Skip to contents

Ceftazidime-avibactam in children (Franzese 2022)

Source: vignettes/articles/Franzese_2022_ceftazidime_avibactam.Rmd
Franzese_2022_ceftazidime_avibactam.Rmd

Model and source

Franzese 2022 extended the adult ceftazidime-avibactam population PK models of Li 2019 (see vignette("Li_2019_ceftazidime_avibactam") on the package site) to children aged 3 months to < 18 years by adding PK data from one single-dose phase I study and two multiple-dose phase II studies (complicated intra-abdominal infection, cIAI, and complicated urinary tract infection, cUTI). As in Li 2019, the two analytes were modelled separately – two NONMEM control streams, two data sets (9,628 observations from 2,130 subjects for ceftazidime, 14,223 from 2,403 for avibactam) and two parameter tables – so the extraction is two model files sharing this vignette.

uiCaz <- rxode2::rxode(readModelDb("Franzese_2022_ceftazidime"))
#> ℹ parameter labels from comments will be replaced by 'label()'
uiAvi <- rxode2::rxode(readModelDb("Franzese_2022_avibactam"))
#> ℹ parameter labels from comments will be replaced by 'label()'

Both are two-compartment models with first-order elimination after IV infusion. The pediatric adaptations shared by both analytes are body-weight scaling of all four disposition parameters, BSA-normalized creatinine clearance (NCrCL; bedside Schwartz in children, Cockcroft-Gault x 1.73 / BSA in adults) for subjects older than 2 years, and a Rhodin renal-maturation function of postmenstrual age that replaces NCrCL at 2 years and younger. The ceftazidime weight effect on clearance is a normalized Emax function rather than a power law.

Sources: the main text (Tables 1-4), the supplementary material (CPT-111-635-s001: both final NONMEM control streams, the derivation of the ceftazidime weight function, Tables S1-S3), and the 2024 erratum (doi:10.1002/cpt.3143), which corrects the Table 2 column headings – in the original the ceftazidime and avibactam headings were transposed. No parameter value is affected by the erratum.

Population

Pediatric baseline characteristics (Franzese 2022 Table 1).
Characteristic Phase I (any infection) Phase II cIAI Phase II cUTI Overall
N 32 58 63 153
Female, n (%) 17 (53.1) 16 (27.6) 52 (82.5) 85 (55.6)
Age, years, median (range) 5.7 (0.33-17.3) 10.5 (3.00-17.0) 3.8 (0.25-17.7) 7.57 (0.25-17.7)
Weight, kg, median (range) 20.6 (5.4-60.5) 37.9 (15.4-80.0) 15.3 (4.1-71.0) 25.0 (4.1-80.0)
NCrCL, mL/min/1.73 m^2, median (range) 130 (85.5-489) 107 (59-271) 89 (43-158) 104 (43-489)
Chinese, n (%) 0 6 (10.3) 12 (19.0) 18 (11.8)

The 153 children were added to the adult data sets of Li 2019 (adults with cIAI, cUTI or nosocomial pneumonia including ventilator-associated pneumonia, subjects with renal impairment, and healthy volunteers). No child with HAP/VAP was studied, and no child younger than 2 years was enrolled in the cIAI trial. Pediatric doses (2-hour infusions, Table S1) were 50-12.5 mg/kg q8h (maximum 2,000-500 mg) for children 6 months and older and 40-10 mg/kg q8h for 3 to < 6 months, halved for CrCL 30 to < 50 mL/min.

Source trace

Where every parameter and equation comes from.
Quantity Analyte Value Source
CL, Vc, Q, Vp Ceftazidime 7.75 L/h, 11.2 L, 5.33 L/h, 6.52 L Table S2 theta1-theta4
NCrCL slopes on CL (hinge 100, cap 150) Ceftazidime 0.0103036 / 0.00125182 Table S2 ‘Slope 1’ / ‘Slope 2’; control stream SLOPE1, SLOPE2, NCLCR cap
Emax weight effect on CL Ceftazidime WT50 = 53.5 kg, Hill 1, intercept 0 Table S2 theta14, theta15; Supplementary Methods derivation; control stream TH13
Weight exponents Q / Vc / Vp Ceftazidime 0.67 / 1 / 1 Results ‘Ceftazidime’; control stream TH12, TH5
cIAI and HAP/VAP on CL (bare multipliers) Ceftazidime 1.33 / 1.10 Table S2 theta16, theta17
cUTI and cIAI-or-HAP/VAP on Vc (bare multipliers) Ceftazidime 1.49 / 1.83 Table S2 theta20, theta21
Ventilator on Vc; Asian race on CL and Vc Ceftazidime +0.202; -0.136 (ASN), -0.0844 (CHN); -0.135 (Vc) Table S2 theta22, theta18, theta19, theta23
IIV variances CL, Vc, Q, Vp Ceftazidime 0.154, 0.108, 0.203, 0.0236 Table S2 eta rows; control stream $OMEGA
Residual SDs phase I / phase II-III Ceftazidime 0.172 + 125 ng/mL / 0.374 + 2,560 ng/mL Table S2 theta8-theta11
CL, Vc, Vp, Q Avibactam 10.7 L/h, 11.5 L, 7.56 L, 6.94 L/h Table S3 theta1-theta4
ESRD factor; dialysis CL Avibactam 0.0674; 21.1 L/h Table S3 theta5, theta6
NCrCL power below 80 / slope at or above 80 (cap 150) Avibactam 0.986 / 0.00344 Table S3 theta7, theta8; control stream CLCLCR
Weight exponents CL, Q / Vc, Vp Avibactam 0.67 / 1 Results ‘Avibactam’; control stream TH30, TH14
Adult phase II cIAI on Vc and CL Avibactam +2.17 / +0.431 Table S3 theta9, theta10
cUTI on Vc; phase III cIAI, HAP/VAP, pediatric cIAI on Vc Avibactam +0.412; +0.214 Table S3 theta11, theta12; control stream V1POP
APACHE II on CL; ventilator on Vc Avibactam -0.192; +0.267 Table S3 theta15, theta28
IIV 4x4 block CL, Vc, Vp, Q Avibactam variances 0.3453, 1.139, 1.156, 5.487 Table S3 eta rows
Residual SDs phase I / II / III Avibactam 0.174 + 43.8 ng/mL / 0.498 / 0.364 Table S3 theta17-theta20
Renal maturation (AGE <= 2 y) Both TM50 47.7 weeks, Hill 3.4 Methods ‘Model development’; control streams
Unbound fractions Both 0.85 ceftazidime, 0.92 avibactam Methods ‘Simulations and PK/PD targets’

Covariate-effect reproduction

Each model is solved for one typical subject (no IIV) at a reference covariate setting and at a perturbed one; the ratio of the cl or vc the model computes is compared with the value implied by the source. This has no Monte Carlo component and is asserted tightly.

