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Temocillin (Ngougni Pokem 2022)

Source: vignettes/articles/NgougniPokem_2022_temocillin.Rmd
NgougniPokem_2022_temocillin.Rmd

Model and source

  • Citation: Ngougni Pokem P, Wittebole X, Collienne C, Rodriguez-Villalobos H, Tulkens PM, Elens L, Van Bambeke F, Laterre PF. Population Pharmacokinetics of Temocillin Administered by Continuous Infusion in Patients with Septic Shock Associated with Intra-Abdominal Infection and Ascitic Fluid Effusion. Antibiotics (Basel) 2022;11(7):898. doi:10.3390/antibiotics11070898. Parameter estimates from Table 4; model structure, covariate equation and error model from Supplementary Table S1 (Pmetrics model file).
  • Description: Three-compartment intravenous population PK model for UNBOUND temocillin in plasma and ascitic fluid of critically ill adults with septic shock associated with complicated intra-abdominal infection and ascitic fluid effusion, given a 2 g loading dose over 30 min followed by a continuous infusion of 6 g/24 h. Plasma disposition is two-compartment (central plus one peripheral compartment, parameterised with first-order distribution rate constants); a third compartment with its own volume represents the ascitic fluid, exchanging with the central compartment by first-order rate constants and drained by a non-renal clearance (the abdominal drain). Clearance from the central compartment is proportional to measured urinary creatinine clearance normalised to the cohort median of 39.9 mL/min. Fitted in Pmetrics with the non-parametric adaptive grid (NPAG) algorithm; the discrete joint density is approximated here by independent lognormal marginals centred on the published medians with variances from the published CV%, so the shape of the joint density is not recoverable from this encoding. Residual error is the Pmetrics lambda model on the published assay SD polynomial.
  • Article: https://doi.org/10.3390/antibiotics11070898
  • Supplement (Pmetrics model file, Table S1): https://www.mdpi.com/article/10.3390/antibiotics11070898/s1

The model describes unbound temocillin. The authors measured unbound concentrations directly by ultrafiltration and modelled only those, because temocillin protein binding is saturable and the unbound fraction cannot be computed linearly from total concentration.

Population

Nineteen critically ill adults in septic shock associated with a complicated intra-abdominal infection and ascitic fluid effusion were enrolled in the intensive care unit of the Cliniques universitaires Saint-Luc (Brussels, Belgium). Median age was 56 years (21-74), median weight 67 kg (45-95), and 6 patients (31.6%) were male. Renal function was low: measured urinary creatinine clearance had a median of 39.9 mL/min (20.55-149.3). Plasma albumin was 22.3 g/L (13.7-30.8). Eleven patients had spontaneous bacterial peritonitis (all cirrhotic), four had secondary peritonitis, three had infected pancreatic necrosis and one had a liver abscess (Table 1). Every patient received a 2 g loading dose over 30 min followed by a continuous infusion of 6 g/24 h, and contributed plasma and ascitic fluid samples between 0.5 and 96 h (114 unbound concentrations in total). Ascitic fluid was collected through the abdominal drain.

The same information is available programmatically via readModelDb("NgougniPokem_2022_temocillin")()$population.

Source trace

Equation / parameter Value Source location
lvc (V) log(13.90) L Table 4, V row, median
lcl (CLi) log(2.56) L/h Table 4, CLi row, median
lk12 log(4.62) 1/h Table 4, K12 row, median
lk21 log(5.85) 1/h Table 4, K21 row, median
lk13 log(0.24) 1/h Table 4, K13 row, median
lk31 log(0.15) 1/h Table 4, K31 row, median
lv_ascites (V3) log(28.93) L Table 4, V3 row, median
lcl_ascites (CL30) log(2.94) L/h Table 4, CL30 row, median
etalvc … etalcl_ascites log(CV^2 + 1) Table 4, CV (%) column: 29.15, 37.33, 58.47, 67.20, 110.67, 137.94, 55.87, 48.75
addSd, propSd (plasma) 0.1 mg/L, 0.1 Table S1 #Err, first polynomial row; Results section 2.4
addSd_Cascites, propSd_Cascites 0.1 mg/L, 0.1 Table S1 #Err, second polynomial row
lambdaSd 2.26 mg/L Table S1 #Err, L=2.26; Results section 2.4
cl = CLi * (CRCL / 39.9) n/a Table S1 #Sec, Ke = CLi*(CLCRurinary/39.9)/V; Results section 2.4
k30 = CL30 / V3 n/a Table S1 #Sec, K30 = CL30/V3
d/dt(central), d/dt(peripheral1), d/dt(ascites) n/a Table S1 #Dif, XP(1)-XP(3); Figure 1
Cc = central / vc, Cascites = ascites / v_ascites n/a Table S1 #Out, Y(1) = X(1)/V, Y(2) = X(3)/V3
Error sqrt((C0 + C1*Y)^2 + lambda^2) n/a Table S1 legend; section 4.6.1

