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Ceftaroline in critically ill adults with and without CRRT (Adamiszak 2025)

Source: vignettes/articles/Adamiszak_2025_ceftaroline.Rmd
Adamiszak_2025_ceftaroline.Rmd

Model and source

  • Citation: Adamiszak A, Pietrzkiewicz K, Bartkowska-Sniatkowska A, Smuszkiewicz P, Kusza K, Grzeskowiak E, Bienert A (2025). Do Critically Ill Patients Undergoing Continuous Renal Replacement Therapy Require Ceftaroline Dosage Adjustments? Ceftaroline PopPK Model and Dosage Simulations with the Probability of Target Attainment Analysis Based on Retrospective Data. Antibiotics 14(4):347. doi:10.3390/antibiotics14040347.
  • Description: Five-compartment population PK model for ceftaroline in critically ill adults with and without continuous renal replacement therapy (CRRT): a two-compartment patient model (first-order elimination from the central, pre-filter compartment) joined to three CRRT-machine compartments (filter, post-filter return limb and effluent) whose transfer rate constants are circuit flow divided by compartment volume, all gated on by a time-varying CRRT-running indicator. Creatinine clearance (power model centred at 159 mL/min/1.73 m^2) on clearance; CRRT modality (CVVHD, CVVHDF) on the central volume; any CRRT on the peripheral volume and intercompartmental clearance. Between-occasion variability on clearance, between-subject variability on the central and peripheral volumes and intercompartmental clearance, and proportional residual error for each of the three sampled matrices (systemic pre-filter plasma, post-filter plasma, effluent).
  • Article: https://doi.org/10.3390/antibiotics14040347
  • Supplement (final-model mlxtran syntax, Table S1): https://www.mdpi.com/article/10.3390/antibiotics14040347/s1
  • Authors’ Simulx 2024R1 project and PTA workbooks: https://github.com/arkadiusz-adamiszak/Ceftaroline_ICU_Retrospective 
mod <- readModelDb("Adamiszak_2025_ceftaroline")
ui <- rxode2::rxode(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2
#> as a work-around try putting the mu-referenced expression on a simple line
mod_typ <- rxode2::zeroRe(ui)
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2
#> as a work-around try putting the mu-referenced expression on a simple line
th <- ui$theta

The model joins a two-compartment patient model to three compartments that stand for the CRRT machine, following the cefepime structure of Al-Shaer et al. that the paper cites (Figure 1). Blood leaves the patient’s central (pre-filter) compartment at the blood flow rate Qb into the filter (circuit_plasma, volume VCRRT). From the filter, drug passes at Qb into the post-filter return limb (circuit_postfilter), which returns it to the patient at Qb, and at the effluent flow rate Qeff into the effluent compartment (circuit_dialysate), which washes out at Qeff. Every transfer rate constant is flow / volume (Methods 4.2). All circuit terms are multiplied by the time-varying indicator RRT_CRRT_ACTIVE (the mlxtran regressor IS_CRRT), so a patient whose CRRT is stopped reverts to the two-compartment model.

The paper’s Figure 1 calls the last compartment “Effluent”. It is carried here as circuit_dialysate, not circuit_effluent, because drug flows through it and out at Qeff; circuit_effluent is the accumulating waste bag, from which nothing leaves. Its concentration is the effluent assay (Ceffluent).

Population

Adamiszak 2025 pooled concentrations from four published studies of critically ill adults receiving 400-600 mg of ceftaroline fosamil every 8-12 h as a 1 h infusion (Alarcia-Lacalle 2021, Chauzy 2019, Chauzy 2022, Kalaria 2021). The concentrations were digitised from those papers’ figures with WebPlotDigitizer 4.7: 296 plasma concentrations from 29 patients not on CRRT, and 24 pre-filter (systemic), 23 post-filter and 23 effluent concentrations from 4 patients on CRRT. Table 1 gives the 33 patients as 36% female, median age 51 years (range 21-77), median weight 75.5 kg (49-111.8) and median MDRD creatinine clearance 159 mL/min/1.73 m^2 (42-309). Of the four CRRT patients two were on CVVHD and two on CVVHDF, with blood flow 250 [250-300] mL/min and effluent flow 3200 [2700-3660] mL/h.

The same information is available programmatically via readModelDb("Adamiszak_2025_ceftaroline")()$population.

Source trace

Every ini() value carries an in-file comment naming its source. Table 2 of the article is mis-rendered in the HTML version; the values below were read from the PDF layout.

Equation / parameter Value Source location
ODE system, outputs, dosing into Acent – Supplement, “Monolix model syntax”; identical to ModelFile/Syntax_v2_SameClbody+IS_CRRT+Q.txt in the authors’ Simulx project
Transfer rate constant k = flow / V – Methods 4.2 equation
Continuous covariate (COV / median COV)^theta – Methods 4.2 equation; median 159 from Table 1 (Simulx logtClCr_Pros = log(ClCr_Pros/159))
Categorical covariate exp(theta) – Methods 4.2 equation
Modality on VCentral, any-CRRT on VPeripheral and Q, no-CRRT reference – Results 2.2; Simulx covariate definitions tCRRT_NaRef_CVVHD_CVVHDF, tCRRT_NaRef_CRRT
lcl (Cl) 11.23 L/h Table 2, Final Model
e_crcl_cl 0.68 Table 2
lvc (VCentral) 20.04 L Table 2
e_cvvhd_vc, e_cvvhdf_vc 0.47, -0.42 Table 2
lq (Q), e_crrt_q 8.80 L/h, 0.99 Table 2
lvp (VPeripheral), e_crrt_vp 16.85 L, 0.99 Table 2
lvfilter (VCRRT) 2.69 L Table 2
lvpostfilter (VPost-filter) 1.15 L Table 2
lvdialysate (VEffluent) 0.60 L Table 2
etaiov_cl_1, etaiov_cl_2 IOV 34.96% CV Table 2
etalvc, etalq, etalvp IIV 3.70, 16.40, 38.60% CV Table 2
propSd, propSd_Cpostfilter, propSd_Ceffluent 0.29, 0.16, 0.13 Table 2 (bPre, bPost, bEff)
Free fraction 0.8 for PTA – Methods 4.3 (~20% protein binding); Simulx FreeCcent = 0.8*Ccent

Simulation helpers

Dose rows go into the central state; observation rows carry dvid = 1 and no compartment, so all three outputs (Cc, Cpostfilter, Ceffluent) are returned at every observation time. The CRRT flows are supplied in the units the covariate register uses, blood flow in mL/min and effluent flow in mL/h.

