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Tigecycline (Yang 2021)

Source: vignettes/articles/Yang_2021_tigecycline.Rmd
Yang_2021_tigecycline.Rmd

Model and source

The main article gives only the final clearance equation. The volume of distribution, the between-subject variability and the residual error are in Supplementary Table S10.

Population

Yang and colleagues ran a therapeutic-drug-monitoring study at the PLA General Hospital in Beijing between October 2018 and March 2019. They enrolled 67 adults (over 18 years) treated with intravenous tigecycline for hospital-acquired pneumonia, complicated skin and skin-structure infection or complicated intra-abdominal infection. There were 50 men and 17 women, with a mean age of 65.5 years (SD 23) and a mean weight of 64.83 kg (SD 14.96). Patients received one of three regimens (Table 1):

  • 100 mg loading dose, then 50 mg every 12 h (24 patients);
  • 100 mg every 12 h (29 patients);
  • 50 mg every 12 h (14 patients).

At steady state, samples were drawn at one or more of 0, 0.5, 1.5, 3, 6, 9 and 12 h after a dose. Most were troughs. The study collected 186 concentrations, one of them below the 50 ng/mL limit of quantification. The lung was the infection site in most of the 58 patients with outcome data (Table 2). Acinetobacter baumannii was isolated in 24 of them, alone or with K. pneumoniae or E. coli.

The sparse, trough-heavy data supported only a one-compartment model, fitted in NONMEM 6. The covariates screened were sex, age, body weight, direct and total bilirubin, albumin, ALT, AST, GGT, ALP, blood urea nitrogen (BUN) and creatinine. Age and BUN both reduced the objective function, but only BUN on clearance survived backward elimination.

The same information is available programmatically via readModelDb("Yang_2021_tigecycline")()$population.

Source trace

Equation / parameter Value Source location
One-compartment IV model n/a Results, “Construction of the Base Model and Full Regression Model”; Supplement, “Compartment model selection”
cl = exp(lcl + etalcl) * (BUN / 9)^e_bun_cl n/a Results: “CL = 25.2 * (BUN/9)^-0.271”
lcl log(25.2) L/h Table S10, CL = 25.2 L/h (RSE 7.9%)
lvc log(417) L Table S10, V = 417 L (RSE 33.3%)
e_bun_cl -0.271 Table S10, theta BUN (CL) = -0.271 (RSE 43.2%); same value in the Results equation
etalcl 0.587^2 = 0.3446 Table S10, eta (CL) = 0.587 (RSE 11.3%), read as an SD (see below)
propSd 0.576 Table S10, epsilon (prop) = 0.576 (RSE 10.5%), read as an SD; proportional error per Supplement “Base model”
Reference BUN 9 mmol/L Results equation; Table 5 footnote

Typical-value check against Table 5

The paper’s Table 5 reports the typical-value AUC0-24/MIC at steady state for maintenance doses of 50 and 100 mg every 12 h. It does this in four BUN strata (medians 4.7, 8.3, 14.5 and 34.2 mmol/L), using the broth-microdilution MIC50 of 4 mg/L and MIC90 of 8 mg/L. At steady state, AUC0-24 is twice the maintenance dose divided by CL. So Table 5 tests the clearance equation directly, including the sign of the BUN exponent.

The model is solved with between-subject and residual variability removed. It runs to steady state with 20 doses every 12 h, given as 1-hour infusions (the paper does not state the infusion time). PKNCA computes AUC over the last 24 h.

strata <- tibble::tibble(
  stratum = c("Normal", "Compensated", "Decompensated", "Renal failure"),
  bun_range = c("1.8-7.5", "7.5-9", "9-20", "20-48.3"),
  BUN = c(4.7, 8.3, 14.5, 34.2)
)

tv_design <- tidyr::expand_grid(dose = c(50, 100), strata) |>
  dplyr::mutate(
    id = dplyr::row_number(),
    treatment = sprintf("%g mg q12h, BUN %.1f", dose, BUN)
  )

dose_times <- seq(0, 228, by = 12)
obs_times <- sort(unique(c(seq(216, 240, by = 0.25), 216.5, 217)))