baseCov <- data.frame(
  AGE = 30, PAGE = 30 * 52.18 + 40, WT = 70, CRCL = 80,
  DIS_CIAI = 0, DIS_CUTI = 0, DIS_HABP = 0, DIS_VABP = 0, MECH_VENT = 0,
  RACE_ASIAN_OTH = 0, RACE_CHINESE = 0, RACE_JAPANESE = 0,
  APACHE_II_SEV = 0, RENALIMP_ESRD = 0, RRT_HEMODIAL_STATUS = 0,
  STUDY_CIAI_PH2 = 0, STUDY_CAZAVI_PHASE2 = 0, STUDY_CAZAVI_PHASE3 = 1,
  STUDY_CAZAVI_PED_PHASE2 = 0
)

typicalParams <- function(ui, ...) {
  cov <- baseCov
  ch <- list(...)
  for (nm in names(ch)) cov[[nm]] <- ch[[nm]]
  cov <- cov[, intersect(names(cov), ui$all.covs), drop = FALSE]
  ev <- data.frame(
    id = 1L, time = c(0, 1), amt = c(1000, 0), evid = c(1L, 0L),
    dur = c(2, 0), cmt = "central"
  )
  ev <- cbind(ev, cov[rep(1L, 2L), , drop = FALSE])
  s <- rxode2::rxSolve(rxode2::zeroRe(ui), ev, returnType = "data.frame")
  c(cl = s$cl[1], vc = s$vc[1], q = s$q[1], vp = s$vp[1])
}

crefCaz <- 1 / 0.0103036 # CRCL where the ceftazidime spline equals 1
refCaz <- typicalParams(uiCaz, CRCL = crefCaz)
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
refAvi <- typicalParams(uiAvi)
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
emaxWt <- function(wt) wt / (53.5 + wt) * (53.5 + 70) / 70

checks <- tribble(
  ~Check, ~Analyte, ~Model, ~Expected,
  "CL at reference (L/h)", "Ceftazidime", unname(refCaz["cl"]), 7.75,
  "CL, CRCL 300 / CRCL 150 (cap)", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = 300)["cl"] / typicalParams(uiCaz, CRCL = 150)["cl"]), 1,
  "CL, CRCL 150 / reference", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = 150)["cl"] / refCaz["cl"]), 0.0103036 * 100 + 0.00125182 * 50,
  "CL, WT 53.5 / 70 kg (Emax at WT50)", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = crefCaz, WT = 53.5)["cl"] / refCaz["cl"]), 0.5 * (1 + 53.5 / 70),
  "CL, WT 15 / 70 kg", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = crefCaz, WT = 15)["cl"] / refCaz["cl"]), emaxWt(15),
  "CL, AGE 1 y at PMA 47.7 wk / reference", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = crefCaz, AGE = 1, PAGE = 47.7)["cl"] / refCaz["cl"]), 0.5,
  "Q, WT 35 / 70 kg", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = crefCaz, WT = 35)["q"] / refCaz["q"]), 0.5^0.67,
  "CL, cIAI", "Ceftazidime", unname(typicalParams(uiCaz, CRCL = crefCaz, DIS_CIAI = 1)["cl"] / refCaz["cl"]), 1.33,
  "CL, HAP", "Ceftazidime", unname(typicalParams(uiCaz, CRCL = crefCaz, DIS_HABP = 1)["cl"] / refCaz["cl"]), 1.1,
  "Vc, cUTI", "Ceftazidime", unname(typicalParams(uiCaz, CRCL = crefCaz, DIS_CUTI = 1)["vc"] / refCaz["vc"]), 1.49,
  "Vc, VAP + ventilator", "Ceftazidime",
  unname(typicalParams(uiCaz, CRCL = crefCaz, DIS_VABP = 1, MECH_VENT = 1)["vc"] / refCaz["vc"]), 1.83 * 1.202,
  "CL, Chinese", "Ceftazidime", unname(typicalParams(uiCaz, CRCL = crefCaz, RACE_CHINESE = 1)["cl"] / refCaz["cl"]), 1 - 0.0844,
  "CL, Japanese", "Ceftazidime", unname(typicalParams(uiCaz, CRCL = crefCaz, RACE_JAPANESE = 1)["cl"] / refCaz["cl"]), 1,
  "Vc, Japanese", "Ceftazidime", unname(typicalParams(uiCaz, CRCL = crefCaz, RACE_JAPANESE = 1)["vc"] / refCaz["vc"]), 1 - 0.135,
  "CL at reference (L/h)", "Avibactam", unname(refAvi["cl"]), 10.7,
  "CL, CRCL 150 / 80", "Avibactam", unname(typicalParams(uiAvi, CRCL = 150)["cl"] / refAvi["cl"]), 1 + 0.00344 * 70,
  "CL, CRCL 250 / 80 (cap)", "Avibactam", unname(typicalParams(uiAvi, CRCL = 250)["cl"] / refAvi["cl"]), 1 + 0.00344 * 70,
  "CL, CRCL 40 / 80", "Avibactam", unname(typicalParams(uiAvi, CRCL = 40)["cl"] / refAvi["cl"]), 0.5^0.986,
  "CL, ESRD (any CRCL)", "Avibactam", unname(typicalParams(uiAvi, CRCL = 5, RENALIMP_ESRD = 1)["cl"] / refAvi["cl"]), 0.0674,
  "CL, ESRD on hemodialysis (L/h)", "Avibactam",
  unname(typicalParams(uiAvi, CRCL = 5, RENALIMP_ESRD = 1, RRT_HEMODIAL_STATUS = 1)["cl"]), 21.1,
  "CL, WT 35 / 70 kg", "Avibactam", unname(typicalParams(uiAvi, WT = 35)["cl"] / refAvi["cl"]), 0.5^0.67,
  "Vp, WT 35 / 70 kg", "Avibactam", unname(typicalParams(uiAvi, WT = 35)["vp"] / refAvi["vp"]), 0.5,
  "CL, AGE 1 y at PMA 47.7 wk", "Avibactam",
  unname(typicalParams(uiAvi, AGE = 1, PAGE = 47.7, CRCL = 150)["cl"] / refAvi["cl"]), 0.5,
  "CL, APACHE II elevated", "Avibactam", unname(typicalParams(uiAvi, APACHE_II_SEV = 1)["cl"] / refAvi["cl"]), 1 - 0.192,
  "CL, adult phase II cIAI study", "Avibactam",
  unname(typicalParams(uiAvi, DIS_CIAI = 1, STUDY_CIAI_PH2 = 1)["cl"] / refAvi["cl"]), 1.431,
  "Vc, adult phase II cIAI study", "Avibactam",
  unname(typicalParams(uiAvi, DIS_CIAI = 1, STUDY_CIAI_PH2 = 1)["vc"] / refAvi["vc"]), 1 + 2.17,
  "Vc, phase III or pediatric cIAI", "Avibactam", unname(typicalParams(uiAvi, DIS_CIAI = 1)["vc"] / refAvi["vc"]), 1.214,
  "Vc, cUTI", "Avibactam", unname(typicalParams(uiAvi, DIS_CUTI = 1)["vc"] / refAvi["vc"]), 1.412,
  "Vc, HAP + ventilator", "Avibactam",
  unname(typicalParams(uiAvi, DIS_HABP = 1, MECH_VENT = 1)["vc"] / refAvi["vc"]), 1.214 * 1.267
) |>
  mutate(`Rel. diff` = Model / Expected - 1)
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'

