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Meropenem (Rancic 2024)

Source: vignettes/articles/Rancic_2024_meropenem.Rmd
Rancic_2024_meropenem.Rmd

Model and source

  • Citation: Rancic A, Milosavljevic MN, Rosic N, Milovanovic D, Folic M, Ruzic Zecevic D, Petrovic N, Milojevic Corbic M, Dabanovic V, Jankovic SM. Population pharmacokinetics of meropenem in critically ill patients. Open Med (Wars). 2024;19(1):20241004. doi:10.1515/med-2024-1004. PMCID PMC11278387.
  • Description: One-compartment intravenous population PK model for meropenem in critically ill adults in intensive care (Rancic 2024). Clearance combines a multiplicative power term in serum creatinine and white blood cell count with additive shifts for hypertension and for concomitant vancomycin or colistimethate; the central volume carries no covariates. NOTE: the published central volume (2.05 L) is roughly ten-fold smaller than the value implied by the paper’s own reported peak concentrations, so simulated peaks are correspondingly high - see the validation vignette.
  • Article: https://doi.org/10.1515/med-2024-1004 (Open Medicine, open access; PMCID PMC11278387)

No supplementary material accompanies the article; the Data Availability statement offers the raw data “upon motivated request to the corresponding author” only. Every value below therefore comes from the main text and its five tables.

Population

The model was fitted to 101 critically ill adults treated in the intensive care unit of the University Clinical Centre Kragujevac, Serbia, all with a severe infection (meningitis, pneumonia, sepsis, septic shock or febrile neutropenia) caused by a multi-resistant Gram-negative organism. Mean age was 62.4 +/- 14.9 years (range 21 - 86), mean total body weight 79.0 +/- 13.8 kg (range 48 - 130), and 39 of 101 (38.6%) were women. Mean serum creatinine was 94.5 +/- 63.7 umol/L (range 40 - 452), so most of the cohort was not renally impaired – the authors emphasise augmented renal clearance rather than renal failure as the dominant phenomenon in this population (Discussion). Recorded comorbidities were hypertension 32.7%, chronic renal failure 11.9%, neoplasm 17.8%, cerebral infarction 20.8%, pneumonia 31.7% and urinary tract infection 35.6% (Table 1).

Meropenem was given as an intermittent intravenous infusion of 1,000 - 2,000 mg every 8 or 12 h, for a mean total daily dose of 3,000 +/- 693 mg/day (range 2,000 - 6,000). Twenty-seven patients (26.7%) received antibiotic polytherapy: 17 (16.8%) vancomycin, 7 (6.9%) colistin, and 3 (2.97%) both. Patients entered the study only after at least three days of continuous meropenem, i.e. at steady state, and contributed exactly two plasma samples each (202 observations total): the first 5 - 30 min after the end of the infusion (mean 40.69 +/- 16.67 mg/L, range 13.07 - 88.95) and the second 3 - 4 h after the end of the infusion (mean 12.55 +/- 7.62 mg/L, range 2.06 - 36.28).

The same information is available programmatically via the model’s population metadata (readModelDb("Rancic_2024_meropenem")()$population).

pop <- rxode2::rxode(readModelDb("Rancic_2024_meropenem"))$population
#> ℹ parameter labels from comments will be replaced by 'label()'
str(pop, max.level = 1)
#> List of 11
#>  $ species       : chr "human"
#>  $ n_subjects    : int 101
#>  $ n_studies     : int 1
#>  $ n_observations: int 202
#>  $ age_range     : chr "21 - 86 years (mean 62.37 +/- 14.89)"
#>  $ weight_range  : chr "48 - 130 kg (mean 78.97 +/- 13.76)"
#>  $ sex_female_pct: num 38.6
#>  $ disease_state : chr "Critically ill adults in the intensive care unit with severe infection (meningitis, pneumonia, sepsis, septic s"| __truncated__
#>  $ dose_range    : chr "1,000 - 2,000 mg meropenem every 8 or 12 h by intermittent intravenous infusion (total daily dose mean 3,000 +/"| __truncated__
#>  $ regions       : chr "Serbia (Intensive Care Unit, University Clinical Centre Kragujevac)."
#>  $ notes         : chr "Prospective observational case-series. Two plasma samples per patient: the first 5 - 30 min after the end of th"| __truncated__

Source trace

Every ini() entry in inst/modeldb/specificDrugs/Rancic_2024_meropenem.R carries an in-file comment pointing at its origin. They are collected here for review.

Equation / parameter Value Source location
Structural model: one compartment, IV, no absorption n/a Methods 2.3: NONMEM “ADVAN 1 subroutine (version 5, level 1.1, double precision) … a single-compartment model without absorption”
Final clearance equation CL = 5.29 * CRE^1e-6 * WBC^-0.165 + 1e-6*HTA + 0.825*VAN + 1.28*COL Abstract; Results paragraph following Table 2 (the display equation itself is a figure in the PDF and is transcribed from the Abstract, which prints it in full)
lcl = log(5.29) 5.29 L/h Table 3, row “Clearance (L/h) (theta 1)”; SE 0.038, 95% CI 5.215 - 5.365
lvc = log(2.05) 2.05 L Table 3, row “Volume of distribution (L) (theta 2)”; SE 0.006, 95% CI 2.039 - 2.061
e_creat_cl 0.000001 Abstract equation; Table 3 row “Effect of CRE” prints estimate, SE and both CI limits as 0.0000
e_wbc_cl -0.165 Table 3, row “Effect of WBCs”; SE 0.0545, 95% CI -0.219 to -0.110
e_dis_hypert_cl 0.000001 Abstract equation; Table 3 row “Effect of HTA” prints estimate, SE and both CI limits as 0.0000
e_conmed_vancomycin_cl 0.825 L/h Table 3, row “Effect of VAN”; SE 0.054, 95% CI 0.770 - 0.879
e_conmed_colistimethate_cl 1.28 L/h Table 3, row “Effect of COL”; SE 0.05, 95% CI 1.23 - 1.33
etalcl variance 0.0215 Table 3, row “Inter-individual variance of CL (omega^2 CL)”; SE 0.0146, 95% CI 0.0000 - 0.0501
Exponential IIV placement (multiplies the whole bracket) n/a Table 2, base / univariate / full model rows, all of the form [...] x Exp[ETA(1)]
propSd = sqrt(0.44) = 0.6633 0.44 (variance) Table 3, row “Residual error variance (sigma^2 CL)”; SE 0.066, 95% CI 0.310 - 0.570. Form from Methods 2.3; see Errata
Volume: no covariates, no IIV n/a Table 3 reports no volume covariate rows and no omega^2 V; the Table 3 footnote defines ETA(2) and theta16 - theta20 but no estimates for them appear anywhere
Cohort demographics n/a Table 1
Covariate screen (24 screened, 13 in the full model, 5 retained) n/a Results paragraphs 3 - 4; Table 2

The covariate screen

Table 2 of the paper records the objective-function value for the base model, for each univariate covariate model, and for the full model. Only the five covariates that survived backward deletion at p < 0.01 appear in the final model; the rest are recorded in the model file’s covariatesDataExcluded metadata (where a canonical register name exists) or in the narrative here.