tv_events <- dplyr::bind_rows(
  tidyr::expand_grid(tv_design, time = dose_times) |>
    dplyr::mutate(evid = 1L, amt = dose, dur = 1, cmt = "central"),
  tidyr::expand_grid(tv_design, time = obs_times) |>
    dplyr::mutate(evid = 0L, amt = 0, dur = 0, cmt = "central")
) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  as.data.frame()
mod <- readModelDb("Yang_2021_tigecycline")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_tv <- rxode2::rxSolve(
  mod_typical,
  events = tv_events,
  keep = c("treatment", "dose", "BUN"),
  rtol = 1e-10, atol = 1e-12
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl'
#> Warning: multi-subject simulation without without 'omega'
conc_tv <- sim_tv |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment)
dose_tv <- tv_events |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, treatment)

nca_tv <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(conc_tv, Cc ~ time | treatment + id),
  PKNCA::PKNCAdose(dose_tv, amt ~ time | treatment + id),
  intervals = data.frame(start = 216, end = 240, auclast = TRUE, cmax = TRUE, cmin = TRUE)
))

nca_wide <- as.data.frame(nca_tv) |>
  dplyr::select(treatment, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES) |>
  dplyr::left_join(tv_design, by = "treatment")

# Closed-form identity: AUC0-24 at steady state = 2 * dose / CL. The only
# differences are the trapezoid on a 0.25-h grid and integrator error.
cl_tv <- exp(log(25.2)) * (nca_wide$BUN / 9)^-0.271
auc_closed <- 2 * nca_wide$dose / cl_tv
stopifnot(max(abs(nca_wide$auclast / auc_closed - 1)) < 0.005)
table5 <- tibble::tribble(
  ~dose, ~BUN, ~pub_mic50, ~pub_mic90,
  50,    4.7,  0.8,        0.4,
  50,    8.3,  0.95,       0.45,
  50,    14.5, 1.1,        0.55,
  50,    34.2, 1.4,        0.7,
  100,   4.7,  1.6,        0.8,
  100,   8.3,  1.9,        0.95,
  100,   14.5, 2.2,        1.1,
  100,   34.2, 2.75,       1.4
)

t5 <- nca_wide |>
  dplyr::inner_join(table5, by = c("dose", "BUN")) |>
  dplyr::mutate(
    sim_mic50 = auclast / 4,
    sim_mic90 = auclast / 8,
    pct_mic50 = 100 * (sim_mic50 / pub_mic50 - 1),
    pct_mic90 = 100 * (sim_mic90 / pub_mic90 - 1)
  )
stopifnot(nrow(t5) == 8L)

t5 |>
  dplyr::transmute(
    dose = paste(dose, "mg q12h"), stratum, bun_range, BUN,
    sim_mic50 = round(sim_mic50, 3), pub_mic50, pct_mic50 = round(pct_mic50, 1),
    sim_mic90 = round(sim_mic90, 3), pub_mic90, pct_mic90 = round(pct_mic90, 1)
  ) |>
  dplyr::rename(
    "Maintenance dose" = dose,
    "Renal grade" = stratum,
    "BUN range (mmol/L)" = bun_range,
    "BUN median (mmol/L)" = BUN,
    "AUC/MIC50 model (h)" = sim_mic50,
    "AUC/MIC50 Table 5 (h)" = pub_mic50,
    "MIC50 diff (%)" = pct_mic50,
    "AUC/MIC90 model (h)" = sim_mic90,
    "AUC/MIC90 Table 5 (h)" = pub_mic90,
    "MIC90 diff (%)" = pct_mic90
  ) |>
  knitr::kable(caption = "Steady-state AUC0-24/MIC from the typical-value model against Table 5 of Yang 2021.")
Steady-state AUC0-24/MIC from the typical-value model against Table 5 of Yang 2021.
Maintenance dose Renal grade BUN range (mmol/L) BUN median (mmol/L) AUC/MIC50 model (h) AUC/MIC50 Table 5 (h) MIC50 diff (%) AUC/MIC90 model (h) AUC/MIC90 Table 5 (h) MIC90 diff (%)
100 mg q12h Decompensated 9-20 14.5 2.258 2.20 2.6 1.129 1.10 2.6
100 mg q12h Renal failure 20-48.3 34.2 2.849 2.75 3.6 1.424 1.40 1.7
100 mg q12h Normal 1.8-7.5 4.7 1.664 1.60 4.0 0.832 0.80 4.0
100 mg q12h Compensated 7.5-9 8.3 1.941 1.90 2.2 0.971 0.95 2.2
50 mg q12h Decompensated 9-20 14.5 1.129 1.10 2.6 0.564 0.55 2.6
50 mg q12h Renal failure 20-48.3 34.2 1.424 1.40 1.7 0.712 0.70 1.7
50 mg q12h Normal 1.8-7.5 4.7 0.832 0.80 4.0 0.416 0.40 4.0
50 mg q12h Compensated 7.5-9 8.3 0.971 0.95 2.2 0.485 0.45 7.8 
pct_all <- c(t5$pct_mic50, t5$pct_mic90)
# Deterministic comparison against values printed to two significant
# figures. The largest gap is the 50 mg / BUN 8.3 MIC90 cell: the model gives
# 0.485 h, and the table prints 0.45 h, which is half of its own 0.95 h MIC50
# cell rounded down. A positive exponent (+0.271) would invert the BUN trend
# and miss the outer strata by about 50%.
stopifnot(
  max(abs(pct_all)) < 10,
  abs(median(pct_all)) < 5
)