checks |>
  mutate(across(c(Model, Expected), \(x) signif(x, 5)), `Rel. diff` = signif(`Rel. diff`, 2)) |>
  knitr::kable(caption = "Typical-value covariate effects computed by the models against the source values.")
Typical-value covariate effects computed by the models against the source values.
Check Analyte Model Expected Rel. diff
CL at reference (L/h) Ceftazidime 7.75000 7.75000 0
CL, CRCL 300 / CRCL 150 (cap) Ceftazidime 1.00000 1.00000 0
CL, CRCL 150 / reference Ceftazidime 1.09300 1.09300 0
CL, WT 53.5 / 70 kg (Emax at WT50) Ceftazidime 0.88214 0.88214 0
CL, WT 15 / 70 kg Ceftazidime 0.38634 0.38634 0
CL, AGE 1 y at PMA 47.7 wk / reference Ceftazidime 0.50000 0.50000 0
Q, WT 35 / 70 kg Ceftazidime 0.62851 0.62851 0
CL, cIAI Ceftazidime 1.33000 1.33000 0
CL, HAP Ceftazidime 1.10000 1.10000 0
Vc, cUTI Ceftazidime 1.49000 1.49000 0
Vc, VAP + ventilator Ceftazidime 2.19970 2.19970 0
CL, Chinese Ceftazidime 0.91560 0.91560 0
CL, Japanese Ceftazidime 1.00000 1.00000 0
Vc, Japanese Ceftazidime 0.86500 0.86500 0
CL at reference (L/h) Avibactam 10.70000 10.70000 0
CL, CRCL 150 / 80 Avibactam 1.24080 1.24080 0
CL, CRCL 250 / 80 (cap) Avibactam 1.24080 1.24080 0
CL, CRCL 40 / 80 Avibactam 0.50488 0.50488 0
CL, ESRD (any CRCL) Avibactam 0.06740 0.06740 0
CL, ESRD on hemodialysis (L/h) Avibactam 21.10000 21.10000 0
CL, WT 35 / 70 kg Avibactam 0.62851 0.62851 0
Vp, WT 35 / 70 kg Avibactam 0.50000 0.50000 0
CL, AGE 1 y at PMA 47.7 wk Avibactam 0.50000 0.50000 0
CL, APACHE II elevated Avibactam 0.80800 0.80800 0
CL, adult phase II cIAI study Avibactam 1.43100 1.43100 0
Vc, adult phase II cIAI study Avibactam 3.17000 3.17000 0
Vc, phase III or pediatric cIAI Avibactam 1.21400 1.21400 0
Vc, cUTI Avibactam 1.41200 1.41200 0
Vc, HAP + ventilator Avibactam 1.53810 1.53810 0 

# Same parameters on both sides: pure numerical error, so a tight bound.
stopifnot(all(abs(checks$`Rel. diff`) < 1e-6))

Virtual cohort

Franzese 2022 simulated 1,000 patients per indication, age group and dose group, bootstrapping weight, age and NCrCL from a Pfizer database of 457 children with infections (older than 2 years) and taking weight from CDC growth charts (2 years and younger), with between-subject variability resampled from the post hoc random effects of the fitted subjects. None of that subject-level material is published, so the cohort below is a reconstruction (see Assumptions and deviations). Each arm has 100 subjects.

# set.seed() seeds R's RNG, not rxode2's; rxode2 streams are partitioned per
# solver thread, so a CI runner draws a different cohort than a workstation.
# Every assertion below is written to hold for any cohort the model produces.
set.seed(20220301)
rxode2::rxSetSeed(20220301)

N_ARM <- 100L

# Approximate median weight-for-age (kg), sexes pooled (growth-chart medians).
wfa <- data.frame(
  age = c(0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18),
  wt = c(6.0, 7.6, 8.9, 9.8, 11.0, 12.3, 14.3, 16.3, 18.4, 20.7, 23.0, 25.6, 28.6, 32.0, 36.0, 40.5, 45.5, 50.5, 55.0, 58.5, 61.0, 63.0)
)

ageGroups <- tribble(
  ~grp, ~lo, ~hi, ~mgkg,
  "12 to <18 years", 12, 18, 50,
  "6 to <12 years", 6, 12, 50,
  "2 to <6 years", 2, 6, 50,
  "1 to <2 years", 1, 2, 50,
  "6 to <12 months", 0.5, 1, 50,
  "3 to <6 months", 0.25, 0.5, 40,
  "Adults", 18, 80, NA
)

# Adult CrCL bands >= 80 mL/min from Li 2019 Table 3 (bottom block).
adultCrcl <- data.frame(lo = c(80, 150, 180), hi = c(150, 180, 610), n = c(955, 123, 116))

drawCrcl <- function(n, adult, renal) {
  if (renal == "Mild") {
    return(runif(n, 51, 80))
  }
  if (adult) {
    b <- sample(seq_len(nrow(adultCrcl)), n, replace = TRUE, prob = adultCrcl$n)
    return(runif(n, adultCrcl$lo[b], adultCrcl$hi[b]))
  }
  x <- rlnorm(n, log(125), 0.25)
  while (any(x < 80)) {
    low <- x < 80
    x[low] <- rlnorm(sum(low), log(125), 0.25)
  }
  x
}

makeArm <- function(grp, ind, renal, idOffset) {
  g <- ageGroups[ageGroups$grp == grp, ]
  adult <- grp == "Adults"
  age <- runif(N_ARM, g$lo, g$hi)
  wt <- if (adult) {
    pmin(pmax(rlnorm(N_ARM, log(70), 0.23), 40), 150)
  } else {
    approx(wfa$age, wfa$wt, age)$y * exp(rnorm(N_ARM, 0, ifelse(age < 2, 0.12, 0.18)))
  }
  race <- if (adult) {
    sample(c("other", "ASN", "CHN", "JPN"), N_ARM, replace = TRUE, prob = c(1209, 248, 262, 45))
  } else {
    sample(c("other", "ASN", "CHN"), N_ARM, replace = TRUE, prob = c(86.9, 1.3, 11.8))
  }
  vap <- if (ind == "HAP/VAP") rbinom(N_ARM, 1L, 138 / 413) else rep(0L, N_ARM)
  apache <- if (adult && ind != "cUTI") rbinom(N_ARM, 1L, 438 / 1115) else rep(0L, N_ARM)
  amtCaz <- if (adult) rep(2000, N_ARM) else pmin(g$mgkg * wt, 2000)
  data.frame(
    id = idOffset + seq_len(N_ARM), grp = grp, ind = ind, renal = renal,
    AGE = age, PAGE = age * 52.18 + 40, WT = wt, CRCL = drawCrcl(N_ARM, adult, renal),
    DIS_CIAI = as.integer(ind == "cIAI"), DIS_CUTI = as.integer(ind == "cUTI"),
    DIS_VABP = vap, DIS_HABP = as.integer(ind == "HAP/VAP") * (1L - vap),
    MECH_VENT = vap,
    RACE_ASIAN_OTH = as.integer(race == "ASN"), RACE_CHINESE = as.integer(race == "CHN"),
    RACE_JAPANESE = as.integer(race == "JPN"),
    APACHE_II_SEV = apache, RENALIMP_ESRD = 0L, RRT_HEMODIAL_STATUS = 0L,
    STUDY_CIAI_PH2 = 0L, STUDY_CAZAVI_PHASE2 = 0L,
    STUDY_CAZAVI_PHASE3 = as.integer(adult), STUDY_CAZAVI_PED_PHASE2 = as.integer(!adult),
    amtCaz = amtCaz, amtAvi = amtCaz / 4
  )
}

arms <- bind_rows(
  expand.grid(grp = ageGroups$grp, ind = c("cIAI", "cUTI", "HAP/VAP"), renal = "Normal", stringsAsFactors = FALSE),
  expand.grid(
    grp = c("12 to <18 years", "6 to <12 years", "2 to <6 years", "Adults"),
    ind = c("cIAI", "cUTI", "HAP/VAP"), renal = "Mild", stringsAsFactors = FALSE
  )
)
cohort <- bind_rows(lapply(seq_len(nrow(arms)), function(i) {
  makeArm(arms$grp[i], arms$ind[i], arms$renal[i], (i - 1L) * N_ARM)
}))