screen <- tibble::tribble(
  ~Model,                                       ~MOF,      ~dMOF,  ~p,
  "Base: CL = theta1 * Exp[ETA(1)]",             1283.053,  NA,     NA_character_,
  "+ (AGE/50)^theta3",                           1277.958,  5.095,  "<0.05",
  "+ (TBW/70)^theta4",                           1266.640, 16.413,  "<0.01",
  "+ (daily dose)^theta5",                       1282.624,  0.429,  ">0.05",
  "+ (CRE)^theta6",                              1272.552, 10.501,  "<0.01",
  "+ (WBCs)^theta7",                             1267.150, 15.903,  "<0.01",
  "+ theta8 * HTA",                              1262.636, 20.417,  "<0.01",
  "+ theta9 * CRF",                              1282.954,  0.099,  ">0.05",
  "+ theta10 * NEO",                             1280.925,  2.128,  ">0.05",
  "+ theta11 * CI",                              1264.258, 18.795,  "<0.01",
  "+ theta12 * PNE",                             1275.855,  7.198,  "<0.01",
  "+ theta13 * UTI",                             1272.183, 10.870,  "<0.01",
  "+ theta14 * VAN",                             1272.001, 11.052,  "<0.01",
  "+ theta15 * COL",                             1274.813,  8.240,  "<0.01",
  "Full model (all significant covariates)",     1207.153,  NA,     NA_character_,
  "Final model (after backward deletion)",       1224.035, NA,      NA_character_
)

# The MOF differences the paper prints are all relative to the base model.
chk <- screen |>
  dplyr::filter(!is.na(dMOF)) |>
  dplyr::mutate(recomputed = 1283.053 - MOF)
stopifnot(max(abs(chk$recomputed - chk$dMOF)) < 5e-4)

screen |>
  dplyr::rename(
    "Clearance model"    = Model,
    "MOF"                = MOF,
    "Difference vs base" = dMOF,
    "p value"            = p
  ) |>
  knitr::kable(
    digits  = 3,
    caption = paste(
      "Reproduces Table 2 of Rancic 2024. Every printed MOF difference is",
      "verified against the base-model MOF of 1283.053 in the chunk above."
    )
  )
Reproduces Table 2 of Rancic 2024. Every printed MOF difference is verified against the base-model MOF of 1283.053 in the chunk above.
Clearance model MOF Difference vs base p value
Base: CL = theta1 * Exp[ETA(1)] 1283.053 NA NA
+ (AGE/50)^theta3 1277.958 5.095 <0.05
+ (TBW/70)^theta4 1266.640 16.413 <0.01
+ (daily dose)^theta5 1282.624 0.429 >0.05
+ (CRE)^theta6 1272.552 10.501 <0.01
+ (WBCs)^theta7 1267.150 15.903 <0.01
+ theta8 * HTA 1262.636 20.417 <0.01
+ theta9 * CRF 1282.954 0.099 >0.05
+ theta10 * NEO 1280.925 2.128 >0.05
+ theta11 * CI 1264.258 18.795 <0.01
+ theta12 * PNE 1275.855 7.198 <0.01
+ theta13 * UTI 1272.183 10.870 <0.01
+ theta14 * VAN 1272.001 11.052 <0.01
+ theta15 * COL 1274.813 8.240 <0.01
Full model (all significant covariates) 1207.153 NA NA
Final model (after backward deletion) 1224.035 NA NA

Four screened comorbidity flags – chronic renal failure, cerebral infarction, pneumonia and urinary tract infection – are deliberately not given canonical covariate names in the model file. Three of them were significant univariately and were carried into the full model, but none survived backward deletion, so none carries an effect; and their mapping onto the existing register entries (DIS_CUTI is specifically complicated urinary tract infection, DIS_HABP specifically hospital-acquired bacterial pneumonia) is not settled by what this paper reports. They are recorded here rather than minted as new canonical names on the strength of a screen that rejected them.

Virtual cohort

Original observed data are not publicly available. The cohort below is a 101-subject virtual population – the same size as the paper’s – whose covariate distributions reproduce the Table 1 marginals.

Two distributions had to be assumed, because the paper does not report them:

  • Leukocyte count. Table 1 has no WBC row at all, even though WBC is one of the five retained covariates. The unit is settled by internal consistency (see the model file’s covariateData[[WBC]]$notes): only a 10^9/L scale reconciles the final model’s covariate-adjusted clearance with the base model’s 3.80 L/h. The distribution is assumed log-normal with median 10.8 x 10^9/L – the value implied by that same reconciliation – and a 45% geometric CV, truncated to 2 - 40, which spans the range seen in an ICU cohort with severe Gram-negative infection.
  • Dosing regimen mix. The paper reports the daily-dose summary (3,000 +/- 693 mg/day, range 2,000 - 6,000) and the permitted regimens (1,000 - 2,000 mg q8h or q12h) but not the mix. The mix below was chosen to reproduce the reported mean and standard deviation, and that reproduction is asserted in the chunk.
# set.seed() seeds R's RNG, which is what draws the covariates below. It does
# NOT seed rxode2's simulation RNG (that draws etalcl, and its streams are
# partitioned per solver thread), so the cohort's covariates are reproducible
# but its etas are not. Every assertion downstream is either a per-subject
# algebraic identity or a typical-value replication, so none of them depends on
# which etas were drawn. See pattern 12 of
# references/known-vignette-failure-patterns.md.
set.seed(20240701)
rxode2::rxSetSeed(20240701)

n_sub <- 101L

# Regimen mix: 15 / 76 / 7 / 3 reproduces the Table 1 daily-dose mean and SD.
regimens <- tibble::tribble(
  ~regimen,        ~amt,  ~tau, ~n,
  "1000 mg q12h",  1000,    12, 15L,
  "1000 mg q8h",   1000,     8, 76L,
  "2000 mg q12h",  2000,    12,  7L,
  "2000 mg q8h",   2000,     8,  3L
)
stopifnot(sum(regimens$n) == n_sub)

subj <- regimens |>
  dplyr::mutate(daily = amt * 24 / tau) |>
  tidyr::uncount(n) |>
  dplyr::mutate(id = seq_len(dplyr::n()))

# Table 1: total daily dose 3,000 +/- 692.82 mg/day, range 2,000 - 6,000.
stopifnot(
  abs(mean(subj$daily) - 3000) < 50,
  abs(stats::sd(subj$daily) - 692.82) < 50,
  min(subj$daily) == 2000,
  max(subj$daily) == 6000
)

# Serum creatinine: Table 1 mean 94.47 +/- 63.68 umol/L, range 40 - 452. The
# marginal is strongly right-skewed, so a log-normal matched on the mean and SD
# and truncated to the reported range is used.
creat_cv    <- 63.68 / 94.47
creat_sdlog <- sqrt(log(1 + creat_cv^2))
creat_mulog <- log(94.47) - creat_sdlog^2 / 2
subj$CREAT <- pmin(452, pmax(40, stats::rlnorm(n_sub, creat_mulog, creat_sdlog)))

# Leukocyte count: NOT reported by the paper (see prose above). Assumed.
subj$WBC <- pmin(40, pmax(2, stats::rlnorm(n_sub, log(10.8), sqrt(log(1 + 0.45^2)))))

# Comorbidity and comedication indicators, at the Table 1 prevalences. The
# vancomycin and colistimethate flags are NOT mutually exclusive: 17 patients
# received vancomycin, 7 colistin, and 3 both, so 14 / 4 / 3 / 80.
subj$DIS_HYPERT <- 0
subj$DIS_HYPERT[sample.int(n_sub, 33L)] <- 1        # 33/101 = 32.7%

combo <- sample.int(n_sub, 21L)
subj$CONMED_VANCOMYCIN     <- 0
subj$CONMED_COLISTIMETHATE <- 0
subj$CONMED_VANCOMYCIN[combo[1:14]]      <- 1       # vancomycin only
subj$CONMED_COLISTIMETHATE[combo[15:18]] <- 1       # colistimethate only
subj$CONMED_VANCOMYCIN[combo[19:21]]     <- 1       # both
subj$CONMED_COLISTIMETHATE[combo[19:21]] <- 1

stopifnot(
  sum(subj$DIS_HYPERT) == 33L,
  sum(subj$CONMED_VANCOMYCIN) == 17L,
  sum(subj$CONMED_COLISTIMETHATE) == 7L,
  sum(subj$CONMED_VANCOMYCIN == 1 & subj$CONMED_COLISTIMETHATE == 1) == 3L
)

knitr::kable(
  subj |>
    dplyr::group_by(regimen) |>
    dplyr::summarise(
      n              = dplyr::n(),
      `Daily dose`   = unique(daily),
      `Median CREAT` = round(stats::median(CREAT), 1),
      `Median WBC`   = round(stats::median(WBC), 1),
      .groups = "drop"
    ),
  caption = "Virtual cohort by regimen (n = 101, matching the published cohort size)."
)
Virtual cohort by regimen (n = 101, matching the published cohort size).
regimen n Daily dose Median CREAT Median WBC
1000 mg q12h 15 2000 102.7 9.7
1000 mg q8h 76 3000 68.1 10.5
2000 mg q12h 7 4000 101.1 9.6
2000 mg q8h 3 6000 99.2 13.2

The paper’s inclusion criterion was at least three days of continuous therapy, so every subject is dosed for 72 h and the final dosing interval is the one analysed.