# One subject's dosing + observation records. crrt is one of "none", "CVVHD",
# "CVVHDF"; qeff_lh is the effluent flow in L/h, converted to mL/h on the
# record.
make_events <- function(dose, tau, tinf, ndose, obs_times, crcl, crrt = "none",
                        qeff_lh = 0, bfr = 250) {
  doses <- data.frame(
    time = (seq_len(ndose) - 1) * tau, amt = dose, rate = dose / tinf,
    evid = 1L, cmt = "central", dvid = NA_integer_
  )
  obs <- data.frame(
    time = obs_times, amt = NA_real_, rate = NA_real_,
    evid = 0L, cmt = NA_character_, dvid = 1L
  )
  ev <- rbind(doses, obs)
  ev <- ev[order(ev$time, -ev$evid), ]
  on <- as.numeric(crrt != "none")
  ev$CRCL <- crcl
  ev$RRT_CVVHD_STATUS <- as.numeric(crrt == "CVVHD")
  ev$RRT_CVVHDF_STATUS <- as.numeric(crrt == "CVVHDF")
  ev$RRT_CRRT_ACTIVE <- on
  ev$BFR <- bfr * on
  ev$RRT_CRRT_EFFLUENT_FLOW <- qeff_lh * 1000 * on
  ev$OCC <- 1L
  ev
}

replicate_ids <- function(ev, n) {
  out <- ev[rep(seq_len(nrow(ev)), times = n), ]
  out$id <- rep(seq_len(n), each = nrow(ev))
  out
}

# The authors' Simulx target-attainment rule, reproduced exactly below: the
# free concentration is sampled hourly from 0 to 120 h, and the target counts
# as attained when at least 100 of the 120 one-hour intervals have BOTH
# endpoints at or above the MIC.
attained <- function(conc, mic) {
  above <- conc >= mic
  sum(above[-1] & above[-length(above)]) >= 100
}

pta_by_mic <- function(sim, mics) {
  free <- split(0.8 * sim$Cc, sim$id)
  vapply(mics, function(m) mean(vapply(free, attained, logical(1), mic = m)), numeric(1))
}

Typical-value checks against the paper’s own numbers

The Results and Discussion quote several derived quantities. Each is recomputed from the packaged parameters.

cl_at <- function(crcl) exp(th[["lcl"]]) * (crcl / 159)^th[["e_crcl_cl"]]
anchors <- tibble::tribble(
  ~quantity, ~paper, ~model,
  "Cl, non-CRRT median patient (L/h), Discussion", 11.2, cl_at(159),
  "Cl, CRRT simulation patient CrCL 58 (L/h), Discussion", 5.66, cl_at(58),
  "Cl at CrCL 309 vs 159 (ratio), Results: +57%", 1.57, cl_at(309) / cl_at(159),
  "VCentral on CVVHD vs no CRRT (ratio), Results: +60%", 1.60, exp(th[["e_cvvhd_vc"]]),
  "VPeripheral and Q on CRRT vs no CRRT (ratio)", 2.69, exp(th[["e_crrt_vp"]])
)
anchors |>
  mutate(model = signif(model, 4), pct_diff = round(100 * (model / paper - 1), 2)) |>
  knitr::kable()
quantity paper model pct_diff
Cl, non-CRRT median patient (L/h), Discussion 11.20 11.230 0.27
Cl, CRRT simulation patient CrCL 58 (L/h), Discussion 5.66 5.657 -0.05
Cl at CrCL 309 vs 159 (ratio), Results: +57% 1.57 1.571 0.06
VCentral on CVVHD vs no CRRT (ratio), Results: +60% 1.60 1.600 0.00
VPeripheral and Q on CRRT vs no CRRT (ratio) 2.69 2.691 0.04 
stopifnot(all(abs(anchors$model / anchors$paper - 1) < 0.005))

All five agree to the precision printed. The decisive one is the CRRT patient’s 5.66 L/h: it fixes the clearance, the exponent and the centring value 159 simultaneously, and the centring value is never stated in the text.

Circuit clearance at steady state

Because every circuit transfer is linear, at steady state the filter concentration is Qb / (Qb + Qeff) times the systemic concentration and the effluent removes drug at Qeff times that. The total clearance seen by the systemic compartment is therefore Cl + Qb * Qeff / (Qb + Qeff), which must equal dose / AUC over a dosing interval. The solve below checks that identity for a typical patient off CRRT and on each modality.

qb_lh <- 250 * 60 / 1000
ss_cases <- tibble::tribble(
  ~case, ~crcl, ~crrt, ~qeff,
  "No CRRT, CrCL 159", 159, "none", 0,
  "CVVHD, CrCL 58, Qeff 2.5 L/h", 58, "CVVHD", 2.5,
  "CVVHDF, CrCL 58, Qeff 4.0 L/h", 58, "CVVHDF", 4.0
)
ss_rows <- lapply(seq_len(nrow(ss_cases)), function(i) {
  ev <- make_events(600, 12, 1, 20, seq(216, 228, by = 0.02),
    crcl = ss_cases$crcl[i], crrt = ss_cases$crrt[i], qeff_lh = ss_cases$qeff[i]
  )
  s <- as.data.frame(rxode2::rxSolve(mod_typ, ev, returnType = "data.frame"))
  auc <- sum(diff(s$time) * (head(s$Cc, -1) + tail(s$Cc, -1)) / 2)
  expected <- cl_at(ss_cases$crcl[i]) +
    if (ss_cases$qeff[i] > 0) qb_lh * ss_cases$qeff[i] / (qb_lh + ss_cases$qeff[i]) else 0
  data.frame(case = ss_cases$case[i], dose_over_auc = 600 / auc, expected = expected)
})
#> ℹ omega/sigma items treated as zero: 'etaiov_cl_1', 'etaiov_cl_2', 'etalvc', 'etalq', 'etalvp'
#> ℹ omega/sigma items treated as zero: 'etaiov_cl_1', 'etaiov_cl_2', 'etalvc', 'etalq', 'etalvp'
#> ℹ omega/sigma items treated as zero: 'etaiov_cl_1', 'etaiov_cl_2', 'etalvc', 'etalq', 'etalvp'
ss_tab <- bind_rows(ss_rows) |> mutate(pct_diff = 100 * (dose_over_auc / expected - 1))
ss_tab |> mutate(across(where(is.numeric), \(x) signif(x, 4))) |> knitr::kable()
case dose_over_auc expected pct_diff
No CRRT, CrCL 159 11.230 11.230 -1.23e-05
CVVHD, CrCL 58, Qeff 2.5 L/h 7.800 7.800 -1.10e-06
CVVHDF, CrCL 58, Qeff 4.0 L/h 8.815 8.815 -4.30e-06 
stopifnot(all(abs(ss_tab$pct_diff) < 0.5))