cohort |>
  group_by(Renal = renal, `Age group` = grp) |>
  summarise(
    N = n(), `Median WT (kg)` = round(median(WT), 1),
    `Median NCrCL` = round(median(CRCL)),
    `Median ceftazidime dose (mg)` = round(median(amtCaz)), .groups = "drop"
  ) |>
  knitr::kable(caption = "Virtual cohort by renal stratum and age group (all three indications pooled).")
Virtual cohort by renal stratum and age group (all three indications pooled).
Renal Age group N Median WT (kg) Median NCrCL Median ceftazidime dose (mg)
Mild 12 to <18 years 300 53.7 66 2000
Mild 2 to <6 years 300 16.0 66 802
Mild 6 to <12 years 300 29.2 66 1461
Mild Adults 300 71.4 66 2000
Normal 1 to <2 years 300 11.2 129 561
Normal 12 to <18 years 300 53.2 128 2000
Normal 2 to <6 years 300 16.1 125 806
Normal 3 to <6 months 300 6.8 126 271
Normal 6 to <12 months 300 8.7 129 434
Normal 6 to <12 years 300 29.2 128 1459
Normal Adults 300 68.2 124 2000

Simulation

Steady state is imposed with ss = 1 on the first 2-hour infusion and two further q8h doses are given explicitly, so the 0-24 h window is the paper’s AUCss,0-24. The first dosing interval is sampled every 0.1 h for the time-above-threshold calculation; the rest of the window hourly. The paper’s PTA simulations used individual predictions, so residual error is switched off (sigma = NA).

TINF <- 2
obsTimes <- sort(unique(c(seq(0, 8, by = 0.1), 9:24)))
covCols <- setdiff(names(cohort), c("grp", "ind", "renal", "amtCaz", "amtAvi"))

makeEvents <- function(amtCol) {
  dose <- cohort[rep(seq_len(nrow(cohort)), each = 3L), covCols]
  dose$time <- rep(c(0, 8, 16), nrow(cohort))
  dose$amt <- rep(cohort[[amtCol]], each = 3L)
  dose$evid <- 1L
  dose$dur <- TINF
  dose$ss <- rep(c(1L, 0L, 0L), nrow(cohort))
  dose$ii <- 8
  obs <- cohort[rep(seq_len(nrow(cohort)), each = length(obsTimes)), covCols]
  obs$time <- rep(obsTimes, nrow(cohort))
  obs$amt <- 0
  obs$evid <- 0L
  obs$dur <- 0
  obs$ss <- 0L
  obs$ii <- 0
  ev <- rbind(dose, obs)
  ev$cmt <- "central"
  ev[order(ev$id, ev$time, -ev$evid), ]
}

simOne <- function(ui, amtCol, drug) {
  s <- rxode2::rxSolve(ui, makeEvents(amtCol),
    sigma = NA, maxsteps = 500000L, returnType = "data.frame"
  )
  s |>
    transmute(id = as.integer(as.character(id)), time, Cc, drug = drug) |>
    left_join(cohort |> select(id, grp, ind, renal, WT), by = "id")
}

sim <- bind_rows(
  simOne(uiCaz, "amtCaz", "Ceftazidime"),
  simOne(uiAvi, "amtAvi", "Avibactam")
)

# The avibactam OMEGA block gives Q a variance of 5.5 (SD 2.3 on the log
# scale), so a handful of draws are extreme enough (Vc < 0.5 L with Q in the
# hundreds of L/h) that the steady-state solver gives up. Those subjects are
# dropped and counted; more than 1% would signal a real problem.
naIds <- unique(sim$id[sim$drug == "Avibactam" & !is.finite(sim$Cc)])
cat("Avibactam subjects with a failed steady-state solve:", length(naIds), "of", nrow(cohort), "\n")
#> Avibactam subjects with a failed steady-state solve: 0 of 3300
stopifnot(
  all(is.finite(sim$Cc[sim$drug == "Ceftazidime"])),
  length(naIds) <= 0.01 * nrow(cohort)
)
sim <- sim |> filter(!(drug == "Avibactam" & id %in% naIds))

Steady-state profiles 

sim |>
  filter(renal == "Normal", grp %in% c("12 to <18 years", "2 to <6 years", "3 to <6 months", "Adults")) |>
  group_by(drug, ind, grp, time) |>
  summarise(med = median(Cc), lo = quantile(Cc, 0.05), hi = quantile(Cc, 0.95), .groups = "drop") |>
  ggplot(aes(time, med, colour = grp, fill = grp)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.1, colour = NA) +
  geom_line() +
  facet_grid(drug ~ ind, scales = "free_y") +
  scale_y_log10() +
  labs(
    x = "Time within the steady-state 24-hour window (h)",
    y = "Total plasma concentration (mg/L)", colour = "Age group", fill = "Age group"
  ) +
  theme_bw()

Median and 90% prediction interval at the approved doses, normal renal function.

Exposure by body weight 

expo <- sim |>
  group_by(drug, id, grp, ind, renal, WT) |>
  summarise(cmax = max(Cc), .groups = "drop") |>
  filter(renal == "Normal")

expo |>
  mutate(population = ifelse(grp == "Adults", "Adults", "Children")) |>
  ggplot(aes(WT, cmax, colour = population)) +
  geom_point(alpha = 0.3, size = 0.8) +
  geom_smooth(method = "loess", formula = y ~ x, se = FALSE) +
  facet_grid(drug ~ ind, scales = "free_y") +
  scale_x_log10() +
  scale_y_log10() +
  labs(x = "Body weight (kg)", y = "Simulated Cmax,ss (mg/L)", colour = NULL) +
  theme_bw()

Replicates the simulated part of Figure 1b of Franzese 2022 (Cmax,ss against body weight, children against adults with normal renal function): pediatric peak concentrations sit at or above the adult band across the weight range, the pattern the paper describes for its Figure 1 and Table 3.

PKNCA validation 

ncaConc <- sim |>
  filter(!is.na(Cc), time %in% c(0:24)) |>
  select(id, time, Cc, drug)
ncaDose <- sim |>
  filter(time == 0) |>
  distinct(id, drug) |>
  mutate(time = 0)

concObj <- PKNCA::PKNCAconc(ncaConc, Cc ~ time | drug + id, concu = "mg/L", timeu = "h")
doseObj <- PKNCA::PKNCAdose(ncaDose, ~ time | drug + id)
intervals <- data.frame(start = 0, end = 24, cmax = TRUE, auclast = TRUE)
ncaRes <- PKNCA::pk.nca(PKNCA::PKNCAdata(concObj, doseObj, intervals = intervals))

ncaInd <- as.data.frame(ncaRes$result) |>
  select(drug, id, PPTESTCD, PPORRES) |>
  left_join(cohort |> select(id, grp, ind, renal), by = "id")

stopifnot(all(is.finite(ncaInd$PPORRES)))

# Franzese 2022 tabulates geometric means.
ncaGm <- ncaInd |>
  group_by(drug, renal, ind, grp, PPTESTCD) |>
  summarise(PPORRES = exp(mean(log(PPORRES))), .groups = "drop")

auclast over the 0-24 h steady-state window is AUCss,0-24; cmax over the window is Cmax,ss (end of infusion).