# Infusion duration is NOT stated: Methods 2.2 says only "intermittent
# intravenous infusion", with the first sample drawn 5 - 30 min after its end.
# A 30-minute infusion is assumed (see Assumptions and deviations).
inf_dur <- 0.5

# Dense early sampling is needed because the published volume implies a
# ~0.4 h half-life; a coarse grid would understate AUC and mis-fit half-life.
obs_grid <- function(tau) {
  sort(unique(c(seq(0, 1, by = 0.02), seq(1, 4, by = 0.05), seq(4, tau, by = 0.25))))
}

make_subject <- function(row) {
  dose_times <- seq(0, 72 - row$tau, by = row$tau)
  last_dose  <- max(dose_times)
  doses <- tibble::tibble(
    time = dose_times, amt = row$amt, evid = 1L, rate = row$amt / inf_dur,
    cmt = "central"
  )
  # cmt on an observation row must be an ODE STATE name, never the algebraic
  # observable "Cc" (that auto-injects a compartment slot and renumbers the
  # model). rxode2 returns Cc as a column regardless.
  obs <- tibble::tibble(
    time = last_dose + obs_grid(row$tau), amt = NA_real_, evid = 0L,
    rate = NA_real_, cmt = "central"
  )
  dplyr::bind_rows(doses, obs) |>
    dplyr::mutate(
      id = row$id, regimen = row$regimen, last_dose = last_dose, tau = row$tau,
      CREAT = row$CREAT, WBC = row$WBC, DIS_HYPERT = row$DIS_HYPERT,
      CONMED_VANCOMYCIN = row$CONMED_VANCOMYCIN,
      CONMED_COLISTIMETHATE = row$CONMED_COLISTIMETHATE
    )
}

events <- do.call(
  dplyr::bind_rows,
  lapply(seq_len(nrow(subj)), function(i) make_subject(subj[i, ]))
) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

# Disjoint (id, time, evid) keys guard against the silent multi-cohort ID
# collision that merges subjects and doubles the dose.
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Rancic_2024_meropenem")

# Tight solver tolerances: the published volume gives a ~0.4 h half-life, so
# the trough at the end of an 8 - 12 h interval is ~1e-9 of the peak. At
# default tolerances that tail is solver noise and can go negative, which makes
# PKNCA's log-down trapezoid return NaN.
sim <- rxode2::rxSolve(
  mod, events = events,
  keep   = c("regimen", "last_dose", "tau"),
  atol   = 1e-14, rtol = 1e-12,
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'

# `Cc` is the IPRED (no residual error); `sim`/`ipredSim` columns carry it.
stopifnot(all(sim$Cc >= 0, na.rm = TRUE))

Replicating the published clearance equation

The strictest available check on the transcription is the clearance equation itself: it is printed in full in the Abstract and every coefficient is tabulated in Table 3. The model’s typical-value clearance is compared against a direct evaluation of the published equation over a grid of covariate scenarios. This is a pure algebraic identity – the two sides use the same numbers – so the tolerance is at machine precision, not a cohort-derived envelope.

scen <- tidyr::expand_grid(
  CREAT                 = c(40, 94.47, 452),
  WBC                   = c(2, 7.4, 10.8, 25),
  DIS_HYPERT            = c(0, 1),
  CONMED_VANCOMYCIN     = c(0, 1),
  CONMED_COLISTIMETHATE = c(0, 1)
) |>
  dplyr::mutate(id = seq_len(dplyr::n()))

# The published equation, typed out from the Abstract of Rancic 2024.
published_cl <- function(CRE, WBC, HTA, VAN, COL) {
  5.29 * CRE^0.000001 * WBC^(-0.165) +
    0.000001 * HTA + 0.825 * VAN + 1.28 * COL
}
scen$CL_published <- published_cl(
  scen$CREAT, scen$WBC, scen$DIS_HYPERT,
  scen$CONMED_VANCOMYCIN, scen$CONMED_COLISTIMETHATE
)