The Discussion describes total clearance on CRRT as “5.66 L/h + assumed Qeff”. The model’s actual circuit clearance is slightly smaller than Qeff (2.14 rather than 2.5 L/h at Qeff 2.5 L/h), because only the fraction Qb / (Qb + Qeff) of the drug entering the filter reaches the effluent side.

Interrupting CRRT (Figure 5)

Figure 5 simulates 600 mg every 12 h as a 1 h infusion in a CVVHD patient whose effluent flow is 2.5 L/h, with CRRT stopped for 24 h at 48 h and restarted at 4.0 L/h (the Simulx regressor schedule Real_Time: times 0, 48 and 72 h). The covariates change on a dense grid so the solver cannot step over the switch.

grid5 <- seq(0, 120, by = 0.1)
ev5 <- make_events(600, 12, 1, 10, grid5, crcl = 58, crrt = "CVVHD", qeff_lh = 2.5)
off <- ev5$time >= 48 & ev5$time < 72
ev5$RRT_CRRT_ACTIVE[off] <- 0
ev5$BFR[off] <- 0
ev5$RRT_CRRT_EFFLUENT_FLOW[off] <- 0
ev5$RRT_CRRT_EFFLUENT_FLOW[ev5$time >= 72] <- 4000
sim5 <- as.data.frame(rxode2::rxSolve(mod_typ, ev5, returnType = "data.frame"))
#> ℹ omega/sigma items treated as zero: 'etaiov_cl_1', 'etaiov_cl_2', 'etalvc', 'etalq', 'etalvp'

sim5 |>
  select(time, Cc, Cpostfilter, Ceffluent) |>
  pivot_longer(-time, names_to = "output", values_to = "conc") |>
  ggplot(aes(time, conc, colour = output)) +
  geom_line() +
  geom_vline(xintercept = c(48, 72), linetype = "dashed") +
  labs(
    x = "Time (h)", y = "Ceftaroline (mg/L)", colour = NULL,
    title = "Replicates Figure 5 of Adamiszak 2025",
    subtitle = "Typical CVVHD patient, CrCL 58; CRRT off from 48 to 72 h"
  )

While the circuit is stopped its compartments are frozen: no flow enters or leaves them, so the effluent concentration holds at its 48 h value. The systemic trough rises because the circuit clearance is gone.

frozen <- sim5$Ceffluent[sim5$time > 48.05 & sim5$time < 71.95]
trough <- function(t) sim5$Cc[which.min(abs(sim5$time - t))]
stopifnot(
  diff(range(frozen)) < 1e-6 * max(frozen),
  trough(72) > trough(48)
)
c(trough_48h = trough(48), trough_72h = trough(72), effluent_frozen = frozen[1])
#>      trough_48h      trough_72h effluent_frozen 
#>        3.330282        5.045000        2.955091

Virtual cohort and NCA

The paper reports no NCA. The cohort below gives the steady-state exposure the model implies for 600 mg every 12 h (1 h infusion) in four groups of 200: off CRRT at CrCL 80 and at the median 159 mL/min/1.73 m^2, and on CVVHD or CVVHDF at CrCL 58 with Qeff 3.0 L/h. NCA uses the tenth dosing interval (108-120 h).

n_arm <- 200
arms <- tibble::tribble(
  ~treatment, ~crcl, ~crrt, ~qeff,
  "No CRRT, CrCL 80", 80, "none", 0,
  "No CRRT, CrCL 159", 159, "none", 0,
  "CVVHD, Qeff 3.0", 58, "CVVHD", 3.0,
  "CVVHDF, Qeff 3.0", 58, "CVVHDF", 3.0
)
obs_nca <- sort(unique(c(0, seq(108, 120, by = 0.25))))
rxode2::rxSetSeed(20250327)
cohort <- bind_rows(lapply(seq_len(nrow(arms)), function(i) {
  ev <- replicate_ids(make_events(600, 12, 1, 11, obs_nca,
    crcl = arms$crcl[i], crrt = arms$crrt[i], qeff_lh = arms$qeff[i]
  ), n_arm)
  s <- as.data.frame(rxode2::rxSolve(mod, ev, returnType = "data.frame"))
  s$treatment <- arms$treatment[i]
  s
}))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2
#> as a work-around try putting the mu-referenced expression on a simple line

conc <- cohort |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, treatment)
dose <- bind_rows(lapply(arms$treatment, function(tr) {
  data.frame(id = rep(seq_len(n_arm), each = 11), time = rep((0:10) * 12, n_arm), amt = 600, treatment = tr)
}))
conc_obj <- PKNCA::PKNCAconc(conc, Cc ~ time | treatment + id, concu = "mg/L", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose, amt ~ time | treatment + id, doseu = "mg")
intervals <- data.frame(start = 120 - 12, end = 120, cmax = TRUE, cmin = TRUE, auclast = TRUE)
nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
nca_tab <- as.data.frame(nca$result) |>
  filter(PPTESTCD %in% c("cmax", "cmin", "auclast")) |>
  group_by(treatment, PPTESTCD) |>
  summarise(median = median(PPORRES), p05 = quantile(PPORRES, 0.05), p95 = quantile(PPORRES, 0.95), .groups = "drop")
nca_tab |>
  mutate(across(where(is.numeric), \(x) signif(x, 3))) |>
  rename("NCA parameter" = PPTESTCD) |>
  knitr::kable()
treatment NCA parameter median p05 p95
CVVHD, Qeff 3.0 auclast 75.500 46.500 106.00
CVVHD, Qeff 3.0 cmax 15.000 12.300 17.70
CVVHD, Qeff 3.0 cmin 3.200 1.320 5.41
CVVHDF, Qeff 3.0 auclast 72.900 48.700 102.00
CVVHDF, Qeff 3.0 cmax 20.400 17.000 23.40
CVVHDF, Qeff 3.0 cmin 2.420 1.040 4.51
No CRRT, CrCL 159 auclast 55.500 34.300 98.30
No CRRT, CrCL 159 cmax 20.200 17.300 24.60
No CRRT, CrCL 159 cmin 0.809 0.140 2.80
No CRRT, CrCL 80 auclast 86.000 47.200 144.00
No CRRT, CrCL 80 cmax 23.200 19.400 27.80
No CRRT, CrCL 80 cmin 2.220 0.437 5.58