Comparison against the published simulations (Table 3) 

grpLev <- c("12 to <18 years", "6 to <12 years", "2 to <6 years", "1 to <2 years", "6 to <12 months", "3 to <6 months", "Adults")
grpMild <- c("12 to <18 years", "6 to <12 years", "2 to <6 years", "Adults")
# Franzese 2022 Table 3, read column by column (cIAI, cUTI, HAP/VAP).
table3 <- bind_rows(
  tibble(drug = "Ceftazidime", renal = "Normal", grp = rep(grpLev, 3), ind = rep(c("cIAI", "cUTI", "HAP/VAP"), each = 7),
    cmax = c(64.6, 72.4, 68.2, 68.1, 72.1, 64.2, 58.9, 81.5, 91.5, 86.3, 86.0, 90.8, 80.7, 74.0, 71.8, 80.8, 76.4, 76.2, 80.4, 71.4, 65.1),
    auclast = c(618, 650, 572, 577, 637, 617, 602, 821, 864, 760, 767, 846, 820, 828, 747, 785, 691, 698, 769, 745, 712)),
  tibble(drug = "Avibactam", renal = "Normal", grp = rep(grpLev, 3), ind = rep(c("cIAI", "cUTI", "HAP/VAP"), each = 7),
    cmax = c(12.3, 14.2, 13.0, 13.6, 14.0, 12.1, 10.5, 11.9, 13.7, 12.5, 12.9, 13.3, 11.5, 9.73, 13.0, 15.1, 13.8, 14.4, 14.9, 12.9, 10.2),
    auclast = c(121, 136, 118, 125, 132, 121, 107, 121, 136, 118, 125, 132, 121, 113, 121, 136, 118, 125, 132, 121, 105)),
  tibble(drug = "Ceftazidime", renal = "Mild", grp = rep(grpMild, 3), ind = rep(c("cIAI", "cUTI", "HAP/VAP"), each = 4),
    cmax = c(81.6, 93.4, 88.2, 74.9, 103.0, 118.0, 111.0, 94.3, 90.9, 104.0, 98.0, 83.8),
    auclast = c(940, 1020, 892, 917, 1250, 1350, 1190, 1240, 1140, 1230, 1080, 1100)),
  tibble(drug = "Avibactam", renal = "Mild", grp = rep(grpMild, 3), ind = rep(c("cIAI", "cUTI", "HAP/VAP"), each = 4),
    cmax = c(14.7, 17.4, 15.9, 12.7, 14.2, 16.7, 15.3, 11.8, 15.5, 18.5, 17.0, 12.5),
    auclast = c(164, 192, 167, 148, 164, 192, 167, 152, 164, 192, 167, 147))
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = ncaGm, reference = table3,
  by = c("drug", "renal", "ind", "grp"),
  units = c(cmax = "mg/L", auclast = "mg*h/L, 0-24 h at steady state")
)
cmp |>
  dplyr::rename(Analyte = drug, `Renal function` = renal, Indication = ind, `Age group` = grp) |>
  knitr::kable(caption = "Geometric-mean steady-state exposures: Franzese 2022 Table 3 (Reference) against this simulation.")
Geometric-mean steady-state exposures: Franzese 2022 Table 3 (Reference) against this simulation.
NCA parameter Analyte Renal function Indication Age group Reference Simulated % diff
Cmax (mg/L) Ceftazidime Normal cIAI 12 to <18 years 64.6 68.9 +6.7%
Cmax (mg/L) Ceftazidime Normal cIAI 6 to <12 years 72.4 78.2 +7.9%
Cmax (mg/L) Ceftazidime Normal cIAI 2 to <6 years 68.2 67.8 -0.5%
Cmax (mg/L) Ceftazidime Normal cIAI 1 to <2 years 68.1 70.1 +3.0%
Cmax (mg/L) Ceftazidime Normal cIAI 6 to <12 months 72.1 74.3 +3.0%
Cmax (mg/L) Ceftazidime Normal cIAI 3 to <6 months 64.2 64.8 +0.9%
Cmax (mg/L) Ceftazidime Normal cIAI Adults 58.9 54.9 -6.8%
Cmax (mg/L) Ceftazidime Normal cUTI 12 to <18 years 81.5 86.5 +6.1%
Cmax (mg/L) Ceftazidime Normal cUTI 6 to <12 years 91.5 97.3 +6.4%
Cmax (mg/L) Ceftazidime Normal cUTI 2 to <6 years 86.3 84.8 -1.8%
Cmax (mg/L) Ceftazidime Normal cUTI 1 to <2 years 86 87.6 +1.9%
Cmax (mg/L) Ceftazidime Normal cUTI 6 to <12 months 90.8 93.6 +3.1%
Cmax (mg/L) Ceftazidime Normal cUTI 3 to <6 months 80.7 82.3 +2.0%
Cmax (mg/L) Ceftazidime Normal cUTI Adults 74 74 +0.1%
Cmax (mg/L) Ceftazidime Normal HAP/VAP 12 to <18 years 71.8 74.3 +3.6%
Cmax (mg/L) Ceftazidime Normal HAP/VAP 6 to <12 years 80.8 83.4 +3.2%
Cmax (mg/L) Ceftazidime Normal HAP/VAP 2 to <6 years 76.4 78.8 +3.1%
Cmax (mg/L) Ceftazidime Normal HAP/VAP 1 to <2 years 76.2 79.9 +4.9%
Cmax (mg/L) Ceftazidime Normal HAP/VAP 6 to <12 months 80.4 78.7 -2.1%
Cmax (mg/L) Ceftazidime Normal HAP/VAP 3 to <6 months 71.4 72.5 +1.6%
Cmax (mg/L) Ceftazidime Normal HAP/VAP Adults 65.1 66.5 +2.2%
Cmax (mg/L) Ceftazidime Mild cIAI 12 to <18 years 81.6 87.1 +6.7%
Cmax (mg/L) Ceftazidime Mild cIAI 6 to <12 years 93.4 97.1 +4.0%
Cmax (mg/L) Ceftazidime Mild cIAI 2 to <6 years 88.2 91.1 +3.3%
Cmax (mg/L) Ceftazidime Mild cIAI Adults 74.9 75.4 +0.7%
Cmax (mg/L) Ceftazidime Mild cUTI 12 to <18 years 103 112 +9.0%
Cmax (mg/L) Ceftazidime Mild cUTI 6 to <12 years 118 127 +7.7%
Cmax (mg/L) Ceftazidime Mild cUTI 2 to <6 years 111 111 +0.4%
Cmax (mg/L) Ceftazidime Mild cUTI Adults 94.3 93.3 -1.1%
Cmax (mg/L) Ceftazidime Mild HAP/VAP 12 to <18 years 90.9 92.8 +2.1%
Cmax (mg/L) Ceftazidime Mild HAP/VAP 6 to <12 years 104 108 +3.6%
Cmax (mg/L) Ceftazidime Mild HAP/VAP 2 to <6 years 98 96.4 -1.6%
Cmax (mg/L) Ceftazidime Mild HAP/VAP Adults 83.8 77.3 -7.7%
Cmax (mg/L) Avibactam Normal cIAI 12 to <18 years 12.3 14.7 +19.6%
Cmax (mg/L) Avibactam Normal cIAI 6 to <12 years 14.2 17.3 +21.6%*
Cmax (mg/L) Avibactam Normal cIAI 2 to <6 years 13 15 +15.4%
Cmax (mg/L) Avibactam Normal cIAI 1 to <2 years 13.6 15 +10.7%
Cmax (mg/L) Avibactam Normal cIAI 6 to <12 months 14 18.3 +30.7%*
Cmax (mg/L) Avibactam Normal cIAI 3 to <6 months 12.1 15 +23.6%*
Cmax (mg/L) Avibactam Normal cIAI Adults 10.5 13.2 +25.9%*
Cmax (mg/L) Avibactam Normal cUTI 12 to <18 years 11.9 16.1 +35.6%*
Cmax (mg/L) Avibactam Normal cUTI 6 to <12 years 13.7 17.6 +28.1%*
Cmax (mg/L) Avibactam Normal cUTI 2 to <6 years 12.5 14.3 +14.8%
Cmax (mg/L) Avibactam Normal cUTI 1 to <2 years 12.9 15.3 +18.7%
Cmax (mg/L) Avibactam Normal cUTI 6 to <12 months 13.3 17.3 +30.0%*
Cmax (mg/L) Avibactam Normal cUTI 3 to <6 months 11.5 14.7 +28.0%*
Cmax (mg/L) Avibactam Normal cUTI Adults 9.73 13 +33.5%*
Cmax (mg/L) Avibactam Normal HAP/VAP 12 to <18 years 13 16.8 +29.1%*
Cmax (mg/L) Avibactam Normal HAP/VAP 6 to <12 years 15.1 19.3 +28.1%*
Cmax (mg/L) Avibactam Normal HAP/VAP 2 to <6 years 13.8 15.8 +14.5%
Cmax (mg/L) Avibactam Normal HAP/VAP 1 to <2 years 14.4 14.5 +0.9%
Cmax (mg/L) Avibactam Normal HAP/VAP 6 to <12 months 14.9 16 +7.7%
Cmax (mg/L) Avibactam Normal HAP/VAP 3 to <6 months 12.9 13.6 +5.6%
Cmax (mg/L) Avibactam Normal HAP/VAP Adults 10.2 13 +27.8%*
Cmax (mg/L) Avibactam Mild cIAI 12 to <18 years 14.7 19.5 +33.0%*
Cmax (mg/L) Avibactam Mild cIAI 6 to <12 years 17.4 22.6 +29.7%*
Cmax (mg/L) Avibactam Mild cIAI 2 to <6 years 15.9 19 +19.7%
Cmax (mg/L) Avibactam Mild cIAI Adults 12.7 16 +25.8%*
Cmax (mg/L) Avibactam Mild cUTI 12 to <18 years 14.2 18.7 +31.9%*
Cmax (mg/L) Avibactam Mild cUTI 6 to <12 years 16.7 22.3 +33.3%*