Fifteen of the 16 cells of Table 5 are reproduced within 5%. The model is slightly above the table throughout, consistent with values rounded down to two digits. The remaining cell (50 mg, BUN 8.3, MIC90) differs by 7.8% because the table prints 0.45 h where half of its own 0.95 h MIC50 cell would be 0.475 h. CL falls as BUN rises, so exposure is highest in renal failure, as in the paper.

The comparison below repeats the check in terms of AUC0-24 itself. The Table 5 MIC50 column is converted back to AUC by multiplying by 4 mg/L.

published_auc <- table5 |>
  dplyr::mutate(
    treatment = sprintf("%g mg q12h, BUN %.1f", dose, BUN),
    auclast = pub_mic50 * 4
  ) |>
  dplyr::select(treatment, auclast)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_tv,
  reference = published_auc,
  by = "treatment",
  params = "auclast",
  units = c(auclast = "mg*h/L"),
  tolerance_pct = 20
)
knitr::kable(cmp, caption = "Simulated vs. published steady-state AUC0-24 (Table 5 MIC50 column x 4 mg/L). * differs from reference by >20%.")
Simulated vs. published steady-state AUC0-24 (Table 5 MIC50 column x 4 mg/L). * differs from reference by >20%.
NCA parameter treatment Reference Simulated % diff
AUClast (mg*h/L) 50 mg q12h, BUN 4.7 3.2 3.33 +4.0%
AUClast (mg*h/L) 50 mg q12h, BUN 8.3 3.8 3.88 +2.2%
AUClast (mg*h/L) 50 mg q12h, BUN 14.5 4.4 4.52 +2.6%
AUClast (mg*h/L) 50 mg q12h, BUN 34.2 5.6 5.7 +1.7%
AUClast (mg*h/L) 100 mg q12h, BUN 4.7 6.4 6.66 +4.0%
AUClast (mg*h/L) 100 mg q12h, BUN 8.3 7.6 7.76 +2.2%
AUClast (mg*h/L) 100 mg q12h, BUN 14.5 8.8 9.03 +2.6%
AUClast (mg*h/L) 100 mg q12h, BUN 34.2 11 11.4 +3.6%

Table 5 is labelled fAUC, but its values equal total (bound plus unbound) dose/CL with no unbound fraction applied. The comparison above therefore uses total AUC.

Observed concentrations by regimen (Figure 1)

Figure 1 of the paper shows the observed mean (+SD) concentrations in each regimen, binned by time after the last dose (< 6 h, 6-8 h, >= 8 h). The bar heights and error bars were digitised by the maintainers from the published figure.