AUC over a steady-state interval depends only on the total clearance, so its median must sit at dose / (typical Cl + circuit clearance); between-subject spread in the volumes and Q does not move it.

auc_check <- nca_tab |>
  filter(PPTESTCD == "auclast") |>
  left_join(arms, by = "treatment") |>
  mutate(
    cl_total = cl_at(crcl) + ifelse(qeff > 0, qb_lh * qeff / (qb_lh + qeff), 0),
    expected = 600 / cl_total,
    pct_diff = 100 * (median / expected - 1)
  )
auc_check |> select(treatment, median, expected, pct_diff) |>
  mutate(across(where(is.numeric), \(x) signif(x, 3))) |> knitr::kable()
treatment median expected pct_diff
CVVHD, Qeff 3.0 75.5 73.6 2.650
CVVHDF, Qeff 3.0 72.9 73.6 -0.861
No CRRT, CrCL 159 55.5 53.4 3.810
No CRRT, CrCL 80 86.0 85.2 0.871 
stopifnot(all(abs(auc_check$pct_diff) < 10))

Probability of target attainment

The authors’ Simulx project and PTA workbooks are deposited with the paper. They were run with a parameter set that differs from the published Table 2 (see Assumptions and deviations), so this section first reproduces the deposit with the deposit’s own parameters, which tests the model’s structure and the authors’ target-attainment rule, and then shows what Table 2 implies.

Reproducing the deposited simulation, subject by subject

The Simulx project stores the individual parameters of every simulated patient and whether each attained 100% fT>MIC. The 50 patients of the first replicate (no CRRT, CrCL 80, the same patients in all ten regimens) are embedded below, together with their outcomes at five MICs; each is re-solved with the packaged ODE system with covariate effects neutralised so the individual values enter unchanged.