Cmax (mg/L) Avibactam Mild cUTI 2 to <6 years 15.3 18.1 +18.3%
Cmax (mg/L) Avibactam Mild cUTI Adults 11.8 13.2 +11.8%
Cmax (mg/L) Avibactam Mild HAP/VAP 12 to <18 years 15.5 18.4 +18.7%
Cmax (mg/L) Avibactam Mild HAP/VAP 6 to <12 years 18.5 21.1 +13.9%
Cmax (mg/L) Avibactam Mild HAP/VAP 2 to <6 years 17 19.1 +12.2%
Cmax (mg/L) Avibactam Mild HAP/VAP Adults 12.5 15.7 +25.4%*
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI 12 to <18 years 618 636 +2.9%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI 6 to <12 years 650 677 +4.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI 2 to <6 years 572 528 -7.8%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI 1 to <2 years 577 556 -3.7%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI 6 to <12 months 637 607 -4.8%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI 3 to <6 months 617 588 -4.7%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cIAI Adults 602 548 -9.0%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI 12 to <18 years 821 830 +1.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI 6 to <12 years 864 863 -0.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI 2 to <6 years 760 699 -8.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI 1 to <2 years 767 712 -7.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI 6 to <12 months 846 826 -2.4%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI 3 to <6 months 820 777 -5.2%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal cUTI Adults 828 756 -8.7%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP 12 to <18 years 747 756 +1.2%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP 6 to <12 years 785 802 +2.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP 2 to <6 years 691 701 +1.5%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP 1 to <2 years 698 730 +4.6%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP 6 to <12 months 769 711 -7.5%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP 3 to <6 months 745 736 -1.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Normal HAP/VAP Adults 712 740 +3.9%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cIAI 12 to <18 years 940 979 +4.2%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cIAI 6 to <12 years 1020 1010 -0.8%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cIAI 2 to <6 years 892 846 -5.2%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cIAI Adults 917 906 -1.2%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cUTI 12 to <18 years 1250 1380 +10.4%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cUTI 6 to <12 years 1350 1390 +3.1%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cUTI 2 to <6 years 1190 1080 -8.9%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild cUTI Adults 1240 1170 -5.5%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild HAP/VAP 12 to <18 years 1140 1130 -1.0%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild HAP/VAP 6 to <12 years 1230 1230 +0.4%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild HAP/VAP 2 to <6 years 1080 1020 -5.6%
AUClast (mg*h/L, 0-24 h at steady state) Ceftazidime Mild HAP/VAP Adults 1100 1010 -8.0%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI 12 to <18 years 121 137 +13.2%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI 6 to <12 years 136 150 +9.9%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI 2 to <6 years 118 126 +6.7%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI 1 to <2 years 125 126 +0.5%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI 6 to <12 months 132 149 +13.2%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI 3 to <6 months 121 128 +5.8%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cIAI Adults 107 129 +20.9%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI 12 to <18 years 121 158 +30.3%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI 6 to <12 years 136 150 +10.1%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI 2 to <6 years 118 126 +6.4%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI 1 to <2 years 125 124 -0.6%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI 6 to <12 months 132 147 +11.5%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI 3 to <6 months 121 136 +12.6%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal cUTI Adults 113 127 +12.1%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP 12 to <18 years 121 157 +29.8%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP 6 to <12 years 136 168 +23.4%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP 2 to <6 years 118 126 +6.5%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP 1 to <2 years 125 122 -2.2%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP 6 to <12 months 132 136 +3.2%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP 3 to <6 months 121 121 +0.3%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Normal HAP/VAP Adults 105 129 +23.3%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cIAI 12 to <18 years 164 204 +24.4%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cIAI 6 to <12 years 192 222 +15.5%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cIAI 2 to <6 years 167 172 +3.1%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cIAI Adults 148 187 +26.4%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cUTI 12 to <18 years 164 208 +26.8%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cUTI 6 to <12 years 192 229 +19.0%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cUTI 2 to <6 years 167 175 +5.0%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild cUTI Adults 152 153 +0.9%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild HAP/VAP 12 to <18 years 164 204 +24.2%*
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild HAP/VAP 6 to <12 years 192 210 +9.5%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild HAP/VAP 2 to <6 years 167 171 +2.5%
AUClast (mg*h/L, 0-24 h at steady state) Avibactam Mild HAP/VAP Adults 147 179 +21.6%* 
pct <- ncaGm |>
  inner_join(
    table3 |> pivot_longer(c(cmax, auclast), names_to = "PPTESTCD", values_to = "ref"),
    by = c("drug", "renal", "ind", "grp", "PPTESTCD")
  ) |>
  mutate(pct_diff = 100 * (PPORRES / ref - 1))