Typical-value checks against closed forms

With the random effects removed, a constant infusion at rate R0 has an exact steady state. The ascitic compartment’s drain adds elimination on top of the central clearance:

  • Cc_ss = R0 / (CL + Vc * k13 * k30 / (k31 + k30))
  • Cascites_ss / Cc_ss = k13 * Vc / ((k31 + k30) * V3)
mod <- readModelDb("NgougniPokem_2022_temocillin")
mod_typ <- rxode2::zeroRe(mod)
#> Warning: No sigma parameters in the model

# Event helper: loading dose over 30 min into central, then a continuous
# infusion from 0.5 h. The infusion is split into 24 h records so it can run
# for as long as needed. Observation rows carry dvid = 1 and no cmt: the model
# has two error endpoints (Cc, Cascites), and a forward solve returns both
# columns at every observation time.
make_events <- function(ld_mg, inf_mg_per_day, t_end, obs_times) {
  n_inf <- ceiling((t_end - 0.5) / 24)
  doses <- tibble(
    time = c(0, 0.5 + 24 * (seq_len(n_inf) - 1)),
    amt = c(ld_mg, rep(inf_mg_per_day, n_inf)),
    rate = c(ld_mg / 0.5, rep(inf_mg_per_day / 24, n_inf)),
    evid = 1L, cmt = "central", dvid = NA_integer_
  )
  obs <- tibble(
    time = obs_times, amt = NA_real_, rate = NA_real_,
    evid = 0L, cmt = NA_character_, dvid = 1L
  )
  bind_rows(doses, obs) |> arrange(time, desc(evid))
}

ev_typ <- make_events(2000, 6000, 480, c(0.5, 24, 96, 480)) |>
  mutate(id = 1L, CRCL = 39.9)
sim_typ <- rxode2::rxSolve(mod_typ, events = ev_typ, useLinCmt = FALSE) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk12', 'etalk21', 'etalk13', 'etalk31', 'etalv_ascites', 'etalcl_ascites'

p <- c(vc = 13.90, cl = 2.56, k12 = 4.62, k21 = 5.85, k13 = 0.24,
       k31 = 0.15, v3 = 28.93, cl30 = 2.94)
k30 <- p[["cl30"]] / p[["v3"]]
r0 <- 6000 / 24
cl_drain <- p[["vc"]] * p[["k13"]] * k30 / (p[["k31"]] + k30)
css_cf <- r0 / (p[["cl"]] + cl_drain)
ratio_cf <- p[["k13"]] * p[["vc"]] / ((p[["k31"]] + k30) * p[["v3"]])

ss <- sim_typ[sim_typ$time == 480, ]
check_typ <- tibble(
  Quantity = c("Plasma Cc at steady state (mg/L)",
               "Ascitic / plasma concentration ratio at steady state",
               "Effective drain clearance from central (L/h)"),
  `Closed form` = c(css_cf, ratio_cf, cl_drain),
  `Simulated (480 h)` = c(ss$Cc, ss$Cascites / ss$Cc, NA)
)
knitr::kable(check_typ, digits = 3)
Quantity Closed form Simulated (480 h)
Plasma Cc at steady state (mg/L) 63.982 63.982
Ascitic / plasma concentration ratio at steady state 0.458 0.458
Effective drain clearance from central (L/h) 1.347 NA 

# Same parameters on both sides, so the difference is numerical error only.
stopifnot(
  abs(ss$Cc / css_cf - 1) < 1e-3,
  abs((ss$Cascites / ss$Cc) / ratio_cf - 1) < 1e-3
)

For a typical patient at the cohort median CRCL, the drain adds 1.35 L/h to the 2.56 L/h central clearance. The steady-state unbound plasma concentration is 64 mg/L. The ascitic/plasma unbound concentration ratio of 0.46 matches the paper’s reported ascitic fluid penetration (AUC ratio) of 46.0% (Results section 2.3). Because the unbound fractions in plasma (56.4%) and ascitic fluid (57.4%) were nearly equal, the total and unbound ratios coincide.

