paper’s dose-design objective).

# Per-cohort steady-state window (last dose to last dose + tau).
ss_windows <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(
    start_ss = max(time),
    tau      = max(time) - sort(unique(time), decreasing = TRUE)[2],
    .groups  = "drop"
  ) |>
  dplyr::mutate(end_ss = start_ss + tau)

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::inner_join(ss_windows |> dplyr::select(cohort, start_ss, end_ss),
                    by = "cohort") |>
  dplyr::filter(time >= start_ss, time <= end_ss) |>
  dplyr::select(id, time, Cc, cohort)

dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::inner_join(ss_windows |> dplyr::select(cohort, start_ss),
                    by = "cohort") |>
  dplyr::filter(time == start_ss) |>
  dplyr::select(id, time, amt, cohort)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca,
  Cc ~ time | cohort + id,
  concu = "mg/L", timeu = "hr"
)
dose_obj <- PKNCA::PKNCAdose(
  dose_df,
  amt ~ time | cohort + id,
  doseu = "mg"
)

intervals <- ss_windows |>
  dplyr::mutate(
    start   = start_ss,
    end     = end_ss,
    cmax    = TRUE,
    tmax    = TRUE,
    cmin    = TRUE,
    auclast = TRUE,
    cav     = TRUE
  ) |>
  dplyr::select(start, end, cmax, tmax, cmin, auclast, cav)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj,
                             intervals = as.data.frame(intervals))
nca_res  <- PKNCA::pk.nca(nca_data)
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=104, end=112: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval
#> Warning in .f(data_conc = .l[[1L]][[i]], data_dose = .l[[2L]][[i]],
#> data_intervals = .l[[3L]][[i]], : Error with interval start=156, end=168: No
#> data for interval

Comparison against the paper’s published design targets

Marques-Minana 2010 designed Table 5 by simulating the model with the final parameters and selecting per-PMA / per-coadministration doses that produced a trough vancomycin serum concentration close to 7.5 mg/L without exceeding a peak of 20.0 mg/L (Results paragraph 5; Table 5 caption). For each cohort the reference Cmin and Cmax come directly from that design target. The simulated typical-value Cmax (sampled at 4 h post-dose, matching the paper’s Cmax sampling protocol) and Cmin (the value at the end of the dosing interval) are tabulated alongside.

typ_summary <- sim_typical |>
  dplyr::inner_join(ss_windows, by = "cohort") |>
  dplyr::filter(time >= start_ss, time <= end_ss) |>
  dplyr::mutate(time_in_tau = time - start_ss) |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(
    cmax = Cc[which.min(abs(time_in_tau - 4))],
    cmin = min(Cc, na.rm = TRUE),
    .groups = "drop"
  )

published <- tibble::tribble(
  ~cohort,            ~cmax, ~cmin,
  "typical_q12h",      20.5,   7.5,
  "typical_amx_q8h",   20.0,   7.5,
  "typical_spi_q8h",   20.0,   7.5
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = typ_summary,
  reference = published,
  by        = "cohort",
  units     = c(cmax = "mg/L", cmin = "mg/L"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated typical-value steady-state Cmax (4 h post-dose) and Cmin vs. the Marques-Minana 2010 Table 5 design targets. * differs from reference by >20%."
)
Simulated typical-value steady-state Cmax (4 h post-dose) and Cmin vs. the Marques-Minana 2010 Table 5 design targets. * differs from reference by >20%.
NCA parameter cohort Reference Simulated % diff
Cmax (mg/L) typical_q12h 20.5 19.4 -5.5%
Cmax (mg/L) typical_amx_q8h 20 14.8 -25.8%*
Cmax (mg/L) typical_spi_q8h 20 15.2 -24.2%*
Cmin (mg/L) typical_q12h 7.5 7.65 +2.0%
Cmin (mg/L) typical_amx_q8h 7.5 6.9 -8.0%
Cmin (mg/L) typical_spi_q8h 7.5 7.47 -0.4%

Flag any starred rows in the narrative. The typical_q12h row is the specific cohort the paper modelled in Figure 3 (Results paragraph 5 reports peak below 20.5 and trough near 7.5 mg/L); the other two rows are derived from Table 5 entries that were selected against the same design targets. Discrepancies should be interpreted against the paper’s stated objective (<= 20 / ~ 7.5 mg/L) rather than against a single published estimate.