pct |>
  group_by(Analyte = drug, Parameter = PPTESTCD) |>
  summarise(
    `Median % diff` = round(median(pct_diff), 1),
    `90th pct of |% diff|` = round(quantile(abs(pct_diff), 0.9), 1), .groups = "drop"
  ) |>
  knitr::kable(caption = "Agreement with Table 3 across the 33 arms.")
Agreement with Table 3 across the 33 arms.
Analyte Parameter Median % diff 90th pct of |% diff|
Avibactam auclast 11.5 26.0
Avibactam cmax 23.6 32.7
Ceftazidime auclast -1.2 8.6
Ceftazidime cmax 3.0 7.5 

# The cohort is a reconstruction from marginal summaries, so the two sides
# differ by which subjects were drawn; assert on the centre and a robust
# quantile only. A mis-transcribed clearance, dose or unit moves the whole
# distribution by tens of percent.
caz <- pct[pct$drug == "Ceftazidime", ]
avi <- pct[pct$drug == "Avibactam", ]
stopifnot(
  abs(median(caz$pct_diff)) < 10,
  quantile(abs(caz$pct_diff), 0.9) < 20,
  # Avibactam runs high by a systematic, explained offset (next section).
  median(avi$pct_diff) > -10,
  median(avi$pct_diff) < 35
)

Ceftazidime reproduces Table 3 closely across all ages, indications and both renal strata (median differences of a few percent on both AUCss,0-24 and Cmax,ss). Avibactam runs systematically high – by roughly a tenth on AUCss,0-24 and a fifth on Cmax,ss – and the explanation is in the next section.

Why the avibactam simulation runs high

Franzese 2022 did not simulate from the OMEGA matrix: it resampled each fitted subject’s post hoc random effects, pediatric ones for simulated children and adult ones for simulated adults. If the fitted children’s avibactam clearance EBEs are centred above zero – a pediatric offset the covariates do not capture (the pediatric-study terms CLPED and V1PED were tested in the control stream but held at zero in the final model) – then the paper’s simulated children inherit it and a simulation centred on the typical value does not.

Table 2 (as corrected by the erratum) makes the offset visible without any knowledge of the cohort: in a child, ceftazidime and avibactam are dosed in a 4:1 ratio, so (AUCcaz / AUCavi) / 4 is the subject’s avibactam-to-ceftazidime clearance ratio. The models’ typical-value ratio for a child aged over 2 years with no infection-type effect on ceftazidime clearance can be computed across the weights and NCrCL values that cover most of the children (10-45 kg; NCrCL 90-150 mL/min/1.73 m^2, bracketing the Table 1 cohort medians of 89-130). The ratio is somewhat higher right at the avibactam hinge of 80, where the ceftazidime spline is lowest relative to its own reference.

ratioGrid <- expand.grid(WT = c(10, 15, 20, 30, 45), CRCL = c(90, 100, 125, 150))
ratioGrid$ratio <- mapply(function(wt, crcl) {
  typicalParams(uiAvi, WT = wt, CRCL = crcl, AGE = 8)["cl"] /
    typicalParams(uiCaz, WT = wt, CRCL = crcl, AGE = 8)["cl"]
}, ratioGrid$WT, ratioGrid$CRCL)
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq'
#> Warning: No sigma parameters in the model
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'

# Franzese 2022 Table 2 (erratum), phase I and phase II cUTI cohorts: no
# ceftazidime infection-type clearance effect applies to either.
table2 <- tribble(
  ~cohort, ~aucCaz, ~aucAvi,
  "Phase I, 3 months to <2 years", 888, 143,
  "Phase I, 2 to <6 years", 794, 127,
  "Phase I, 6 to <12 years", 814, 121,
  "Phase I, 12 to <18 years", 821, 124,
  "Phase II cUTI, 3 to <6 months", 736, 132,
  "Phase II cUTI, 6 months to <1 year", 859, 113,
  "Phase II cUTI, 1 to <2 years", 883, 117,
  "Phase II cUTI, 2 to <6 years", 789, 123,
  "Phase II cUTI, 6 to <12 years", 993, 153,
  "Phase II cUTI, 12 to <18 years", 843, 139
) |>
  mutate(ratio = aucCaz / aucAvi / 4)

tibble(
  Quantity = c(
    "Model typical CLavi / CLcaz, children > 2 y (range over WT 10-45 kg, NCrCL 90-150)",
    "Table 2 post hoc CLavi / CLcaz, median of 10 pediatric cohorts (range)"
  ),
  Value = c(
    sprintf("%.2f-%.2f", min(ratioGrid$ratio), max(ratioGrid$ratio)),
    sprintf("%.2f (%.2f-%.2f)", median(table2$ratio), min(table2$ratio), max(table2$ratio))
  )
) |>
  knitr::kable(caption = "Avibactam-to-ceftazidime clearance ratio: typical values against the fitted children.")
Avibactam-to-ceftazidime clearance ratio: typical values against the fitted children.
Quantity Value
Model typical CLavi / CLcaz, children > 2 y (range over WT 10-45 kg, NCrCL 90-150) 1.28-1.53
Table 2 post hoc CLavi / CLcaz, median of 10 pediatric cohorts (range) 1.61 (1.39-1.90) 

# Both sides are deterministic transcriptions / typical values.
stopifnot(median(table2$ratio) > max(ratioGrid$ratio))

The fitted children’s median ratio exceeds the largest typical-value ratio the two models produce over that covariate range. Because the ceftazidime simulation reproduces Table 3 (which used the same resampling), the excess is on the avibactam side: the fitted children’s avibactam clearance is on average higher than the avibactam typical value predicts, by roughly the amount the simulation above overshoots Table 3 on AUCss,0-24. The larger overshoot on Cmax,ss points to the same kind of offset in the resampled central-volume random effects. That is a property of the published model – its avibactam typical values are not centred on the pediatric data – not an extraction error, and a parametric simulation of children from this model will over-predict avibactam exposure by about this much.

Joint PK/PD target attainment (Table 4)

The joint target is 50% of the dosing interval with free ceftazidime above the MIC (8 mg/L, fu = 0.85) and free avibactam above 1 mg/L (fu = 0.92), achieved simultaneously.

fT <- sim |>
  filter(time < 8) |>
  mutate(free = ifelse(drug == "Ceftazidime", 0.85 * Cc, 0.92 * Cc), thr = ifelse(drug == "Ceftazidime", 8, 1)) |>
  group_by(drug, id) |>
  summarise(ft = mean(free > thr), .groups = "drop") |>
  pivot_wider(names_from = drug, values_from = ft) |>
  filter(!is.na(Avibactam)) |>
  left_join(cohort |> select(id, grp, ind, renal), by = "id")

ptaSim <- fT |>
  group_by(renal, ind, grp) |>
  summarise(
    caz = 100 * mean(Ceftazidime >= 0.5), avi = 100 * mean(Avibactam >= 0.5),
    joint = 100 * mean(Ceftazidime >= 0.5 & Avibactam >= 0.5), .groups = "drop"
  )

table4 <- bind_rows(
  tibble(renal = "Normal", grp = rep(grpLev, 3), ind = rep(c("cIAI", "cUTI", "HAP/VAP"), each = 7),
    published = c(96, 90, 82, 82, 90, 93, 95, 99, 97, 94, 94, 98, 98, 97, 99, 97, 92, 92, 97, 98, 95)),
  tibble(renal = "Mild", grp = rep(grpMild, 3), ind = rep(c("cIAI", "cUTI", "HAP/VAP"), each = 4),
    published = c(99, 100, 100, 99, 99, 100, 100, 99, 99, 100, 100, 99))
)