The virtual cohort has 200 patients per regimen, all at steady state, each sampled at the protocol times of 0.5, 1.5, 3, 6, 9 and 12 h after a dose. The paper does not report the BUN distribution. BUN is drawn log-normally with a median of 8.3 mmol/L and a log-SD of 0.78, which puts the 5th and 95th percentiles near 2.3 and 30 mmol/L, then clamped to the observed 1.8-48.3 mmol/L range.

rxode2::rxSetSeed(20210616)
set.seed(20210616)

n_arm <- 200L
regimens <- tibble::tibble(
  regimen = c("100 mg LD + 50 mg q12h", "100 mg q12h", "50 mg q12h"),
  first_dose = c(100, 100, 50),
  maint_dose = c(50, 100, 50)
)

make_arm <- function(k, n, id_offset) {
  reg <- regimens[k, ]
  subj <- tibble::tibble(
    id = id_offset + seq_len(n),
    regimen = reg$regimen,
    BUN = pmin(pmax(stats::rlnorm(n, log(8.3), 0.78), 1.8), 48.3)
  )
  doses <- tidyr::expand_grid(subj, time = dose_times) |>
    dplyr::mutate(
      evid = 1L,
      amt = ifelse(time == 0, reg$first_dose, reg$maint_dose),
      dur = 1, cmt = "central"
    )
  obs <- tidyr::expand_grid(subj, time = 228 + c(0.5, 1.5, 3, 6, 9, 12)) |>
    dplyr::mutate(evid = 0L, amt = 0, dur = 0, cmt = "central")
  dplyr::bind_rows(doses, obs)
}

fig1_events <- dplyr::bind_rows(
  make_arm(1, n_arm, 0L),
  make_arm(2, n_arm, n_arm),
  make_arm(3, n_arm, 2L * n_arm)
) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  as.data.frame()
stopifnot(!anyDuplicated(unique(fig1_events[, c("id", "time", "evid")])))
sim_fig1 <- rxode2::rxSolve(mod, events = fig1_events, keep = c("regimen", "BUN")) |>
  as.data.frame() |>
  dplyr::mutate(
    tad = time - 228,
    bin = dplyr::case_when(tad < 6 ~ "< 6 h", tad < 8 ~ "6-8 h", TRUE ~ ">= 8 h"),
    bin = factor(bin, levels = c("< 6 h", "6-8 h", ">= 8 h"))
  )
#> ℹ parameter labels from comments will be replaced by 'label()'

fig1_obs <- tibble::tribble(
  ~regimen,                 ~bin,     ~obs_mean, ~obs_sd,
  "100 mg LD + 50 mg q12h", "< 6 h",  0.261,     0.230,
  "100 mg LD + 50 mg q12h", "6-8 h",  0.256,     0.304,
  "100 mg LD + 50 mg q12h", ">= 8 h", 0.261,     0.319,
  "100 mg q12h",            "< 6 h",  0.841,     0.636,
  "100 mg q12h",            "6-8 h",  0.299,     0.309,
  "100 mg q12h",            ">= 8 h", 0.355,     0.317,
  "50 mg q12h",             "< 6 h",  0.072,     0.028,
  "50 mg q12h",             "6-8 h",  0.112,     0.084,
  "50 mg q12h",             ">= 8 h", 0.276,     0.240
) |>
  dplyr::mutate(bin = factor(bin, levels = levels(sim_fig1$bin)))

fig1_sim <- sim_fig1 |>
  dplyr::group_by(regimen, bin) |>
  dplyr::summarise(sim_mean = mean(sim), sim_sd = stats::sd(sim), .groups = "drop")

fig1_cmp <- dplyr::inner_join(fig1_obs, fig1_sim, by = c("regimen", "bin"))
stopifnot(nrow(fig1_cmp) == 9L)