mod_typ <- rxode2::zeroRe(rxode2::rxode(mod), "omega")
#> ℹ parameter labels from comments will be replaced by 'label()'
ev_typ <- scen |>
  dplyr::mutate(time = 0, amt = 1000, evid = 1L, rate = 2000, cmt = "central")
sim_typ <- rxode2::rxSolve(mod_typ, ev_typ, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalcl'
#> Warning: multi-subject simulation without without 'omega'
#> Warning: column 'CREAT' has only 'NA' values for id '1'
#> Warning: column 'WBC' has only 'NA' values for id '1'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '1'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '1'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '1'
#> Warning: column 'CREAT' has only 'NA' values for id '2'
#> Warning: column 'WBC' has only 'NA' values for id '2'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '2'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '2'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '2'
#> Warning: column 'CREAT' has only 'NA' values for id '3'
#> Warning: column 'WBC' has only 'NA' values for id '3'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '3'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '3'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '3'
#> Warning: column 'CREAT' has only 'NA' values for id '4'
#> Warning: column 'WBC' has only 'NA' values for id '4'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '4'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '4'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '4'
#> Warning: column 'CREAT' has only 'NA' values for id '5'
#> Warning: column 'WBC' has only 'NA' values for id '5'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '5'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '5'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '5'
#> Warning: column 'CREAT' has only 'NA' values for id '6'
#> Warning: column 'WBC' has only 'NA' values for id '6'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '6'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '6'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '6'
#> Warning: column 'CREAT' has only 'NA' values for id '7'
#> Warning: column 'WBC' has only 'NA' values for id '7'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '7'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '7'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '7'
#> Warning: column 'CREAT' has only 'NA' values for id '8'
#> Warning: column 'WBC' has only 'NA' values for id '8'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '8'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '8'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '8'
#> Warning: column 'CREAT' has only 'NA' values for id '9'
#> Warning: column 'WBC' has only 'NA' values for id '9'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '9'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '9'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '9'
#> Warning: column 'CREAT' has only 'NA' values for id '10'
#> Warning: column 'WBC' has only 'NA' values for id '10'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '10'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '10'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '10'
#> Warning: column 'CREAT' has only 'NA' values for id '11'
#> Warning: column 'WBC' has only 'NA' values for id '11'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '11'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '11'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '11'
#> Warning: column 'CREAT' has only 'NA' values for id '12'
#> Warning: column 'WBC' has only 'NA' values for id '12'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '12'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '12'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '12'
#> Warning: column 'CREAT' has only 'NA' values for id '13'
#> Warning: column 'WBC' has only 'NA' values for id '13'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '13'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '13'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '13'
#> Warning: column 'CREAT' has only 'NA' values for id '14'
#> Warning: column 'WBC' has only 'NA' values for id '14'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '14'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '14'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '14'
#> Warning: column 'CREAT' has only 'NA' values for id '15'
#> Warning: column 'WBC' has only 'NA' values for id '15'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '15'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '15'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '15'
#> Warning: column 'CREAT' has only 'NA' values for id '16'
#> Warning: column 'WBC' has only 'NA' values for id '16'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '16'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '16'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '16'
#> Warning: column 'CREAT' has only 'NA' values for id '17'
#> Warning: column 'WBC' has only 'NA' values for id '17'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '17'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '17'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '17'
#> Warning: column 'CREAT' has only 'NA' values for id '18'
#> Warning: column 'WBC' has only 'NA' values for id '18'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '18'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '18'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '18'
#> Warning: column 'CREAT' has only 'NA' values for id '19'
#> Warning: column 'WBC' has only 'NA' values for id '19'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '19'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '19'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '19'
#> Warning: column 'CREAT' has only 'NA' values for id '20'
#> Warning: column 'WBC' has only 'NA' values for id '20'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '20'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '20'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '20'
#> Warning: column 'CREAT' has only 'NA' values for id '21'
#> Warning: column 'WBC' has only 'NA' values for id '21'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '21'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '21'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '21'
#> Warning: column 'CREAT' has only 'NA' values for id '22'
#> Warning: column 'WBC' has only 'NA' values for id '22'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '22'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '22'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '22'
#> Warning: column 'CREAT' has only 'NA' values for id '23'
#> Warning: column 'WBC' has only 'NA' values for id '23'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '23'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '23'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '23'
#> Warning: column 'CREAT' has only 'NA' values for id '24'
#> Warning: column 'WBC' has only 'NA' values for id '24'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '24'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '24'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '24'
#> Warning: column 'CREAT' has only 'NA' values for id '25'
#> Warning: column 'WBC' has only 'NA' values for id '25'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '25'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '25'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '25'
#> Warning: column 'CREAT' has only 'NA' values for id '26'
#> Warning: column 'WBC' has only 'NA' values for id '26'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '26'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '26'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '26'
#> Warning: column 'CREAT' has only 'NA' values for id '27'
#> Warning: column 'WBC' has only 'NA' values for id '27'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '27'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '27'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '27'
#> Warning: column 'CREAT' has only 'NA' values for id '28'
#> Warning: column 'WBC' has only 'NA' values for id '28'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '28'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '28'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '28'
#> Warning: column 'CREAT' has only 'NA' values for id '29'
#> Warning: column 'WBC' has only 'NA' values for id '29'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '29'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '29'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '29'
#> Warning: column 'CREAT' has only 'NA' values for id '30'
#> Warning: column 'WBC' has only 'NA' values for id '30'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '30'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '30'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '30'
#> Warning: column 'CREAT' has only 'NA' values for id '31'
#> Warning: column 'WBC' has only 'NA' values for id '31'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '31'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '31'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '31'
#> Warning: column 'CREAT' has only 'NA' values for id '32'
#> Warning: column 'WBC' has only 'NA' values for id '32'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '32'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '32'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '32'
#> Warning: column 'CREAT' has only 'NA' values for id '33'
#> Warning: column 'WBC' has only 'NA' values for id '33'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '33'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '33'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '33'
#> Warning: column 'CREAT' has only 'NA' values for id '34'
#> Warning: column 'WBC' has only 'NA' values for id '34'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '34'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '34'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '34'
#> Warning: column 'CREAT' has only 'NA' values for id '35'
#> Warning: column 'WBC' has only 'NA' values for id '35'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '35'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '35'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '35'
#> Warning: column 'CREAT' has only 'NA' values for id '36'
#> Warning: column 'WBC' has only 'NA' values for id '36'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '36'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '36'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '36'
#> Warning: column 'CREAT' has only 'NA' values for id '37'
#> Warning: column 'WBC' has only 'NA' values for id '37'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '37'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '37'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '37'
#> Warning: column 'CREAT' has only 'NA' values for id '38'
#> Warning: column 'WBC' has only 'NA' values for id '38'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '38'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '38'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '38'
#> Warning: column 'CREAT' has only 'NA' values for id '39'
#> Warning: column 'WBC' has only 'NA' values for id '39'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '39'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '39'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '39'
#> Warning: column 'CREAT' has only 'NA' values for id '40'
#> Warning: column 'WBC' has only 'NA' values for id '40'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '40'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '40'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '40'
#> Warning: column 'CREAT' has only 'NA' values for id '41'
#> Warning: column 'WBC' has only 'NA' values for id '41'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '41'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '41'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '41'
#> Warning: column 'CREAT' has only 'NA' values for id '42'
#> Warning: column 'WBC' has only 'NA' values for id '42'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '42'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '42'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '42'
#> Warning: column 'CREAT' has only 'NA' values for id '43'
#> Warning: column 'WBC' has only 'NA' values for id '43'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '43'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '43'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '43'
#> Warning: column 'CREAT' has only 'NA' values for id '44'
#> Warning: column 'WBC' has only 'NA' values for id '44'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '44'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '44'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '44'
#> Warning: column 'CREAT' has only 'NA' values for id '45'
#> Warning: column 'WBC' has only 'NA' values for id '45'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '45'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '45'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '45'
#> Warning: column 'CREAT' has only 'NA' values for id '46'
#> Warning: column 'WBC' has only 'NA' values for id '46'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '46'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '46'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '46'
#> Warning: column 'CREAT' has only 'NA' values for id '47'
#> Warning: column 'WBC' has only 'NA' values for id '47'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '47'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '47'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '47'
#> Warning: column 'CREAT' has only 'NA' values for id '48'