# Simulx project, Simulation/individualParameters.txt, rep 1, group
# 200mg_12h_1h (identical in every group); Vcrrt, Vpost and Veff are constant.
deposit_indiv <- data.frame(
  cl = c(6.4961794, 4.662855, 7.4240015, 3.8788189, 5.8942644, 10.817915, 6.0281723, 8.1881701, 5.1236503, 15.195177, 7.2456477, 7.7380762, 7.6639258, 10.172442, 5.6749265, 9.1180561, 10.52485, 8.2013931, 3.9015253, 9.6435158, 7.2002555, 7.1088918, 5.3512294, 9.6353486, 4.8387506, 9.020375, 8.6931984, 3.6304658, 8.4863661, 10.103719, 6.1315362, 4.5984642, 6.2725378, 4.0911669, 13.006448, 4.584552, 5.6993418, 8.2255944, 7.0115528, 5.66695, 6.6143811, 6.3230041, 7.3387383, 9.0297494, 6.8274751, 4.9305876, 4.1924907, 5.1088857, 6.3929459, 10.486686),
  vc = c(17.517099, 20.06928, 17.789941, 20.309148, 18.878148, 21.110847, 17.994143, 19.656911, 20.671644, 17.616616, 18.785646, 19.910304, 20.659127, 21.565209, 19.130513, 18.797654, 18.720116, 21.568991, 20.477434, 22.674459, 21.126418, 19.722911, 17.888304, 18.360435, 21.753535, 20.530853, 19.235181, 19.488572, 18.414684, 18.21322, 20.120523, 23.422876, 19.133384, 21.155923, 21.70151, 18.118647, 22.279828, 20.199647, 21.138882, 19.903336, 21.066787, 17.910571, 20.013432, 17.637206, 18.607206, 21.274346, 21.232958, 18.724435, 19.75982, 16.609326),
  vp = c(14.751305, 10.292979, 15.786613, 16.315114, 5.0930563, 18.797139, 16.018509, 10.879837, 19.357267, 28.453531, 22.82975, 18.805903, 17.786848, 14.1145, 12.084895, 12.536435, 30.952588, 23.848388, 11.200077, 16.047077, 17.591019, 12.02733, 13.113841, 13.019271, 13.255965, 9.491153, 13.473767, 13.538015, 27.630161, 15.606442, 12.884037, 10.826067, 23.497408, 14.983165, 12.206697, 10.708366, 6.9206913, 18.738555, 23.161132, 10.105402, 12.401239, 15.867724, 15.763941, 24.226245, 19.134211, 12.782613, 14.821284, 14.939544, 18.159728, 20.881435),
  q = c(9.0095658, 7.9024139, 10.00919, 7.6878717, 8.2277892, 8.4397031, 8.4550573, 5.97621, 7.2880863, 8.3484842, 8.9671843, 8.1078035, 6.4960869, 9.1665907, 7.9767893, 9.6640974, 9.1255323, 7.8129333, 7.3058127, 7.5533867, 7.3251212, 6.5917457, 7.6686488, 8.1377737, 7.7371678, 9.2769543, 8.4900937, 6.9668873, 9.2664163, 8.4193413, 8.2911208, 7.589762, 7.0086952, 9.9544229, 7.6250764, 7.5695791, 9.0787738, 9.1749376, 7.7809058, 9.2931385, 8.197149, 7.8385202, 8.1678028, 9.0625337, 7.348901, 6.9044172, 7.8726294, 7.9717164, 9.3437781, 8.4869314)
)
deposit_outcome <- tibble::tribble(
  ~regimen, ~mic, ~attained,
  "200mg_12h_1h", 0.25, "11111011101110111111111010111011110111111111111110",
  "300mg_12h_1h", 0.25, "11111111101111111111111111111111110111111111111111",
  "400mg_12h_1h", 0.25, "11111111111111111111111111111111110111111111111111",
  "600mg_12h_1h", 0.25, "11111111111111111111111111111111111111111111111111",
  "800mg_12h_1h", 0.25, "11111111111111111111111111111111111111111111111111",
  "200mg_8h_2h", 0.25, "11111111111111111111111111111111111111111111111111",
  "300mg_8h_2h", 0.25, "11111111111111111111111111111111111111111111111111",
  "400mg_8h_2h", 0.25, "11111111111111111111111111111111111111111111111111",
  "600mg_8h_2h", 0.25, "11111111111111111111111111111111111111111111111111",
  "800mg_8h_2h", 0.25, "11111111111111111111111111111111111111111111111111",
  "200mg_12h_1h", 0.5, "11011010101000100010101010010011110110111100111110",
  "300mg_12h_1h", 0.5, "11111010101110100110111010011011110111111111111110",
  "400mg_12h_1h", 0.5, "11111011101110111111111010111011110111111111111110",
  "600mg_12h_1h", 0.5, "11111111101111111111111111111111110111111111111111",
  "800mg_12h_1h", 0.5, "11111111111111111111111111111111110111111111111111",
  "200mg_8h_2h", 0.5, "11111111101111111111111111111111110111111111111111",
  "300mg_8h_2h", 0.5, "11111111111111111111111111111111111111111111111111",
  "400mg_8h_2h", 0.5, "11111111111111111111111111111111111111111111111111",
  "600mg_8h_2h", 0.5, "11111111111111111111111111111111111111111111111111",
  "800mg_8h_2h", 0.5, "11111111111111111111111111111111111111111111111111",
  "200mg_12h_1h", 1, "01010000100000000010000010010001010100000000011000",
  "300mg_12h_1h", 1, "01010010100000100010001010010001110110010000011110",
  "400mg_12h_1h", 1, "11011010101000100010101010010011110110111100111110",
  "600mg_12h_1h", 1, "11111010101110100110111010011011110111111111111110",
  "800mg_12h_1h", 1, "11111011101110111111111010111011110111111111111110",
  "200mg_8h_2h", 1, "11111010101110100110111010011011110111111110111110",
  "300mg_8h_2h", 1, "11111011101111111111111011111011110111111111111110",
  "400mg_8h_2h", 1, "11111111101111111111111111111111110111111111111111",
  "600mg_8h_2h", 1, "11111111111111111111111111111111111111111111111111",
  "800mg_8h_2h", 1, "11111111111111111111111111111111111111111111111111",
  "200mg_12h_1h", 2, "00000000000000000000000000000000000000000000000000",
  "300mg_12h_1h", 2, "00010000000000000010000000010000010000000000001000",
  "400mg_12h_1h", 2, "01010000100000000010000010010001010100000000011000",
  "600mg_12h_1h", 2, "01010010100000100010001010010001110110010000011110",
  "800mg_12h_1h", 2, "11011010101000100010101010010011110110111100111110",
  "200mg_8h_2h", 2, "01010000100000000010000010010001010100000000011100",
  "300mg_8h_2h", 2, "11011010100000100010001010010011110110111100111110",
  "400mg_8h_2h", 2, "11111010101110100110111010011011110111111110111110",
  "600mg_8h_2h", 2, "11111011101111111111111011111011110111111111111110",
  "800mg_8h_2h", 2, "11111111101111111111111111111111110111111111111111",
  "200mg_12h_1h", 4, "00000000000000000000000000000000000000000000000000",
  "300mg_12h_1h", 4, "00000000000000000000000000000000000000000000000000",
  "400mg_12h_1h", 4, "00000000000000000000000000000000000000000000000000",
  "600mg_12h_1h", 4, "00010000000000000010000000010000010000000000001000",
  "800mg_12h_1h", 4, "01010000100000000010000010010001010100000000011000",
  "200mg_8h_2h", 4, "00000000000000000000000000000000000000000000000000",
  "300mg_8h_2h", 4, "00010000000000000010000000010000010000000000001000",
  "400mg_8h_2h", 4, "01010000100000000010000010010001010100000000011100",
  "600mg_8h_2h", 4, "11011010100000100010001010010011110110111100111110",
  "800mg_8h_2h", 4, "11111010101110100110111010011011110111111110111110" 
)
regimens <- tibble::tribble(
  ~regimen, ~dose, ~tau, ~tinf,
  "200mg_12h_1h", 200, 12, 1, "300mg_12h_1h", 300, 12, 1, "400mg_12h_1h", 400, 12, 1,
  "600mg_12h_1h", 600, 12, 1, "800mg_12h_1h", 800, 12, 1, "200mg_8h_2h", 200, 8, 2,
  "300mg_8h_2h", 300, 8, 2, "400mg_8h_2h", 400, 8, 2, "600mg_8h_2h", 600, 8, 2,
  "800mg_8h_2h", 800, 8, 2
)
n_dep <- nrow(deposit_indiv)
dep_params <- data.frame(
  id = seq_len(n_dep),
  lcl = log(deposit_indiv$cl), lvc = log(deposit_indiv$vc),
  lvp = log(deposit_indiv$vp), lq = log(deposit_indiv$q),
  e_crcl_cl = 0, e_cvvhd_vc = 0, e_cvvhdf_vc = 0, e_crrt_vp = 0, e_crrt_q = 0,
  lvfilter = log(3.16963895935259), lvpostfilter = log(1.47519683424012),
  lvdialysate = log(0.6657024155795507),
  etaiov_cl_1 = 0, etaiov_cl_2 = 0, etalvc = 0, etalq = 0, etalvp = 0
)
replay <- bind_rows(lapply(seq_len(nrow(regimens)), function(i) {
  r <- regimens[i, ]
  ev <- replicate_ids(make_events(r$dose, r$tau, r$tinf, 240 / r$tau, 0:120, crcl = 159), n_dep)
  # All variability is already in the individual values, so the solve
  # warns that a multi-subject simulation has no omega; that is intended.
  s <- suppressWarnings(as.data.frame(rxode2::rxSolve(mod_typ, ev, params = dep_params, returnType = "data.frame")))
  free <- split(0.8 * s$Cc, s$id)
  bind_rows(lapply(c(0.25, 0.5, 1, 2, 4), function(m) {
    data.frame(regimen = r$regimen, mic = m, model = vapply(free, attained, logical(1), mic = m))
  }))
}))
replay <- bind_rows(lapply(split(replay, paste(replay$regimen, replay$mic)), function(d) {
  key <- deposit_outcome$regimen == d$regimen[1] & deposit_outcome$mic == d$mic[1]
  d$deposit <- strsplit(deposit_outcome$attained[key], "")[[1]] == "1"
  d
}))