Virtual cohort

The observed data are not public. The virtual cohort draws measured urinary creatinine clearance from a log-normal distribution with median 39.9 mL/min, truncated to the observed range 20.55-149.3 mL/min (Table 1). The log-scale SD of 0.75 is an assumption chosen to give the right-skewed shape the paper describes. The Discussion reports a cohort mean of 58.1 +/- 37.4 mL/min.

set.seed(2022)
draw_crcl <- function(n) {
  x <- numeric(0)
  while (length(x) < n) {
    y <- exp(rnorm(2 * n, log(39.9), 0.75))
    x <- c(x, y[y >= 20.55 & y <= 149.3])
  }
  x[seq_len(n)]
}

n_vpc <- 200
grid <- c(seq(0, 12, by = 0.5), seq(13, 96, by = 1))
ev1 <- make_events(2000, 6000, 96, grid)
cohort <- tibble(id = seq_len(n_vpc), CRCL = draw_crcl(n_vpc))
events_vpc <- tidyr::crossing(cohort, ev1) |>
  mutate(regimen = "2 g LD + 6 g/24 h") |>
  arrange(id, time, desc(evid))

summary(cohort$CRCL)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   20.94   33.72   51.15   57.82   77.81  142.88

Simulation 

rxode2::rxSetSeed(2022)
sim <- rxode2::rxSolve(
  mod, events = events_vpc, keep = c("regimen", "CRCL"),
  useLinCmt = FALSE
) |> as.data.frame()

Figure 3: visual predictive check 

# Replicates Figure 3 of Ngougni Pokem 2022: unbound plasma (a) and ascitic
# fluid (b) after 2 g over 30 min then 6 g/24 h, 5th/50th/95th percentiles.
vpc <- sim |>
  select(id, time, Cc, Cascites) |>
  pivot_longer(c(Cc, Cascites), names_to = "matrix", values_to = "conc") |>
  mutate(matrix = recode(matrix,
                         Cc = "(a) Plasma, unbound",
                         Cascites = "(b) Ascitic fluid, unbound")) |>
  group_by(matrix, time) |>
  summarise(
    Q05 = quantile(conc, 0.05), Q50 = quantile(conc, 0.50),
    Q95 = quantile(conc, 0.95), .groups = "drop"
  )

ggplot(vpc, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~matrix, ncol = 1, scales = "free_y") +
  labs(x = "Time (h)", y = "Unbound temocillin (mg/L)",
       title = "Simulated 5th, 50th and 95th percentiles",
       caption = "Replicates Figure 3 of Ngougni Pokem 2022.")

The paper’s Figure 3 VPC simulates each enrolled patient’s own covariates and sampling times. From 24 to 96 h its plasma median runs between about 35 and 75 mg/L, and its ascitic-fluid median between about 17 and 35 mg/L. The simulated medians here (about 45 and 18 mg/L) fall inside those bands. The simulated 5th percentiles stay near 20 mg/L (plasma) and 4 mg/L (ascitic fluid). The paper’s 5th percentiles approach zero. The approximation of the non-parametric density by log-normal marginals changes the tails more than the centre (see Assumptions and deviations).

Early concentrations 

early <- sim |>
  filter(time == 0.5) |>
  summarise(
    plasma_median = median(Cc), plasma_min = min(Cc), plasma_max = max(Cc),
    ascites_median = median(Cascites), ascites_min = min(Cascites),
    ascites_max = max(Cascites)
  )
tibble(
  Matrix = c("Plasma, unbound", "Ascitic fluid, unbound"),
  `Observed median (range), 30 min after LD` = c("85.9 (35.9-125.5)", "3.0 (1.0-15.7)"),
  `Simulated median (range)` = c(
    sprintf("%.1f (%.1f-%.1f)", early$plasma_median, early$plasma_min, early$plasma_max),
    sprintf("%.1f (%.1f-%.1f)", early$ascites_median, early$ascites_min, early$ascites_max)
  )
) |>
  knitr::kable(caption = "Observed values from Results section 2.3.")
Observed values from Results section 2.3.
Matrix Observed median (range), 30 min after LD Simulated median (range)
Plasma, unbound 85.9 (35.9-125.5) 79.7 (23.9-161.3)
Ascitic fluid, unbound 3.0 (1.0-15.7) 2.5 (0.3-25.6) 

stopifnot(
  # Structural: the end-of-loading-dose plasma level is set by the dose and
  # Vc/k12; a mis-transcribed volume or dose shifts it by tens of percent.
  abs(early$plasma_median / 85.9 - 1) < 0.25
)