#> Warning: column 'WBC' has only 'NA' values for id '48'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '48'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '48'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '48'
#> Warning: column 'CREAT' has only 'NA' values for id '49'
#> Warning: column 'WBC' has only 'NA' values for id '49'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '49'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '49'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '49'
#> Warning: column 'CREAT' has only 'NA' values for id '50'
#> Warning: column 'WBC' has only 'NA' values for id '50'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '50'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '50'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '50'
#> Warning: column 'CREAT' has only 'NA' values for id '51'
#> Warning: column 'WBC' has only 'NA' values for id '51'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '51'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '51'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '51'
#> Warning: column 'CREAT' has only 'NA' values for id '52'
#> Warning: column 'WBC' has only 'NA' values for id '52'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '52'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '52'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '52'
#> Warning: column 'CREAT' has only 'NA' values for id '53'
#> Warning: column 'WBC' has only 'NA' values for id '53'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '53'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '53'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '53'
#> Warning: column 'CREAT' has only 'NA' values for id '54'
#> Warning: column 'WBC' has only 'NA' values for id '54'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '54'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '54'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '54'
#> Warning: column 'CREAT' has only 'NA' values for id '55'
#> Warning: column 'WBC' has only 'NA' values for id '55'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '55'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '55'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '55'
#> Warning: column 'CREAT' has only 'NA' values for id '56'
#> Warning: column 'WBC' has only 'NA' values for id '56'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '56'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '56'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '56'
#> Warning: column 'CREAT' has only 'NA' values for id '57'
#> Warning: column 'WBC' has only 'NA' values for id '57'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '57'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '57'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '57'
#> Warning: column 'CREAT' has only 'NA' values for id '58'
#> Warning: column 'WBC' has only 'NA' values for id '58'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '58'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '58'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '58'
#> Warning: column 'CREAT' has only 'NA' values for id '59'
#> Warning: column 'WBC' has only 'NA' values for id '59'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '59'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '59'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '59'
#> Warning: column 'CREAT' has only 'NA' values for id '60'
#> Warning: column 'WBC' has only 'NA' values for id '60'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '60'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '60'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '60'
#> Warning: column 'CREAT' has only 'NA' values for id '61'
#> Warning: column 'WBC' has only 'NA' values for id '61'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '61'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '61'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '61'
#> Warning: column 'CREAT' has only 'NA' values for id '62'
#> Warning: column 'WBC' has only 'NA' values for id '62'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '62'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '62'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '62'
#> Warning: column 'CREAT' has only 'NA' values for id '63'
#> Warning: column 'WBC' has only 'NA' values for id '63'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '63'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '63'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '63'
#> Warning: column 'CREAT' has only 'NA' values for id '64'
#> Warning: column 'WBC' has only 'NA' values for id '64'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '64'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '64'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '64'
#> Warning: column 'CREAT' has only 'NA' values for id '65'
#> Warning: column 'WBC' has only 'NA' values for id '65'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '65'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '65'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '65'
#> Warning: column 'CREAT' has only 'NA' values for id '66'
#> Warning: column 'WBC' has only 'NA' values for id '66'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '66'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '66'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '66'
#> Warning: column 'CREAT' has only 'NA' values for id '67'
#> Warning: column 'WBC' has only 'NA' values for id '67'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '67'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '67'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '67'
#> Warning: column 'CREAT' has only 'NA' values for id '68'
#> Warning: column 'WBC' has only 'NA' values for id '68'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '68'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '68'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '68'
#> Warning: column 'CREAT' has only 'NA' values for id '69'
#> Warning: column 'WBC' has only 'NA' values for id '69'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '69'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '69'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '69'
#> Warning: column 'CREAT' has only 'NA' values for id '70'
#> Warning: column 'WBC' has only 'NA' values for id '70'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '70'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '70'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '70'
#> Warning: column 'CREAT' has only 'NA' values for id '71'
#> Warning: column 'WBC' has only 'NA' values for id '71'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '71'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '71'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '71'
#> Warning: column 'CREAT' has only 'NA' values for id '72'
#> Warning: column 'WBC' has only 'NA' values for id '72'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '72'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '72'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '72'
#> Warning: column 'CREAT' has only 'NA' values for id '73'
#> Warning: column 'WBC' has only 'NA' values for id '73'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '73'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '73'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '73'
#> Warning: column 'CREAT' has only 'NA' values for id '74'
#> Warning: column 'WBC' has only 'NA' values for id '74'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '74'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '74'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '74'
#> Warning: column 'CREAT' has only 'NA' values for id '75'
#> Warning: column 'WBC' has only 'NA' values for id '75'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '75'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '75'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '75'
#> Warning: column 'CREAT' has only 'NA' values for id '76'
#> Warning: column 'WBC' has only 'NA' values for id '76'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '76'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '76'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '76'
#> Warning: column 'CREAT' has only 'NA' values for id '77'
#> Warning: column 'WBC' has only 'NA' values for id '77'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '77'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '77'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '77'
#> Warning: column 'CREAT' has only 'NA' values for id '78'
#> Warning: column 'WBC' has only 'NA' values for id '78'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '78'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '78'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '78'
#> Warning: column 'CREAT' has only 'NA' values for id '79'
#> Warning: column 'WBC' has only 'NA' values for id '79'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '79'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '79'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '79'
#> Warning: column 'CREAT' has only 'NA' values for id '80'
#> Warning: column 'WBC' has only 'NA' values for id '80'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '80'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '80'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '80'
#> Warning: column 'CREAT' has only 'NA' values for id '81'
#> Warning: column 'WBC' has only 'NA' values for id '81'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '81'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '81'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '81'
#> Warning: column 'CREAT' has only 'NA' values for id '82'
#> Warning: column 'WBC' has only 'NA' values for id '82'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '82'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '82'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '82'
#> Warning: column 'CREAT' has only 'NA' values for id '83'
#> Warning: column 'WBC' has only 'NA' values for id '83'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '83'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '83'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '83'
#> Warning: column 'CREAT' has only 'NA' values for id '84'
#> Warning: column 'WBC' has only 'NA' values for id '84'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '84'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '84'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '84'
#> Warning: column 'CREAT' has only 'NA' values for id '85'
#> Warning: column 'WBC' has only 'NA' values for id '85'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '85'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '85'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '85'
#> Warning: column 'CREAT' has only 'NA' values for id '86'
#> Warning: column 'WBC' has only 'NA' values for id '86'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '86'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '86'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '86'
#> Warning: column 'CREAT' has only 'NA' values for id '87'
#> Warning: column 'WBC' has only 'NA' values for id '87'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '87'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '87'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '87'
#> Warning: column 'CREAT' has only 'NA' values for id '88'
#> Warning: column 'WBC' has only 'NA' values for id '88'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '88'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '88'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '88'
#> Warning: column 'CREAT' has only 'NA' values for id '89'
#> Warning: column 'WBC' has only 'NA' values for id '89'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '89'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '89'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '89'
#> Warning: column 'CREAT' has only 'NA' values for id '90'
#> Warning: column 'WBC' has only 'NA' values for id '90'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '90'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '90'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '90'
#> Warning: column 'CREAT' has only 'NA' values for id '91'
#> Warning: column 'WBC' has only 'NA' values for id '91'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '91'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '91'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '91'
#> Warning: column 'CREAT' has only 'NA' values for id '92'
#> Warning: column 'WBC' has only 'NA' values for id '92'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '92'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '92'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '92'
#> Warning: column 'CREAT' has only 'NA' values for id '93'
#> Warning: column 'WBC' has only 'NA' values for id '93'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '93'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '93'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '93'
#> Warning: column 'CREAT' has only 'NA' values for id '94'
#> Warning: column 'WBC' has only 'NA' values for id '94'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '94'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '94'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '94'
#> Warning: column 'CREAT' has only 'NA' values for id '95'
#> Warning: column 'WBC' has only 'NA' values for id '95'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '95'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '95'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '95'
#> Warning: column 'CREAT' has only 'NA' values for id '96'
#> Warning: column 'WBC' has only 'NA' values for id '96'
#> Warning: column 'DIS_HYPERT' has only 'NA' values for id '96'
#> Warning: column 'CONMED_VANCOMYCIN' has only 'NA' values for id '96'
#> Warning: column 'CONMED_COLISTIMETHATE' has only 'NA' values for id '96'