Assumptions and deviations

  • Additive interindividual variability on linear-scale parameters. Marques-Minana 2010 selected an additive interindividual error model in Step 4 of model building (Methods “Pharmacokinetic analysis”; Results paragraph 2). The packaged model preserves that choice by adding the etas directly to the linear-scale cl and vc outside the exp() wrapper (i.e., cl = exp(lcl) * ... + etalcl), with variances derived from the paper’s published w_CL (CV%) = 35.6 and w_V_d (CV%) = 19.3 interpreted as SD divided by the typical-individual TVP. The eta names carry the canonical l prefix to match the parameter names (the IIV-name convention pairs lcl with etalcl), but the etas themselves are applied additively on the linear scale rather than the more common multiplicative form exp(lcl + etalcl) that maps log-scale etas back to lognormal IIV. A reader inspecting the model() block should focus on the + etalcl placement OUTSIDE the exp() as the indicator of additive application. A consequence is that very large negative eta draws can produce non-physical negative individual CL or V draws; in practice the SDs are small enough relative to the typical values (35.6% and 19.3%) that this is rare in the simulated cohort.
  • PMA covariate via the canonical PAGE (months) column. The source paper carries PMA in weeks and the Table 3 theta1 coefficient applies to PMA-weeks directly. The packaged model uses the canonical PAGE column (in months, per inst/references/covariate-columns.md) and converts back to weeks inside model() via pma_wk = PAGE * 4.35. Numerically equivalent.
  • No allometric exponent on weight. Marques-Minana 2010 publishes the CL and V equations with WT entering linearly (TVCL = theta1 * PMA * (1 + theta2 * AMX) * wt; TVV = theta3 * (1 - theta4 * SPI) * wt), with no separately estimated allometric exponent. The packaged model retains the linear form exactly. Step 3 evaluated both linear and non-linear covariate forms for the continuous demographic predictors; the linear PMA term was selected.
  • Other demographic covariates not retained. The paper screened nine demographic predictors (gestational age, postnatal age, postmenstrual age, weight, birth weight, height, body surface area, urine output, sex) and 21 coadministered drugs as covariates of CL and V. After incorporation of postmenstrual age as a CL covariate, the remaining demographic predictors were correlated with PMA and fell out of the model (Discussion paragraph 4). The only drug effects retained were amoxicillin-clavulanic acid on CL and spironolactone on V. Serum creatinine was not screened because in neonates serum creatinine reflects maternal more than neonatal renal function in the first weeks of life (Discussion paragraph 6, citing Guignard & Drukker 1999 and Anderson et al. 2006).
  • Validation cohort (n = 41) not used for estimation. An external validation set of 41 neonates with similar demographics was used to evaluate the model via mean prediction error and root mean squared prediction error (Table 4 column “Final”). The validation set did not contribute to the parameter estimates carried in the packaged ini() block; only the 70-patient development set did.
  • Reference Cmax / Cmin from the paper’s design target, not from observed data. Marques-Minana 2010 designed the Table 5 dosing nomogram by simulating the model under each PMA / coadministration combination and selecting doses that produced a trough close to 7.5 mg/L and a peak below 20 mg/L (Results paragraph 5; Table 5 caption). The “published” Cmax / Cmin used in the comparison table above are therefore the design targets the paper aimed at, not independent observations. For the typical_q12h cohort, Figure 3 and Results paragraph 5 separately confirm that the simulated Cmax did not exceed 20.5 mg/L and the simulated Cmin was near 7.5 mg/L, which is the closest the paper comes to an observed-vs-predicted check for this regimen.
  • Race / ethnicity. Marques-Minana 2010 enrolled patients at a single-site Spanish NICU and did not tabulate race or ethnicity. The packaged model does not include race as a covariate; the population metadata records the cohort as not reported.