PKNCA validation

The paper reports no formal NCA table. The Discussion gives the mean steady-state unbound plasma concentration observed in this cohort (61.8 +/- 25.7 mg/L), and Results section 2.3 gives the ascitic/plasma AUC ratio (46.0%). PKNCA computes the average concentration over 72-96 h for each matrix and the 0-96 h AUC used for the ratio.

doses <- events_vpc |>
  filter(evid == 1) |>
  select(id, time, amt, regimen)
dose_obj <- PKNCA::PKNCAdose(doses, amt ~ time | regimen + id)

intervals <- data.frame(
  start = c(0, 72), end = c(96, 96),
  auclast = c(TRUE, FALSE), cav = c(FALSE, TRUE)
)

# Plasma
conc_pl <- sim |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, regimen)
nca_pl <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(conc_pl, Cc ~ time | regimen + id),
  dose_obj, intervals = intervals
))

# Ascitic fluid
conc_as <- sim |>
  filter(!is.na(Cascites)) |>
  select(id, time, Cascites, regimen)
nca_as <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(conc_as, Cascites ~ time | regimen + id),
  dose_obj, intervals = intervals
))

# The published 61.8 mg/L is a cohort MEAN, so compare it with the mean of the
# per-subject simulated values (ncaComparisonTable() would otherwise take the
# median, which for this right-skewed exposure sits well below the mean).
cav_mean <- as.data.frame(nca_pl) |>
  filter(PPTESTCD == "cav", start == 72) |>
  group_by(regimen) |>
  summarise(cav = mean(PPORRES), .groups = "drop")
published <- tibble(regimen = "2 g LD + 6 g/24 h", cav = 61.8)
cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = cav_mean,
  reference = published,
  by = "regimen",
  units = c(cav = "mg/L"),
  tolerance_pct = 20
)
knitr::kable(cmp, caption = paste(
  "Unbound plasma average concentration, 72-96 h: observed cohort mean",
  "(Discussion) vs. mean of the virtual cohort.",
  "* differs from reference by >20%."
))
Unbound plasma average concentration, 72-96 h: observed cohort mean (Discussion) vs. mean of the virtual cohort. * differs from reference by >20%.
NCA parameter regimen Reference Simulated % diff
Cavg (mg/L) 2 g LD + 6 g/24 h 61.8 56.4 -8.7% 

# Ascitic / plasma AUC0-96 ratio, per virtual patient.
auc_ratio <- as.data.frame(nca_pl) |>
  filter(PPTESTCD == "auclast", start == 0) |>
  select(id, auc_pl = PPORRES) |>
  inner_join(
    as.data.frame(nca_as) |>
      filter(PPTESTCD == "auclast", start == 0) |>
      select(id, auc_as = PPORRES),
    by = "id"
  ) |>
  mutate(ratio = auc_as / auc_pl)

# The same ratio for the typical patient (no random effects, CRCL 39.9).
ev_typ96 <- make_events(2000, 6000, 96, grid) |>
  mutate(id = 1L, CRCL = 39.9, regimen = "2 g LD + 6 g/24 h")
sim_typ96 <- rxode2::rxSolve(mod_typ, events = ev_typ96, keep = "regimen",
                             useLinCmt = FALSE) |>
  as.data.frame() |>
  mutate(id = 1L) # a single-subject solve returns no id column
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk12', 'etalk21', 'etalk13', 'etalk31', 'etalv_ascites', 'etalcl_ascites'
dose_typ <- PKNCA::PKNCAdose(
  ev_typ96 |> filter(evid == 1) |> select(id, time, amt, regimen),
  amt ~ time | regimen + id
)
int_typ <- data.frame(start = 0, end = 96, auclast = TRUE)
auc_typ_pl <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(sim_typ96 |> select(id, time, Cc, regimen),
                   Cc ~ time | regimen + id),
  dose_typ, intervals = int_typ
)) |> as.data.frame() |> pull(PPORRES)
auc_typ_as <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(sim_typ96 |> select(id, time, Cascites, regimen),
                   Cascites ~ time | regimen + id),
  dose_typ, intervals = int_typ
)) |> as.data.frame() |> pull(PPORRES)
ratio_typ <- auc_typ_as / auc_typ_pl