cl_model <- sim_typ |>
  dplyr::group_by(id) |>
  dplyr::summarise(CL_model = dplyr::first(cl), V_model = dplyr::first(vc),
                   .groups = "drop")

cmp_cl <- dplyr::left_join(scen, cl_model, by = "id")
rel_err <- abs(cmp_cl$CL_model - cmp_cl$CL_published) / cmp_cl$CL_published

cat(sprintf(
  "Clearance-equation replication over %d covariate scenarios: max relative error %.3g\n",
  nrow(cmp_cl), max(rel_err)
))
#> Clearance-equation replication over 96 covariate scenarios: max relative error 2.14e-15
# Algebraic identity, not a simulated statistic: machine precision is correct.
stopifnot(max(rel_err) < 1e-10)

# The volume carries no covariates, so it must be exactly 2.05 L everywhere.
stopifnot(max(abs(cmp_cl$V_model - 2.05)) < 1e-10)
cmp_cl |>
  dplyr::filter(CREAT == 94.47, WBC %in% c(7.4, 10.8)) |>
  dplyr::transmute(
    `CREAT (umol/L)`      = CREAT,
    `WBC (10^9/L)`        = WBC,
    HTA                   = DIS_HYPERT,
    VAN                   = CONMED_VANCOMYCIN,
    COL                   = CONMED_COLISTIMETHATE,
    `CL published (L/h)`  = round(CL_published, 4),
    `CL model (L/h)`      = round(CL_model, 4)
  ) |>
  knitr::kable(
    caption = paste(
      "Typical-value clearance from the packaged model against a direct",
      "evaluation of the Rancic 2024 Abstract equation, at the cohort-mean",
      "creatinine. The CREAT exponent of 1e-6 makes the creatinine term",
      "1.0000 to four decimal places at every plausible value, which is why",
      "the covariate is numerically inert."
    )
  )
Typical-value clearance from the packaged model against a direct evaluation of the Rancic 2024 Abstract equation, at the cohort-mean creatinine. The CREAT exponent of 1e-6 makes the creatinine term 1.0000 to four decimal places at every plausible value, which is why the covariate is numerically inert.
CREAT (umol/L) WBC (10^9/L) HTA VAN COL CL published (L/h) CL model (L/h)
94.47 7.4 0 0 0 3.8022 3.8022
94.47 7.4 0 0 1 5.0822 5.0822
94.47 7.4 0 1 0 4.6272 4.6272
94.47 7.4 0 1 1 5.9072 5.9072
94.47 7.4 1 0 0 3.8022 3.8022
94.47 7.4 1 0 1 5.0822 5.0822
94.47 7.4 1 1 0 4.6272 4.6272
94.47 7.4 1 1 1 5.9072 5.9072
94.47 10.8 0 0 0 3.5723 3.5723
94.47 10.8 0 0 1 4.8523 4.8523
94.47 10.8 0 1 0 4.3973 4.3973
94.47 10.8 0 1 1 5.6773 5.6773
94.47 10.8 1 0 0 3.5723 3.5723
94.47 10.8 1 0 1 4.8523 4.8523
94.47 10.8 1 1 0 4.3973 4.3973
94.47 10.8 1 1 1 5.6773 5.6773

Two facts about the covariate model are visible in that table. First, the creatinine and hypertension effects are estimated at (essentially) zero and change clearance by less than one part in 10^5, even though both survived backward deletion at p < 0.01. Second, the vancomycin and colistimethate effects are additive shifts, so at a typical clearance near 3.6 L/h they are worth +23% and +36% respectively, and +59% together.

Steady-state profiles 

# rxSolve returns observation records only (dose rows are not echoed back), so
# every row here is already an observation.
sim_int <- sim |>
  dplyr::mutate(tad = time - last_dose)

sim_int |>
  dplyr::group_by(regimen, tad) |>
  dplyr::summarise(
    Q05 = stats::quantile(Cc, 0.05), Q50 = stats::median(Cc),
    Q95 = stats::quantile(Cc, 0.95), .groups = "drop"
  ) |>
  ggplot(aes(tad, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  geom_hline(yintercept = c(40.69, 12.55), linetype = "dashed", colour = "firebrick") +
  facet_wrap(~regimen) +
  scale_y_log10() +
  labs(
    x = "Time after the last dose (h)", y = "Meropenem Cc (mg/L, log scale)",
    caption = "Dashed lines: mean observed C1 and C2 from Rancic 2024 Table 1."
  ) +
  theme_bw()
Simulated steady-state meropenem profiles over the final dosing interval, by regimen. Ribbons are the 5th - 95th percentiles across the 101-subject cohort; the dashed lines mark the mean concentrations the paper actually observed (40.69 mg/L 5 - 30 min after the end of the infusion, 12.55 mg/L 3 - 4 h after it).

Simulated steady-state meropenem profiles over the final dosing interval, by regimen. Ribbons are the 5th - 95th percentiles across the 101-subject cohort; the dashed lines mark the mean concentrations the paper actually observed (40.69 mg/L 5 - 30 min after the end of the infusion, 12.55 mg/L 3 - 4 h after it).

The predicted profile is far more peaked than the observed concentrations: it overshoots the observed peak and has already fallen below the observed 3 - 4 h concentration by about an hour. That is the signature of an under-estimated volume with a correctly estimated clearance, and it is quantified in the Errata below.

PKNCA validation 

# Only `!is.na(Cc)` -- adding `time > 0` or `Cc > 0` would drop the time-zero
# row that anchors AUC.
sim_nca <- sim_int |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, regimen, tau, time = tad, Cc)

# Time-zero row is produced by the observation grid itself (obs_grid starts at
# 0); assert it rather than assume it.
stopifnot(
  sim_nca |> dplyr::group_by(id) |> dplyr::summarise(has0 = any(time == 0)) |>
    dplyr::pull(has0) |> all()
)

conc_obj <- PKNCA::PKNCAconc(as.data.frame(sim_nca), Cc ~ time | regimen + id)

dose_df <- sim_int |>
  dplyr::distinct(id, regimen) |>
  dplyr::left_join(subj |> dplyr::select(id, amt), by = "id") |>
  dplyr::mutate(time = 0)
dose_obj <- PKNCA::PKNCAdose(as.data.frame(dose_df), amt ~ time | regimen + id)

# One interval per regimen, spanning that regimen's dosing interval.
intervals <- regimens |>
  dplyr::transmute(
    regimen, start = 0, end = tau,
    cmax = TRUE, tmax = TRUE, auclast = TRUE, ctrough = TRUE, half.life = TRUE
  ) |>
  as.data.frame()

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_wide <- as.data.frame(nca_res) |>
  dplyr::select(regimen, id, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)
stopifnot(nrow(nca_wide) == n_sub, !anyNA(nca_wide$auclast), !anyNA(nca_wide$half.life))

Internal identities

These two checks compare the NCA output against closed forms built from each subject’s own simulated cl and vc. Both sides use the same drawn parameters, so the only difference is numerical (trapezoidal and log-linear regression error) and a tight bound is the correct assertion – these are not cohort statistics whose spread depends on which etas were drawn.

per_subj <- sim_int |>
  dplyr::group_by(id, regimen, tau) |>
  dplyr::summarise(cl = dplyr::first(cl), vc = dplyr::first(vc), .groups = "drop") |>
  dplyr::left_join(subj |> dplyr::select(id, amt), by = "id") |>
  dplyr::left_join(nca_wide, by = c("id", "regimen")) |>
  dplyr::mutate(
    auc_closed  = amt / cl,                 # steady-state AUC over one interval
    thalf_closed = log(2) * vc / cl,
    auc_pct     = 100 * (auclast - auc_closed) / auc_closed,
    thalf_pct   = 100 * (half.life - thalf_closed) / thalf_closed,
    accum       = 1 / (1 - exp(-(cl / vc) * tau))
  )

cat(sprintf("AUC over the interval vs Dose/CL: median %.4f%%, max |diff| %.4f%%\n",
            stats::median(per_subj$auc_pct), max(abs(per_subj$auc_pct))))
#> AUC over the interval vs Dose/CL: median -0.0074%, max |diff| 0.0190%
cat(sprintf("NCA half-life vs log(2)*V/CL:     median %.4f%%, max |diff| %.4f%%\n",
            stats::median(per_subj$thalf_pct), max(abs(per_subj$thalf_pct))))
#> NCA half-life vs log(2)*V/CL:     median 0.0000%, max |diff| 0.0000%
cat(sprintf("Steady-state accumulation factor: max %.8f (1.0 = no accumulation)\n",
            max(per_subj$accum)))
#> Steady-state accumulation factor: max 1.00001773 (1.0 = no accumulation)