Each block of 50 rows is in the deposit’s subject order, so the model’s outcome for a subject sits next to the deposit’s. Agreement per regimen:

agree <- replay |>
  group_by(regimen) |>
  summarise(subjects_x_mics = n(), agreement = mean(model == deposit), .groups = "drop")
knitr::kable(agree)
regimen subjects_x_mics agreement
200mg_12h_1h 250 1
200mg_8h_2h 250 1
300mg_12h_1h 250 1
300mg_8h_2h 250 1
400mg_12h_1h 250 1
400mg_8h_2h 250 1
600mg_12h_1h 250 1
600mg_8h_2h 250 1
800mg_12h_1h 250 1
800mg_8h_2h 250 1 
stopifnot(mean(replay$model == replay$deposit) > 0.99)

The model reproduces 100% of the 2500 subject-level outcomes. This pins the two-compartment patient model and the target-attainment rule.

Reproducing the deposited PTA, including the CRRT arms

The CRRT arms of the workbooks test the circuit compartments, the flow-unit conversions and the modality effects. Here the packaged model is solved with the deposit’s population parameters and between-subject SDs (Simulx stores Monolix omega as SDs), 200 virtual patients per scenario, the same patients for both regimens.

# PTA_100%MIC.xlsx, sheets ClCr130, CVVHD2.5 and CVVHDF4.0.
deposit_pta <- tibble::tribble(
  ~scenario, ~regimen, ~mic, ~pta,
  "ClCr130", "600mg/12h_inf1h", 0.25, 0.90,
  "ClCr130", "600mg/12h_inf1h", 0.5, 0.72,
  "ClCr130", "600mg/12h_inf1h", 1, 0.40,
  "ClCr130", "600mg/12h_inf1h", 2, 0.10,
  "ClCr130", "600mg/12h_inf1h", 4, 0.00,
  "ClCr130", "300mg/8h_inf2h", 0.25, 0.96,
  "ClCr130", "300mg/8h_inf2h", 0.5, 0.84,
  "ClCr130", "300mg/8h_inf2h", 1, 0.52,
  "ClCr130", "300mg/8h_inf2h", 2, 0.14,
  "ClCr130", "300mg/8h_inf2h", 4, 0.00,
  "CVVHD2.5", "600mg/12h_inf1h", 0.25, 1.00,
  "CVVHD2.5", "600mg/12h_inf1h", 0.5, 1.00,
  "CVVHD2.5", "600mg/12h_inf1h", 1, 0.96,
  "CVVHD2.5", "600mg/12h_inf1h", 2, 0.69,
  "CVVHD2.5", "600mg/12h_inf1h", 4, 0.10,
  "CVVHD2.5", "300mg/8h_inf2h", 0.25, 1.00,
  "CVVHD2.5", "300mg/8h_inf2h", 0.5, 1.00,
  "CVVHD2.5", "300mg/8h_inf2h", 1, 1.00,
  "CVVHD2.5", "300mg/8h_inf2h", 2, 0.72,
  "CVVHD2.5", "300mg/8h_inf2h", 4, 0.02,
  "CVVHDF4.0", "600mg/12h_inf1h", 0.25, 1.00,
  "CVVHDF4.0", "600mg/12h_inf1h", 0.5, 0.98,
  "CVVHDF4.0", "600mg/12h_inf1h", 1, 0.76,
  "CVVHDF4.0", "600mg/12h_inf1h", 2, 0.24,
  "CVVHDF4.0", "600mg/12h_inf1h", 4, 0.00,
  "CVVHDF4.0", "300mg/8h_inf2h", 0.25, 1.00,
  "CVVHDF4.0", "300mg/8h_inf2h", 0.5, 1.00,
  "CVVHDF4.0", "300mg/8h_inf2h", 1, 0.88,
  "CVVHDF4.0", "300mg/8h_inf2h", 2, 0.32,
  "CVVHDF4.0", "300mg/8h_inf2h", 4, 0.00
)
deposit_theta <- c(
  lcl = log(11.1542415458086), e_crcl_cl = 0.6601751687579716,
  lvc = log(19.6835954243472), e_cvvhd_vc = 0.3611754610067365,
  e_cvvhdf_vc = -0.9366628084220988, lvp = log(16.3441671451621),
  e_crrt_vp = 0.88390106619693, lq = log(8.1596747033188),
  e_crrt_q = 1.2836794972224, lvfilter = log(3.16963895935259),
  lvpostfilter = log(1.47519683424012), lvdialysate = log(0.6657024155795507)
)
deposit_omega <- lotri::lotri(
  etaiov_cl_1 ~ 0.3333396262193932^2,
  etaiov_cl_2 ~ 0.3333396262193932^2,
  etalvc ~ 0.0732214424026686^2,
  etalq ~ 0.1254604403675975^2,
  etalvp ~ 0.317920380478243^2
)
scenarios <- tibble::tribble(
  ~scenario, ~crcl, ~crrt, ~qeff,
  "ClCr130", 130, "none", 0,
  "CVVHD2.5", 58, "CVVHD", 2.5,
  "CVVHDF4.0", 58, "CVVHDF", 4.0
)
pta_regimens <- tibble::tribble(
  ~regimen, ~dose, ~tau, ~tinf,
  "600mg/12h_inf1h", 600, 12, 1,
  "300mg/8h_inf2h", 300, 8, 2
)
mics <- c(0.25, 0.5, 1, 2, 4)

run_pta <- function(sc, rg, theta = NULL, omega = NULL, n = 200, seed = 1) {
  ev <- replicate_ids(make_events(rg$dose, rg$tau, rg$tinf, 240 / rg$tau, 0:120,
    crcl = sc$crcl, crrt = sc$crrt, qeff_lh = sc$qeff
  ), n)
  rxode2::rxSetSeed(seed)
  s <- if (is.null(theta)) {
    rxode2::rxSolve(mod, ev, returnType = "data.frame")
  } else {
    rxode2::rxSolve(mod, ev, params = theta, omega = omega, returnType = "data.frame")
  }
  pta_by_mic(as.data.frame(s), mics)
}