tibble(
  Quantity = c("Typical patient (CRCL 39.9 mL/min)",
               "Virtual cohort, median (5th-95th percentile)"),
  `Published median (range)` = "46.0 (30.0-61.6)",
  `Simulated ascitic / plasma AUC0-96 (%)` = c(
    sprintf("%.1f", 100 * ratio_typ),
    sprintf("%.1f (%.1f-%.1f)", 100 * median(auc_ratio$ratio),
            100 * quantile(auc_ratio$ratio, 0.05),
            100 * quantile(auc_ratio$ratio, 0.95))
  )
) |> knitr::kable()
Quantity Published median (range) Simulated ascitic / plasma AUC0-96 (%)
Typical patient (CRCL 39.9 mL/min) 46.0 (30.0-61.6) 43.9
Virtual cohort, median (5th-95th percentile) 46.0 (30.0-61.6) 36.2 (5.5-202.4) 

stopifnot(
  # Centre of the cohort: a mis-transcribed CL, V or covariate reference
  # moves the mean exposure by tens of percent.
  abs(cav_mean$cav / 61.8 - 1) < 0.25,
  # Deterministic typical-value ratio (no cohort draw involved).
  abs(ratio_typ - 0.46) < 0.05
)

For the typical patient the 0-96 h AUC ratio is slightly below the steady-state concentration ratio of the closed-form check above. That is expected: the ascitic compartment takes several hours to fill, and the paper reports that peak ascitic concentrations were reached between 12 and 96 h. The virtual cohort’s median ratio is lower and its spread much wider than the observed 30-62% range. Large CVs on K13 (111%) and K31 (138%) make individual penetration very variable under independent log-normal marginals. That is the same limitation discussed for the PTA below.

Probability of target attainment (Tables 5 and 6)

The paper simulated three regimens and six CRCL values and reported the probability that unbound concentrations stay above the MIC for the whole window (100% fT > MIC). Plasma was evaluated from 0 to 96 h (here from the end of the loading infusion, 0.5 h, because concentrations are zero at time 0). Ascitic fluid was evaluated from 24 to 96 h. Each regimen-by-CRCL arm below has 200 virtual patients.

regimens <- tibble(
  regimen = c("(1) 2 g LD + 6 g/24 h", "(2) 4 g LD + 6 g/24 h",
              "(3) 2 g LD + 8 g/24 h"),
  ld = c(2000, 4000, 2000),
  inf = c(6000, 6000, 8000)
)
crcl_values <- c(20, 39.9, 60, 90, 120, 150)
pta_grid <- c(0.5, seq(1, 96, by = 1))
n_arm <- 200

arms <- tidyr::crossing(regimens, CRCL = crcl_values) |>
  mutate(arm = row_number())
events_pta <- lapply(seq_len(nrow(arms)), function(i) {
  tidyr::crossing(
    id = (arms$arm[i] - 1L) * n_arm + seq_len(n_arm),
    make_events(arms$ld[i], arms$inf[i], 96, pta_grid)
  ) |>
    mutate(regimen = arms$regimen[i], CRCL = arms$CRCL[i])
}) |>
  bind_rows() |>
  arrange(id, time, desc(evid))
stopifnot(!anyDuplicated(unique(events_pta[, c("id", "time", "evid")])))

rxode2::rxSetSeed(898)
sim_pta <- rxode2::rxSolve(
  mod, events = events_pta, keep = c("regimen", "CRCL"),
  useLinCmt = FALSE
) |> as.data.frame()

pta <- sim_pta |>
  group_by(regimen, CRCL, id) |>
  summarise(
    min_pl = min(Cc[time >= 0.5]),
    min_as = min(Cascites[time >= 24]),
    .groups = "drop"
  ) |>
  group_by(regimen, CRCL) |>
  summarise(
    plasma_8 = 100 * mean(min_pl > 8), plasma_16 = 100 * mean(min_pl > 16),
    ascites_8 = 100 * mean(min_as > 8), ascites_16 = 100 * mean(min_as > 16),
    .groups = "drop"
  )