stopifnot(
  # Trapezoidal / log-down error on a dense grid over a mono-exponential decay.
  # Realised max 0.017%; the error scales with (k*h)^3 and k varies with the
  # drawn etas (14.7% CV), so 0.2% leaves an order of magnitude of headroom.
  max(abs(per_subj$auc_pct)) < 0.2,
  # Log-linear terminal fit against the analytic half-life. A log-linear
  # regression on a mono-exponential decay recovers log(2)/k exactly whatever k
  # is, so this realises 0.0000% and does not widen with the eta draw.
  max(abs(per_subj$thalf_pct)) < 0.05,
  # With a ~0.4 h half-life and an 8 - 12 h interval, the model accumulates not
  # at all, so a single interval IS the steady-state interval. Realised
  # ~1 + 1e-5 across the cohort; 1.001 leaves three orders of magnitude of
  # headroom over the eta spread while still going red for any volume large
  # enough to matter (V = 21 L would give an accumulation factor of ~1.35).
  max(per_subj$accum) < 1.001
)
per_subj |>
  dplyr::group_by(regimen) |>
  dplyr::summarise(
    n              = dplyr::n(),
    `Cmax (mg/L)`  = round(stats::median(cmax), 1),
    `Tmax (h)`     = round(stats::median(tmax), 2),
    `AUCtau (mg*h/L)` = round(stats::median(auclast), 1),
    `Ctrough (mg/L)`  = signif(stats::median(ctrough), 3),
    `t1/2 (h)`     = round(stats::median(half.life), 3),
    `CL (L/h)`     = round(stats::median(cl), 2),
    .groups = "drop"
  ) |>
  knitr::kable(caption = "Simulated steady-state NCA by regimen (median across the cohort).")
Simulated steady-state NCA by regimen (median across the cohort).
regimen n Cmax (mg/L) Tmax (h) AUCtau (mg*h/L) Ctrough (mg/L) t1/2 (h) CL (L/h)
1000 mg q12h 15 306.9 0.5 241.2 0.00e+00 0.343 4.15
1000 mg q8h 76 318.2 0.5 263.5 2.97e-04 0.374 3.79
2000 mg q12h 7 657.8 0.5 575.3 2.20e-06 0.409 3.48
2000 mg q8h 3 667.3 0.5 598.8 3.30e-03 0.425 3.34

Comparison against the published concentrations

Rancic 2024 reports no NCA parameters, but Table 1 reports the two observed concentrations per patient, and the first of them – drawn 5 - 30 min after the end of the infusion – is a direct observation of Cmax for an intravenous infusion. It is compared against the simulated Cmax below.

# Table 1: C1 = 40.69 +/- 16.67 mg/L, drawn 5 - 30 min after the end of the
# infusion, pooled over all regimens.
published <- tibble::tibble(regimen = regimens$regimen, cmax = 40.69)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = "regimen",
  params        = "cmax",
  units         = c(cmax = "mg/L"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = paste(
    "Simulated steady-state Cmax against the mean concentration Rancic 2024",
    "observed 5 - 30 min after the end of the infusion (Table 1).",
    "* marks a difference above 20%. Every row is starred; this is a known,",
    "reproducible deviation of the published model from the paper's own data",
    "and is analysed in the Errata below. No parameter was tuned."
  )
)
Simulated steady-state Cmax against the mean concentration Rancic 2024 observed 5 - 30 min after the end of the infusion (Table 1). * marks a difference above 20%. Every row is starred; this is a known, reproducible deviation of the published model from the paper’s own data and is analysed in the Errata below. No parameter was tuned.
NCA parameter regimen Reference Simulated % diff
Cmax (mg/L) 1000 mg q12h 40.7 307 +654.3%*
Cmax (mg/L) 1000 mg q8h 40.7 318 +681.9%*
Cmax (mg/L) 2000 mg q12h 40.7 658 +1516.6%*
Cmax (mg/L) 2000 mg q8h 40.7 667 +1540.1%* 
# NOTE ON THE DIRECTION OF THE ARGUMENT. For a one-compartment model the peak
# is Dose/V, so a SMALL volume makes concentrations too HIGH. The observed
# peaks therefore bound V from ABOVE, not below: C <= Dose/V rearranges to
# V <= Dose/C, i.e. the largest observed peak gives V <= 1000/88.95 = 11.2 L,
# which 2.05 L satisfies. A ceiling argument does NOT falsify the published
# volume, and it is worth being explicit about that because the inequality is
# easy to state backwards.
#
# What does falsify 2.05 L is that the model then MISSES the paper's own data
# in two independent, direction-safe ways.

# Typical clearance at the cohort-average covariates (this reproduces the
# paper's own base-model value of 3.80 L/h).
cl_typ <- 5.29 * 10.8^(-0.165) + 0.825 * 0.168 + 1.28 * 0.069

# (a) DECAY RATE -- the strongest check, because the observed side never
#     references V. Two samples per patient pin the elimination rate constant
#     directly: kel = log(C1/C2) / dt. Table 1 gives C1 = 40.69 mg/L and
#     C2 = 12.55 mg/L; Methods 2.2 draws the first 5 - 30 min after the end of
#     the infusion and the second 3 - 4 h after it, so dt spans 2.5 - 3.92 h.
#     The SHORTEST dt gives the fastest decay and hence the SMALLEST implied
#     volume, so it is the conservative end of the range.
dt_obs       <- c(short = 3 - 0.5, long = 4 - 1 / 12)
kel_obs      <- log(40.69 / 12.55) / dt_obs
v_from_decay <- cl_typ / kel_obs

# (b) PEAK MAGNITUDE -- to REPRODUCE (not merely exceed) the mean observed peak
#     at the smallest dose used, the model needs V = Dose / C.
v_from_peak <- 1000 / 40.69

cat(sprintf("Published V                                 : %.2f L\n", 2.05))
#> Published V                                 : 2.05 L
cat(sprintf("V implied by the observed C1/C2 decay       : %.1f - %.1f L\n",
            min(v_from_decay), max(v_from_decay)))
#> V implied by the observed C1/C2 decay       : 8.1 - 12.7 L
cat(sprintf("V implied by the mean observed peak         : %.1f L\n", v_from_peak))
#> V implied by the mean observed peak         : 24.6 L
cat(sprintf("Literature value cited in the Introduction  : %d L\n", 21L))
#> Literature value cited in the Introduction  : 21 L
cat(sprintf("Model half-life, log(2)*V/CL                : %.2f h\n",
            log(2) * 2.05 / cl_typ))
#> Model half-life, log(2)*V/CL                : 0.37 h
cat(sprintf("Half-life implied by the observed decay     : %.2f - %.2f h\n",
            min(log(2) / kel_obs), max(log(2) / kel_obs)))
#> Half-life implied by the observed decay     : 1.47 - 2.31 h
cat(sprintf("Simulated median Cmax, 1000 mg q8h          : %.1f mg/L\n",
            stats::median(per_subj$cmax[per_subj$regimen == "1000 mg q8h"])))
#> Simulated median Cmax, 1000 mg q8h          : 318.2 mg/L

# Deterministic: every number above comes from the paper's own printed values,
# none from the simulated cohort. Both independent routes put the volume at
# least 3.5-fold above the published 2.05 L, at the conservative end of the
# sampling-time range.
stopifnot(
  min(v_from_decay) > 3.5 * 2.05,
  v_from_peak       > 3.5 * 2.05
)

Assumptions and deviations

  • Leukocyte-count units and distribution. The paper never states the units of WBC and Table 1 has no WBC row, yet WBC^(-0.165) is one of only two multiplicative covariate terms in the final model. The unit was settled by internal consistency rather than assumed: solving 5.29 * WBC^(-0.165) + 0.23 = 3.80 (the base model’s typical clearance, with 0.23 the cohort-average contribution of the additive vancomycin and colistimethate terms at their Table 1 prevalences) gives WBC = 10.8 x 10^9/L, a typical leukocytosis. On a cells/uL scale the same arithmetic would need WBC ~ 10,800 and would give a typical clearance of 1.13 L/h – less than a third of the base-model value – so cells/uL is excluded. The simulated distribution (log-normal, median 10.8, 45% CV, truncated to 2 - 40) is an assumption of this vignette, not a published one.
  • Infusion duration. Methods 2.2 says only “intermittent intravenous infusion”. A 30-minute infusion is assumed here, consistent with the first sample being drawn 5 - 30 min after its end. The assumption affects the simulated Cmax by only a few percent at the published half-life of 0.4 h; it does not affect AUC, clearance, or any assertion in this vignette.
  • Dosing-regimen mix. The paper reports the daily-dose mean, SD and range but not the mix of 1,000/2,000 mg and q8h/q12h. The 15/76/7/3 mix used here was chosen to reproduce the published mean and SD, which the cohort chunk asserts.
  • Creatinine distribution. A log-normal matched on the Table 1 mean and SD and truncated to the reported 40 - 452 umol/L range. Because the fitted creatinine exponent is 1e-6, this choice has no effect on any simulated quantity.
  • Screened-but-dropped comorbidities. Chronic renal failure, cerebral infarction, pneumonia and urinary tract infection are documented in the covariate-screen table above rather than given canonical covariate names, for the reason set out in that section.