pta_grid <- tidyr::expand_grid(s = seq_len(nrow(scenarios)), r = seq_len(nrow(pta_regimens)))
dep_rep <- bind_rows(lapply(seq_len(nrow(pta_grid)), function(i) {
  sc <- scenarios[pta_grid$s[i], ]
  rg <- pta_regimens[pta_grid$r[i], ]
  data.frame(
    scenario = sc$scenario, regimen = rg$regimen, mic = mics,
    model = run_pta(sc, rg, deposit_theta, deposit_omega, seed = 1000 + pta_grid$s[i])
  )
})) |>
  left_join(deposit_pta, by = c("scenario", "regimen", "mic"))

dep_rep |>
  mutate(diff = model - pta) |>
  rename("deposit PTA" = pta, "model PTA" = model) |>
  knitr::kable(digits = 2)
scenario regimen mic model PTA deposit PTA diff
ClCr130 600mg/12h_inf1h 0.25 0.90 0.90 0.00
ClCr130 600mg/12h_inf1h 0.50 0.74 0.72 0.02
ClCr130 600mg/12h_inf1h 1.00 0.44 0.40 0.03
ClCr130 600mg/12h_inf1h 2.00 0.14 0.10 0.04
ClCr130 600mg/12h_inf1h 4.00 0.02 0.00 0.02
ClCr130 300mg/8h_inf2h 0.25 0.97 0.96 0.01
ClCr130 300mg/8h_inf2h 0.50 0.84 0.84 0.00
ClCr130 300mg/8h_inf2h 1.00 0.60 0.52 0.07
ClCr130 300mg/8h_inf2h 2.00 0.18 0.14 0.04
ClCr130 300mg/8h_inf2h 4.00 0.02 0.00 0.02
CVVHD2.5 600mg/12h_inf1h 0.25 1.00 1.00 0.00
CVVHD2.5 600mg/12h_inf1h 0.50 1.00 1.00 -0.01
CVVHD2.5 600mg/12h_inf1h 1.00 0.97 0.96 0.01
CVVHD2.5 600mg/12h_inf1h 2.00 0.70 0.69 0.01
CVVHD2.5 600mg/12h_inf1h 4.00 0.09 0.10 -0.01
CVVHD2.5 300mg/8h_inf2h 0.25 1.00 1.00 0.00
CVVHD2.5 300mg/8h_inf2h 0.50 1.00 1.00 0.00
CVVHD2.5 300mg/8h_inf2h 1.00 0.99 1.00 -0.01
CVVHD2.5 300mg/8h_inf2h 2.00 0.73 0.72 0.01
CVVHD2.5 300mg/8h_inf2h 4.00 0.04 0.02 0.02
CVVHDF4.0 600mg/12h_inf1h 0.25 1.00 1.00 -0.01
CVVHDF4.0 600mg/12h_inf1h 0.50 0.96 0.98 -0.02
CVVHDF4.0 600mg/12h_inf1h 1.00 0.76 0.76 0.01
CVVHDF4.0 600mg/12h_inf1h 2.00 0.29 0.24 0.05
CVVHDF4.0 600mg/12h_inf1h 4.00 0.00 0.00 0.00
CVVHDF4.0 300mg/8h_inf2h 0.25 1.00 1.00 0.00
CVVHDF4.0 300mg/8h_inf2h 0.50 0.99 1.00 -0.01
CVVHDF4.0 300mg/8h_inf2h 1.00 0.91 0.88 0.03
CVVHDF4.0 300mg/8h_inf2h 2.00 0.33 0.32 0.01
CVVHDF4.0 300mg/8h_inf2h 4.00 0.00 0.00 0.00 
informative <- dep_rep |> filter(pta > 0.05, pta < 0.95)
c(cells = nrow(informative), mean_abs_diff = mean(abs(informative$model - informative$pta)))
#>         cells mean_abs_diff 
#>   14.00000000    0.02428571
stopifnot(
  # A wrong modality effect or flow conversion moves whole CRRT columns by
  # 0.2-0.5 (a CVVHD effect applied to a CVVHDF patient does exactly that),
  # far beyond the sampling noise of 200 patients.
  mean(abs(informative$model - informative$pta)) < 0.08
)

Table 3 regimens under the published Table 2 parameters

Table 3 lists, per scenario, the lowest-dose regimen reaching 90% PTA. Those regimens come from the deposited parameter set. The table below gives the PTA of each recommended regimen under both parameter sets, for the two 100% fT>MIC columns of Table 3.