published_pta <- tibble(
  regimen = rep(regimens$regimen, each = 6),
  CRCL = rep(crcl_values, 3),
  pub_plasma_8 = 100,
  pub_plasma_16 = c(98, 98, 98, 98, 98, 90, 99, 99, 99, 99, 99, 94,
                    98, 98, 98, 98, 98, 98),
  pub_ascites_8 = c(98, 97, 96, 96, 87, 73, 98, 97, 98, 96, 87, 73,
                    99, 99, 98, 98, 94, 90),
  pub_ascites_16 = c(93, 88, 76, 51, 32, 22, 95, 91, 80, 54, 33, 22,
                     96, 94, 90, 75, 56, 40)
)
pta_cmp <- inner_join(pta, published_pta, by = c("regimen", "CRCL"))

pta_cmp |>
  transmute(
    regimen, CRCL,
    plasma_16 = sprintf("%.0f (%.0f)", plasma_16, pub_plasma_16),
    ascites_8 = sprintf("%.0f (%.0f)", ascites_8, pub_ascites_8),
    ascites_16 = sprintf("%.0f (%.0f)", ascites_16, pub_ascites_16)
  ) |>
  dplyr::rename(
    "Regimen" = regimen,
    "CRCL (mL/min)" = CRCL,
    "Plasma, MIC 16" = plasma_16,
    "Ascitic fluid, MIC 8" = ascites_8,
    "Ascitic fluid, MIC 16" = ascites_16
  ) |>
  knitr::kable(caption = paste(
    "Simulated PTA (%) with the published value from Tables 5 and 6 in",
    "parentheses. Plasma PTA at MIC 8 mg/L is 100% in every published cell."
  ))
Simulated PTA (%) with the published value from Tables 5 and 6 in parentheses. Plasma PTA at MIC 8 mg/L is 100% in every published cell.
Regimen CRCL (mL/min) Plasma, MIC 16 Ascitic fluid, MIC 8 Ascitic fluid, MIC 16
(1) 2 g LD + 6 g/24 h 20.0 100 (98) 94 (98) 86 (93)
(1) 2 g LD + 6 g/24 h 39.9 96 (98) 84 (97) 63 (88)
(1) 2 g LD + 6 g/24 h 60.0 98 (98) 78 (96) 52 (76)
(1) 2 g LD + 6 g/24 h 90.0 94 (98) 74 (96) 43 (51)
(1) 2 g LD + 6 g/24 h 120.0 87 (98) 65 (87) 35 (32)
(1) 2 g LD + 6 g/24 h 150.0 79 (90) 52 (73) 26 (22)
(2) 4 g LD + 6 g/24 h 20.0 98 (99) 94 (98) 85 (95)
(2) 4 g LD + 6 g/24 h 39.9 99 (99) 88 (97) 67 (91)
(2) 4 g LD + 6 g/24 h 60.0 98 (99) 82 (98) 54 (80)
(2) 4 g LD + 6 g/24 h 90.0 96 (99) 64 (96) 38 (54)
(2) 4 g LD + 6 g/24 h 120.0 92 (99) 64 (87) 41 (33)
(2) 4 g LD + 6 g/24 h 150.0 82 (94) 59 (73) 27 (22)
(3) 2 g LD + 8 g/24 h 20.0 100 (98) 95 (99) 84 (96)
(3) 2 g LD + 8 g/24 h 39.9 98 (98) 94 (99) 80 (94)
(3) 2 g LD + 8 g/24 h 60.0 98 (98) 86 (98) 64 (90)
(3) 2 g LD + 8 g/24 h 90.0 98 (98) 82 (98) 56 (75)
(3) 2 g LD + 8 g/24 h 120.0 97 (98) 72 (94) 44 (56)
(3) 2 g LD + 8 g/24 h 150.0 92 (98) 60 (90) 40 (40) 
# Replicates the CRCL dependence of Supplementary Figure S8 / Tables 5-6 at
# MIC 16 mg/L in ascitic fluid.
pta_cmp |>
  select(regimen, CRCL, Simulated = ascites_16, Published = pub_ascites_16) |>
  pivot_longer(c(Simulated, Published), names_to = "source", values_to = "PTA") |>
  ggplot(aes(CRCL, PTA, colour = regimen, linetype = source)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 90, linetype = "dotted") +
  labs(x = "Measured urinary CRCL (mL/min)", y = "PTA (%)",
       title = "Ascitic fluid, 100% fT > 16 mg/L, 24-96 h",
       caption = "Replicates Table 6 and Figure S8b of Ngougni Pokem 2022.")