ptaCmp <- inner_join(table4, ptaSim, by = c("renal", "ind", "grp"))
ptaCmp |>
  mutate(across(c(caz, avi, joint), round)) |>
  dplyr::rename(
    `Renal function` = renal, Indication = ind, `Age group` = grp,
    `Published joint PTA (%)` = published, `Ceftazidime PTA (%)` = caz,
    `Avibactam PTA (%)` = avi, `Joint PTA (%)` = joint
  ) |>
  knitr::kable(caption = "Joint PTA at MIC 8 mg/L: Franzese 2022 Table 4 against this simulation.")
Joint PTA at MIC 8 mg/L: Franzese 2022 Table 4 against this simulation.
Renal function Age group Indication Published joint PTA (%) Ceftazidime PTA (%) Avibactam PTA (%) Joint PTA (%)
Normal 12 to <18 years cIAI 96 90 99 89
Normal 6 to <12 years cIAI 90 85 100 85
Normal 2 to <6 years cIAI 82 66 97 65
Normal 1 to <2 years cIAI 82 73 96 69
Normal 6 to <12 months cIAI 90 81 100 81
Normal 3 to <6 months cIAI 93 82 98 80
Normal Adults cIAI 95 89 100 89
Normal 12 to <18 years cUTI 99 91 100 91
Normal 6 to <12 years cUTI 97 94 100 94
Normal 2 to <6 years cUTI 94 78 96 74
Normal 1 to <2 years cUTI 94 84 98 82
Normal 6 to <12 months cUTI 98 91 97 89
Normal 3 to <6 months cUTI 98 92 100 92
Normal Adults cUTI 97 94 97 91
Normal 12 to <18 years HAP/VAP 99 95 100 95
Normal 6 to <12 years HAP/VAP 97 98 100 98
Normal 2 to <6 years HAP/VAP 92 88 95 84
Normal 1 to <2 years HAP/VAP 92 90 93 83
Normal 6 to <12 months HAP/VAP 97 87 97 84
Normal 3 to <6 months HAP/VAP 98 96 97 93
Normal Adults HAP/VAP 95 97 100 97
Mild 12 to <18 years cIAI 99 97 100 97
Mild 6 to <12 years cIAI 100 98 100 98
Mild 2 to <6 years cIAI 100 97 100 97
Mild Adults cIAI 99 98 100 98
Mild 12 to <18 years cUTI 99 100 99 99
Mild 6 to <12 years cUTI 100 100 100 100
Mild 2 to <6 years cUTI 100 95 100 95
Mild Adults cUTI 99 100 100 100
Mild 12 to <18 years HAP/VAP 99 100 100 100
Mild 6 to <12 years HAP/VAP 100 100 100 100
Mild 2 to <6 years HAP/VAP 100 97 100 97
Mild Adults HAP/VAP 99 100 99 99 

stopifnot(
  # Centre: the parametric simulation sits below the published values (see
  # text), but by points, not tens of points.
  median(ptaCmp$joint - ptaCmp$published) > -15,
  median(ptaCmp$joint - ptaCmp$published) < 5,
  # Structural: the 33% higher ceftazidime CL in cIAI lowers attainment
  # against cUTI at the same ages. Pooled over the six pediatric age groups
  # (600 subjects per side) so the margin, about 9 points in development
  # runs, is several standard errors wide.
  mean(ptaCmp$joint[ptaCmp$renal == "Normal" & ptaCmp$ind == "cIAI" & ptaCmp$grp != "Adults"]) <
    mean(ptaCmp$joint[ptaCmp$renal == "Normal" & ptaCmp$ind == "cUTI" & ptaCmp$grp != "Adults"]),
  # Mild renal impairment raises exposure and therefore attainment.
  mean(ptaCmp$joint[ptaCmp$renal == "Mild"]) > mean(ptaCmp$joint[ptaCmp$renal == "Normal"])
)

Ceftazidime is the limiting analyte almost everywhere: avibactam attainment is close to 100% in every arm. The simulation reproduces the paper’s pattern – attainment highest with mild renal impairment, lowest for cIAI children aged 1 to < 6 years, where the 33% higher ceftazidime clearance in cIAI bites hardest – but sits several points below Table 4. Two documented differences push it that way: the paper resampled post hoc random effects in pairs from the same fitted subject, which carries the positive correlation between the two drugs’ clearances into the joint target, whereas here the two models draw independently; and the paper’s resampled, shrinkage-reinflated random effects are not the same distribution as the OMEGA matrix used here.

Assumptions and deviations

  1. Ceftazidime clearance is the Table S2 value, 7.75 L/h. The printed control stream’s $THETA carries 9.1259 for CL while every other theta agrees with Table S2 to rounding. Table S2 is the final run (its footnote identifies it as run121, and the control stream’s header says run121 re-parameterized the weight function of run120, the likely source of the initial values). The simulated adult and pediatric ceftazidime AUCs above match Table 3 with 7.75; with 9.13 every arm would sit about 15% low.
  2. The avibactam control stream holds initial values. Its $THETA matches the Li 2019 estimates and its $OMEGA BLOCK(4) is a 0.1 / 0.001 starting guess; all avibactam values are from Table S3. Its functional forms are used as printed.
  3. Covariates held at zero in the final avibactam control stream (sex, race, age powers, pediatric-study CL and Vc terms, the study-15 terms) are omitted from model(); sex, race and augmented renal clearance are listed under covariatesDataExcluded. The augmented-renal-clearance multiplier TH13 is held at 1, so RENAL_ARC has no effect.
  4. Residual strata. The avibactam PH2 flag tests the adult phase 2 study numbers (STDY = 2001/2002), not PHASE, so pediatric phase II records fall in the avibactam phase I stratum. The ceftazidime stream tests PHASE = 2 or 3, which includes the pediatric phase II studies (the control streams’ STDY = 15 branch shows those studies carry PHASE = 2). The pediatric phase 2 studies therefore have their own indicator, STUDY_CAZAVI_PED_PHASE2, used only by the ceftazidime model.
  5. Pediatric phase I subjects (suspected or confirmed infection) are taken to carry no infection-type indicator (DIS_* = 0); the paper does not state their POP code.
  6. The virtual cohort is a reconstruction. Child weights are drawn around approximate growth-chart medians for age, child NCrCL (normal stratum) lognormally around 125 mL/min/1.73 m^2 truncated at 80 (the Table 1 cohort medians are 89-130), adult weights and NCrCL from the Li 2019 adult summaries, and race from Table 1 (children) and Li 2019 (adults). The Pfizer covariate database the paper bootstrapped is not public.
  7. Ventilation and APACHE II in the simulation. As in the Li 2019 vignette, a third of HAP/VAP subjects are ventilated (138 of 413 adult nosocomial-pneumonia subjects had VAP) and 39% of adult cIAI and HAP/VAP subjects have an elevated APACHE II score (438 of 1,115); children have no APACHE score.
  8. Between-subject variability is drawn from the published OMEGA matrices, independently for the two analytes, whereas the paper resampled paired, shrinkage-reinflated post hoc random effects. This explains the avibactam exposure offset and the lower joint PTA discussed above. A few avibactam draws (extreme Q and Vc) fail the steady-state solve and are dropped.
  9. Table 2 headings. The original Table 2 transposed the ceftazidime and avibactam column headings; the values used here follow the 2024 erratum.