fig1_cmp |>
  dplyr::mutate(dplyr::across(c(sim_mean, sim_sd), \(x) round(x, 3))) |>
  dplyr::rename(
    "Regimen" = regimen,
    "Time after dose" = bin,
    "Observed mean (mg/L)" = obs_mean,
    "Observed SD (mg/L)" = obs_sd,
    "Model mean (mg/L)" = sim_mean,
    "Model SD (mg/L)" = sim_sd
  ) |>
  knitr::kable(caption = "Mean (SD) concentration by regimen and time bin: digitised Figure 1 against the model (with between-subject and residual variability).")
Mean (SD) concentration by regimen and time bin: digitised Figure 1 against the model (with between-subject and residual variability).
Regimen Time after dose Observed mean (mg/L) Observed SD (mg/L) Model mean (mg/L) Model SD (mg/L)
100 mg LD + 50 mg q12h < 6 h 0.261 0.230 0.247 0.209
100 mg LD + 50 mg q12h 6-8 h 0.256 0.304 0.214 0.217
100 mg LD + 50 mg q12h >= 8 h 0.261 0.319 0.166 0.183
100 mg q12h < 6 h 0.841 0.636 0.445 0.364
100 mg q12h 6-8 h 0.299 0.309 0.362 0.335
100 mg q12h >= 8 h 0.355 0.317 0.310 0.313
50 mg q12h < 6 h 0.072 0.028 0.212 0.185
50 mg q12h 6-8 h 0.112 0.084 0.184 0.186
50 mg q12h >= 8 h 0.276 0.240 0.155 0.156 
dplyr::bind_rows(
  fig1_cmp |> dplyr::transmute(regimen, bin, source = "Observed (Figure 1)", mean = obs_mean, sd = obs_sd),
  fig1_cmp |> dplyr::transmute(regimen, bin, source = "Model", mean = sim_mean, sd = sim_sd)
) |>
  ggplot(aes(bin, mean, fill = source)) +
  geom_col(position = position_dodge(width = 0.8), width = 0.7) +
  geom_errorbar(aes(ymin = mean, ymax = mean + sd), position = position_dodge(width = 0.8), width = 0.25) +
  facet_wrap(~regimen) +
  labs(
    x = "Time after last dose", y = "Tigecycline concentration (mg/L)", fill = NULL,
    title = "Figure 1: mean + SD concentration by regimen",
    caption = "Replicates Figure 1 of Yang 2021 (observed bars digitised)."
  ) +
  theme(legend.position = "bottom")

The model reproduces the overall concentration level of 0.1-0.4 mg/L and the size of the spread: the model SD is close to its mean in every bin, as the observed SD is. Several bin means differ, however. Most of the gaps come from two features of the observed figure that a one-compartment steady-state model cannot produce:

  • In the 100 mg q12h arm, the < 6 h mean (0.84 mg/L) is nearly twice the model’s (about 0.45 mg/L).
  • Observed means are flat or rising toward the trough in the loading-dose arm (0.26 mg/L in every bin) and in the 50 mg q12h arm (0.07 mg/L at < 6 h, 0.28 mg/L at >= 8 h). Model concentrations fall over the dosing interval, so the model sits above the observed early bins of the 50 mg arm and below the observed >= 8 h bins.

Both bins come from small, unbalanced subsets of patients (14 patients received 50 mg q12h), and the paper’s Discussion notes that the varying sampling times limit what the figure shows. The model was fitted to the individual concentrations, not to these bin means. Figure 1 is therefore shown for context and is not used as a gate.

Variance or standard deviation? The two readings of Table S10

Table S10 prints “eta (CL) 0.587” and “epsilon (prop) 0.576” without saying whether these are standard deviations or NONMEM variances (OMEGA and SIGMA). The maintainers encoded the standard-deviation reading:

  • Reading A (encoded): etalcl variance 0.587^2 = 0.345 (CV about 64%), and propSd = 0.576.
  • Reading B (not encoded): etalcl variance 0.587 (CV about 87%), and propSd = sqrt(0.576) = 0.759.

Two pieces of evidence favour reading A, but neither is decisive:

  • Standard errors. The printed relative standard errors (11.3% and 10.5%) are below the smallest value attainable for a variance estimated from 67 subjects. That floor is about sqrt(2/67) = 17%. For a standard deviation the floor is half that.
  • Observed spread. The within-bin spread of Figure 1, compared below, sits closer to reading A.

The typical-value results above (Table 5, PKNCA) are identical under both readings, because only the stochastic spread differs.