r1 <- pta_cmp |> filter(regimen == regimens$regimen[1])
stopifnot(
  # Plasma, MIC 8: the paper reports 100% everywhere.
  min(pta_cmp$plasma_8) > 90,
  # Ascitic fluid, MIC 16, regimen (1): the paper's PTA falls by 71 points
  # from CRCL 20 to 150 mL/min; renal function is the dominant driver.
  r1$ascites_16[r1$CRCL == 20] - r1$ascites_16[r1$CRCL == 150] > 30,
  # Envelope against Table 6 (known deviation; see below).
  median(abs(pta_cmp$ascites_16 - pta_cmp$pub_ascites_16)) < 25
)

In plasma, the simulated PTA matches Table 5 up to a CRCL of about 90 mL/min. At 120-150 mL/min and MIC 16 mg/L it falls 5-15 points below the published 90-98%. In ascitic fluid, the simulated PTA falls with CRCL as Table 6 does, but in most cells it runs 5-25 points below the published values. The exception is MIC 16 mg/L at 120-150 mL/min, where simulated and published PTA are both low and close together. The simulated MIC 16 curve is therefore flatter than the published one. This is the expected signature of replacing the NPAG non-parametric joint density with independent log-normal marginals. With CVs of 111% and 138% on K13 and K31, the log-normal puts more patients in the low-penetration tail than the discrete support points do. The published PTA could not be reproduced from the Table 4 summary statistics with either the mean or the median column (see below). It is recorded as a known deviation.

Assumptions and deviations

  • Median vs. mean column of Table 4. Pmetrics summarises each NPAG marginal by its mean, SD, CV% and median. The mean and median differ almost two-fold for K13 (0.42 vs 0.24 1/h) and K31 (0.33 vs 0.15 1/h). The maintainers encoded the medians, which are the centre of a log-normal marginal. Re-simulating Tables 5 and 6 (1000 virtual patients per arm, log-normal marginals with omega^2 = log(CV^2 + 1)) did not discriminate. The mean absolute difference from Table 6 was 15.1 / 11.9 points (MIC 8 / 16) with the means and 16.0 / 12.3 with the medians. The paper’s text quotes neither column. Both columns give the same steady-state ascitic/plasma ratio (0.47 with the means, 0.46 with the medians).
  • Between-subject variability. The non-parametric joint density is approximated by independent log-normal marginals whose CV equals the Table 4 CV%. No parameter correlations were published. Shrinkage was small (0.01-6.7%, Table 4).
  • Error model. Table S1 gives the Pmetrics lambda model with the assay SD polynomial SD = 0.1 + 0.1*Y for both outputs and lambda = 2.26. The printed formula reads Error = (SD + L^2)^0.5. The maintainers read it as the Pmetrics additive lambda model, (SD^2 + lambda^2)^0.5, with the exponent on SD lost in typesetting. Pmetrics evaluates the polynomial at the observed concentration; this encoding evaluates it at the prediction, as is needed for simulation.
  • Covariate model. The central clearance is proportional to measured urinary creatinine clearance through the origin, exactly as in Table S1 (Ke = CLi*(CLCRurinary/39.9)/V). This differs from the base-model regression in Figure S5 (individual CL = 1.22 + 0.06 x CLCR), which has an intercept. The model therefore has no non-renal central clearance, and it should not be used for patients with CRCL near zero. The CRCL column must be a raw measured (urine-collection) creatinine clearance in mL/min, not a BSA-normalised or Cockcroft-Gault estimate.
  • Sex on CL30. Table 4 footnote b reports a post-hoc difference in individual CL30 between females (3.04 L/h) and males (1.38 L/h). This was not part of the population model and is not encoded (it is listed in covariatesDataExcluded).
  • Ascitic fluid compartment. The compartment is named ascites and declared as a paper-specific compartment. Its specimen is recorded as tissue because the specimen vocabulary has no ascitic or peritoneal fluid entry.
  • Virtual cohort. The CRCL distribution (log-normal, median 39.9 mL/min, log-SD 0.75, truncated to 20.55-149.3 mL/min) is an assumption that matches the reported median and range. The PTA tables use fixed CRCL values, as in the paper.
  • Errata. No correction notice linked to this article was found in Europe PMC as of 2026-10-03.