Errata and internal inconsistencies in the source

The paper is internally inconsistent in four places. All four are recorded faithfully in the model file rather than corrected, and none was tuned.

1. The published volume of distribution is falsified by the paper’s own data. Table 3 reports V = 2.05 L (95% CI 2.039 - 2.061) and the bootstrap in Table 5 reports 1.809 L, so the value is reproducible within the paper and is not a single-cell typo. The base model’s 3.52 L is of the same order, so the discrepancy is systemic rather than a Table 3 misprint.

It is worth being precise about why 2.05 L is wrong, because the obvious argument runs the wrong way. For a one-compartment model the peak is Dose/V, so a small volume makes concentrations too high; C <= Dose/V rearranges to V <= Dose/C, meaning the observed peaks bound the volume from above (the largest reported peak, 88.95 mg/L at the smallest dose, gives V <= 11.2 L). A ceiling argument therefore does not rule out 2.05 L. What rules it out is that the model, at that volume, misses the paper’s own Table 1 in two independent directions:

  • Decay rate. The two samples per patient pin the elimination rate constant without reference to V at all: kel = log(C1/C2)/dt. With C1 = 40.69 mg/L, C2 = 12.55 mg/L and the 2.5 - 3.9 h sampling gap of Methods 2.2, the observed half-life is 1.7 - 2.7 h and the implied volume CL/kel is 8 - 13 L. The published model gives log(2)*V/CL = 0.4 h, four to five-fold too fast.
  • Peak magnitude. Reproducing (not merely exceeding) the mean observed peak of 40.69 mg/L at the smallest dose used requires V = 24.6 L.

Both routes put the volume several-fold above 2.05 L, and the literature value the paper’s own Introduction cites is 21 L. The consequence is visible in the figure and in the NCA comparison: simulated Cmax is roughly eight-fold above the observed mean peak, the simulated half-life is 0.4 h instead of the 1.7 - 2.7 h the observed C1/C2 pair implies, and the simulated 4-hour concentration is far below the observed one. Clearance is unaffected – Dose/(CL*tau) at the typical clearance gives an average steady-state concentration of about 35 mg/L against an observed mean of the two samples of 26.6 mg/L – so the model remains usable for clearance-driven quantities (AUC, total exposure, average concentration) and should not be used for peak, trough, or time-above-MIC without substituting a defensible volume.

2. The sign of the leukocyte effect contradicts the paper’s own prose. Table 3 reports the WBC exponent as -0.165 with a 95% CI of -0.219 to -0.110, i.e. clearance decreases as the leukocyte count rises, and the Abstract’s equation prints WBCs^(-0.165). The Discussion and Conclusion state the opposite: WBC is listed among “the factors that are significantly associated with increased clearance”. The signed estimate and its confidence interval are encoded, per the standing rule that a printed equation beats prose.

3. The variability terms are reported as variances but restated as percentages. Table 3 rows read “Inter-individual variance of CL (omega^2 CL) = 0.0215” and “Residual error variance (sigma^2 CL) = 0.44”, both with standard errors and confidence limits, while the Results prose says “Inter- and intra-individual variability were 2.15 and 44%, respectively” – i.e. it multiplies each variance by 100 and calls the product a percentage. The table’s explicit omega^2 / sigma^2 notation is taken as primary, so the model carries etalcl ~ 0.0215 (a 14.7% CV) and a residual SD of sqrt(0.44) = 0.6633.

The form of the residual needed a further decision. Methods 2.3 describes an “additive” residual on concentration, but an additive SD of 0.66 mg/L on the linear scale is 1.6% of the mean observed peak and cannot generate the paper’s own final-model RMSPE of 15.86 (Table 4) or its observed between-patient CVs of 41% on C1 and 61% on C2 (Table 1); it is roughly 25-fold too small. In NONMEM, an “additive” residual applied to log-transformed observations is exactly a proportional residual once back-transformed to the linear concentration scale, and that is how it is encoded here (Cc ~ prop(0.6633)). A user who wants the literal linear-scale additive reading can substitute Cc ~ add(0.6633) in a copy of the model file.

4. The bootstrap does not reproduce the final model. Table 5 reports the bootstrap means as “comparable to” the final model, but they are not: the clearance intercept is 3.864 against 5.29, the volume 1.809 against 2.05, and the WBC effect +0.001 against -0.165 – a sign change on the covariate that carries most of the covariate model. The bootstrap also reports five effects on the volume of distribution (theta16 - theta20) for which the final model reports no estimates at all. Only the Table 3 final-model estimates are encoded; the bootstrap column is not a second model and is not used.

Session information 

sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.4 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
#>  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
#>  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
#> [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
#> 
#> time zone: UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] ggplot2_4.0.3         tidyr_1.3.2           dplyr_1.2.1          
#> [4] rxode2_5.1.6          PKNCA_0.12.1          nlmixr2lib_0.3.2.9000
#> 
#> loaded via a namespace (and not attached):
#>  [1] gtable_0.3.6        xfun_0.60           bslib_0.12.0       
#>  [4] lattice_0.22-9      vctrs_0.7.3         tools_4.6.1        
#>  [7] generics_0.1.4      parallel_4.6.1      tibble_3.3.1       
#> [10] symengine_0.2.13    pkgconfig_2.0.3     data.table_1.18.6.1
#> [13] checkmate_2.3.4     RColorBrewer_1.1-3  S7_0.2.2           
#> [16] desc_1.4.3          RcppParallel_6.2.1  lifecycle_1.0.5    
#> [19] compiler_4.6.1      farver_2.1.2        textshaping_1.0.5  
#> [22] fontawesome_0.5.3   htmltools_0.5.9     sys_3.4.3          
#> [25] sass_0.4.10         yaml_2.3.12         pillar_1.11.1      
#> [28] pkgdown_2.2.1       crayon_1.5.3        jquerylib_0.1.4    
#> [31] whisker_0.4.1       openssl_2.4.2       cachem_1.1.0       
#> [34] nlme_3.1-169        tidyselect_1.2.1    digest_0.6.39      
#> [37] lotri_1.0.4         purrr_1.2.2         labeling_0.4.3     
#> [40] rxode2ll_2.0.16     fastmap_1.2.0       grid_4.6.1         
#> [43] cli_3.6.6           dparser_1.3.1-13    magrittr_2.0.5     
#> [46] withr_3.0.3         scales_1.4.0        backports_1.5.1    
#> [49] rmarkdown_2.32      otel_0.2.0          askpass_1.2.1      
#> [52] ragg_1.5.2          memoise_2.0.1       evaluate_1.0.5     
#> [55] knitr_1.52          rex_1.2.2           PreciseSums_0.7    
#> [58] rlang_1.3.0         downlit_0.4.5       Rcpp_1.1.2         
#> [61] glue_1.8.1          xml2_1.6.0          jsonlite_2.0.0     
#> [64] R6_2.6.1            systemfonts_1.3.2   fs_2.1.0