mod_B <- rxode2::ini(mod, etalcl ~ 0.587, propSd = sqrt(0.576))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ change initial estimate of `etalcl` to `0.587`
#> ℹ change initial estimate of `propSd` to `0.758946638440411`

sim_B <- rxode2::rxSolve(mod_B, events = fig1_events, keep = c("regimen", "BUN")) |>
  as.data.frame() |>
  dplyr::mutate(
    tad = time - 228,
    bin = dplyr::case_when(tad < 6 ~ "< 6 h", tad < 8 ~ "6-8 h", TRUE ~ ">= 8 h"),
    bin = factor(bin, levels = levels(sim_fig1$bin))
  )

cv_cells <- function(s, label) {
  s |>
    dplyr::group_by(regimen, bin) |>
    dplyr::summarise(cv = stats::sd(sim) / mean(sim), .groups = "drop") |>
    dplyr::mutate(reading = label)
}

cv_tab <- dplyr::bind_rows(
  fig1_obs |> dplyr::transmute(regimen, bin, cv = obs_sd / obs_mean, reading = "Observed (Figure 1)"),
  cv_cells(sim_fig1, "Reading A (SD, encoded)"),
  cv_cells(sim_B, "Reading B (variance)")
)

cv_tab |>
  dplyr::group_by(reading) |>
  dplyr::summarise(
    `Median CV across the 9 cells (%)` = round(100 * stats::median(cv)),
    `Range (%)` = paste0(round(100 * min(cv)), "-", round(100 * max(cv))),
    .groups = "drop"
  ) |>
  dplyr::rename("Source" = reading) |>
  knitr::kable(caption = "Arithmetic CV of concentrations within each regimen x time bin.")
Arithmetic CV of concentrations within each regimen x time bin.
Source Median CV across the 9 cells (%) Range (%)
Observed (Figure 1) 88 39-122
Reading A (SD, encoded) 101 82-111
Reading B (variance) 148 119-170 
pi_band <- function(s, label) {
  s |>
    dplyr::filter(regimen == "100 mg q12h") |>
    dplyr::group_by(tad) |>
    dplyr::summarise(
      Q05 = stats::quantile(Cc, 0.05), Q50 = stats::quantile(Cc, 0.5), Q95 = stats::quantile(Cc, 0.95),
      .groups = "drop"
    ) |>
    dplyr::mutate(reading = label)
}

dplyr::bind_rows(
  pi_band(sim_fig1, "Reading A (SD, encoded)"),
  pi_band(sim_B, "Reading B (variance)")
) |>
  ggplot(aes(tad, Q50, colour = reading, fill = reading)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, colour = NA) +
  geom_line() +
  geom_point() +
  scale_y_log10() +
  labs(
    x = "Time after dose at steady state (h)", y = "Individual concentration (mg/L)",
    colour = NULL, fill = NULL,
    title = "100 mg q12h: 90% interval of individual predictions under the two readings"
  ) +
  theme(legend.position = "bottom")

The observed per-bin CVs come from small, mixed bins, so this comparison cannot settle the question. The scale of Table S10 cannot be verified from the published material. Users who prefer reading B can apply it with rxode2::ini(mod, etalcl ~ 0.587, propSd = sqrt(0.576)), as above.

Assumptions and deviations

  • Scale of the Table S10 variability terms. Encoded as standard deviations (reading A). The section above gives the reasons and shows the alternative.
  • Infusion duration. The paper does not state it. The simulations use 1 h, within the 30-60 minute infusion of the tigecycline label. AUC0-24 at steady state does not depend on the infusion time.
  • BUN distribution. The paper does not report it. Figure 1 uses an assumed log-normal distribution (median 8.3 mmol/L, close to the 9 mmol/L reference and the Table 5 compensated-stratum median), clamped to 1.8-48.3 mmol/L. The Table 5 check uses the printed stratum medians and does not depend on this assumption.
  • No IIV on V. Table S10 reports between-subject variability on CL only, so V carries no eta.
  • Figure 1 values were digitised by the maintainers from the published raster figure. The digitising resolution is about 0.003 mg/L.
  • Table 5 label. The table is headed fAUC0-24/MIC, but its numbers equal total AUC0-24/MIC (twice the maintenance dose over CL, divided by the MIC), with no unbound fraction applied. The comparison uses total AUC.
  • Reference BUN of 9 mmol/L. This is the normalising value in the printed equation. It matches the upper bound of the paper’s compensated renal-insufficiency grade, and the paper does not say it is the cohort median.
  • Negative simulated observations. A proportional residual error with SD 0.576 gives a small fraction of negative simulated observations (sim). The figure comparisons keep them so that the means and SDs stay unbiased.
  • No erratum or correction notice for this article is linked in Europe PMC (checked 2026-10-16).