table3 <- tibble::tribble(
  ~scenario, ~crcl, ~crrt, ~qeff, ~mic, ~dose, ~tau, ~tinf,
  "No CRRT, CrCL 80", 80, "none", 0, 0.25, 300, 12, 1,
  "No CRRT, CrCL 80", 80, "none", 0, 1, 400, 8, 2,
  "No CRRT, CrCL 130", 130, "none", 0, 0.25, 200, 8, 2,
  "No CRRT, CrCL 130", 130, "none", 0, 1, 800, 8, 2,
  "No CRRT, CrCL 210", 210, "none", 0, 0.25, 600, 8, 2,
  "No CRRT, CrCL 300", 300, "none", 0, 0.25, 800, 8, 2,
  "CVVHD, Qeff 2.5", 58, "CVVHD", 2.5, 0.25, 200, 12, 1,
  "CVVHD, Qeff 2.5", 58, "CVVHD", 2.5, 1, 200, 8, 2,
  "CVVHD, Qeff 4.0", 58, "CVVHD", 4.0, 1, 300, 8, 2,
  "CVVHDF, Qeff 2.5", 58, "CVVHDF", 2.5, 1, 300, 8, 2,
  "CVVHDF, Qeff 4.0", 58, "CVVHDF", 4.0, 0.25, 300, 12, 1,
  "CVVHDF, Qeff 4.0", 58, "CVVHDF", 4.0, 1, 400, 8, 2
)
pta_one <- function(row, theta = NULL, omega = NULL) {
  rg <- data.frame(dose = row$dose, tau = row$tau, tinf = row$tinf)
  sc <- data.frame(crcl = row$crcl, crrt = row$crrt, qeff = row$qeff)
  ev <- replicate_ids(make_events(rg$dose, rg$tau, rg$tinf, 240 / rg$tau, 0:120,
    crcl = sc$crcl, crrt = sc$crrt, qeff_lh = sc$qeff
  ), 200)
  rxode2::rxSetSeed(7)
  s <- if (is.null(theta)) {
    rxode2::rxSolve(mod, ev, returnType = "data.frame")
  } else {
    rxode2::rxSolve(mod, ev, params = theta, omega = omega, returnType = "data.frame")
  }
  pta_by_mic(as.data.frame(s), row$mic)
}
table3$pta_deposit <- vapply(seq_len(nrow(table3)), function(i) pta_one(table3[i, ], deposit_theta, deposit_omega), numeric(1))
table3$pta_table2 <- vapply(seq_len(nrow(table3)), function(i) pta_one(table3[i, ]), numeric(1))
table3 |>
  mutate(regimen = sprintf("%d mg q%dh, %d h infusion", dose, tau, tinf)) |>
  select(scenario, mic, regimen, pta_deposit, pta_table2) |>
  rename("MIC (mg/L)" = mic, "PTA, deposit parameters" = pta_deposit, "PTA, Table 2 parameters" = pta_table2) |>
  knitr::kable(digits = 2)
scenario MIC (mg/L) regimen PTA, deposit parameters PTA, Table 2 parameters
No CRRT, CrCL 80 0.25 300 mg q12h, 1 h infusion 0.94 0.94
No CRRT, CrCL 80 1.00 400 mg q8h, 2 h infusion 0.91 0.92
No CRRT, CrCL 130 0.25 200 mg q8h, 2 h infusion 0.90 0.90
No CRRT, CrCL 130 1.00 800 mg q8h, 2 h infusion 0.90 0.90
No CRRT, CrCL 210 0.25 600 mg q8h, 2 h infusion 0.97 0.96
No CRRT, CrCL 300 0.25 800 mg q8h, 2 h infusion 0.90 0.88
CVVHD, Qeff 2.5 0.25 200 mg q12h, 1 h infusion 1.00 1.00
CVVHD, Qeff 2.5 1.00 200 mg q8h, 2 h infusion 0.88 0.90
CVVHD, Qeff 4.0 1.00 300 mg q8h, 2 h infusion 0.97 0.98
CVVHDF, Qeff 2.5 1.00 300 mg q8h, 2 h infusion 0.94 0.97
CVVHDF, Qeff 4.0 0.25 300 mg q12h, 1 h infusion 0.98 0.99
CVVHDF, Qeff 4.0 1.00 400 mg q8h, 2 h infusion 0.98 0.99

Under both parameter sets each recommended regimen lands within a few percentage points of 90%, which is the sampling error of 200 simulated patients at that level, so the difference between the two runs does not change any recommendation in Table 3. For a trough-driven target this is expected: the two runs’ typical clearances differ by less than 2% over the CrCL range simulated (CrCL 58-300 mL/min/1.73 m^2), and the trough concentrations that decide the target depend mainly on clearance.

Assumptions and deviations

  • Two parameter sets. Every value in the model is taken from Table 2 (final model). The authors’ Simulx project, described in the paper as based on the final model, carries a different set (for example Cl 11.15 vs 11.23 L/h, the CVVHD/CVVHDF effects on VCentral 0.361/-0.937 vs 0.47/-0.42, and the CRRT effect on Q 1.284 vs 0.99), and its RSEs differ from Table 2 too, so it is a separate run, not a rounding of Table 2. All numbers quoted in the Results and Discussion (11.2 and 5.66 L/h, +57%, +60%, the 2.69-fold CRRT effect and Q 8.80 L/h) follow Table 2, while the PTA results (Table 3, Table S1 and the workbooks) follow the Simulx set. Table 2 was used because it is the published final model and the whole narrative agrees with it.
  • Between-subject variability scale. Table 2 reports the random effects as %CV; they are converted with omega^2 = log(1 + CV^2). Reading them as Monolix SDs instead (omega = CV / 100) changes the variances by at most 3.5% relative, well inside their 20.8-58.5% RSEs. The deposited run cannot settle the scale because its values differ.
  • IOV on clearance only. Clearance carries between-occasion variability and no between-subject variability (Results 2.2). It is encoded as one eta per occasion, occasion 2 fixed to occasion 1; a simulation with a single occasion per subject therefore gives clearance the IOV magnitude as its total variability, which is what the authors’ Simulx simulations do.
  • The target-attainment rule. The paper describes the target as 100% fT>MIC. The Simulx endpoint is “cumulative time above the MIC of at least 100 h” on an hourly grid from 0 to 120 h, and the subject-level reproduction above shows Simulx counts a one-hour interval only when both of its endpoints are above the MIC. For a 12-hourly regimen that admits a patient whose concentration dips below the MIC around each trough, so the published PTA is more lenient than a literal 100% fT>MIC. The attained() helper follows the authors’ rule so the comparison is like for like.
  • Prose errors in the Results. “CVVHDF decreased VCentral by 52%”: with the Table 2 coefficient -0.42 the effect is exp(-0.42) = 0.657, a 34% decrease; 52% is exp(0.42) - 1. “Patients undergoing CRRT had 269% higher VPeripheral and Q”: exp(0.99) = 2.69 is a 2.69-fold value, i.e. 169% higher. Table 2 and the printed covariate equation agree with each other and were used.
  • Number of patients with two occasions. Methods 4.2 says 18 patients had two CrCL values; the deposited dataset carries a second occasion for 15. This does not affect the model.
  • Dose units. Doses are the labelled ceftaroline fosamil amounts (400-600 mg), entered directly as in the source; the model makes no prodrug-to-active mass correction, as in the authors’ model and simulations.
  • Digitised data. The model was fit to concentrations digitised from other publications’ figures, with only four CRRT patients; the authors caution that the CRRT results need clinical validation.
  • Modality covariates are subject-level. CVVHD/CVVHDF enter the central volume, and any CRRT the peripheral volume and Q, as subject-level covariates. They are not switched off when the circuit stops; only the circuit flows are (Figure 5), which matches the authors’ Simulx project.