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Cefiderocol in pneumonia, BSI/sepsis and cUTI (Kawaguchi 2021)

Source: vignettes/articles/Kawaguchi_2021_cefiderocol.Rmd
Kawaguchi_2021_cefiderocol.Rmd

Model and source

Kawaguchi 2021 updates the same group’s earlier cefiderocol population PK analysis (Kawaguchi_2018_cefiderocol_clcr and its siblings) with the two phase 3 studies, APEKS-NP (pneumonia) and CREDIBLE-CR (pneumonia, bloodstream infection/sepsis or complicated urinary tract infection caused by carbapenem-resistant pathogens). The structure is unchanged – three compartments, intravenous infusion, first-order elimination – but the covariate model is new: clearance now follows Cockcroft-Gault creatinine clearance only up to 150 mL/min, each infection site carries its own factor on clearance, and serum albumin enters the central volume.

mod <- rxode2::rxode(readModelDb("Kawaguchi_2021_cefiderocol"))
#> ℹ parameter labels from comments will be replaced by 'label()'
cat(mod$reference)
#> Kawaguchi N, Katsube T, Echols R, Wajima T. Population pharmacokinetic and pharmacokinetic/pharmacodynamic analyses of cefiderocol, a parenteral siderophore cephalosporin, in patients with pneumonia, bloodstream infection/sepsis, or complicated urinary tract infection. Antimicrob Agents Chemother. 2021;65(3):e01437-20. doi:10.1128/AAC.01437-20

Population 

pop <- mod$population
str(pop[c("n_subjects", "n_studies", "n_observations", "age_range",
          "weight_range", "sex_female_pct")])
#> List of 6
#>  $ n_subjects    : int 516
#>  $ n_studies     : int 5
#>  $ n_observations: int 3427
#>  $ age_range     : chr "18-93 years (per-study medians 36.0 phase 1, 65.0 APEKS-cUTI, 68.0 APEKS-NP, 67.5 CREDIBLE-CR)"
#>  $ weight_range  : chr "25.0-156.0 kg (per-study medians 68.4-76.4 kg)"
#>  $ sex_female_pct: num 40.1

The analysis pooled 3427 plasma concentrations from 516 subjects in five studies (Table 1, Table S1): 91 subjects without infection from two phase 1 studies (healthy volunteers and a renal-impairment study), 238 patients with cUTI or acute uncomplicated pyelonephritis from the phase 2 APEKS-cUTI study, 115 pneumonia patients from APEKS-NP, and 72 patients from CREDIBLE-CR (31 pneumonia, 20 BSI/sepsis, 21 cUTI). Body weight ranged 25-156 kg and Cockcroft-Gault creatinine clearance 4-306 mL/min; the phase 3 patients were markedly hypoalbuminaemic (median 2.7-3.0 g/dL against 4.2 g/dL in the earlier studies). Hemodialysis patients were excluded. About 40% of subjects were female.

Source trace

Every value below comes from Table 2 of the article (final model column) or the final NONMEM control stream printed as Table S2. The two agree everywhere.

Quantity Value Source
Structure: 3-compartment IV, first-order elimination ADVAN11 TRANS4 Results; Table S2
CL (uninfected, CRCL 83.0 mL/min) 4.04 L/h Table 2; footnote b
V1 (uninfected, 72.6 kg, albumin 3.9 g/dL) 7.78 L Table 2; footnote b
Q2 6.19 L/h Table 2
V2 (72.6 kg) 5.77 L Table 2; footnote b
Q3 0.127 L/h Table 2
V3 0.798 L Table 2
CRCL exponent on CL, CRCL capped at 150 mL/min 0.682 Table 2; footnote b; Table S2 CLCR1
Weight exponent on V1 and V2 (shared) 0.580 Table 2; Table S2 WT1
Pneumonia factor on CL 0.981 Table 2; Table S2 PT14
BSI/sepsis factor on CL 1.08 Table 2; Table S2 PT13
cUTI (CREDIBLE-CR) factor on CL 0.872 Table 2; Table S2 PT12
cUTI/AUP (APEKS-cUTI) factor on CL 1.27 Table 2; Table S2 PT11
Albumin exponent on V1, centred at 3.9 g/dL -0.617 Table 2; footnote b; Table S2 ALB2
Any-infection factor on V1 1.39 Table 2; Table S2 PTV
IIV CL, V1, V2 (CV%) 37.5, 56.9, 33.6 Table 2
Covariances CL-V1, CL-V2, V1-V2 0.0886, 0.0792, 0.150 Table 2 (footnotes c-e give R)
Proportional residual error 20.5% Table 2; Table S2 W = IPRED*THETA(7), $SIGMA 1 FIX
Unbound fraction for fT>MIC 0.422 Materials and Methods

The omega scale

Table 2 prints IIV as a percent CV together with the three covariances and their correlation coefficients. That over-determines the scale. If the variance is (CV/100)^2, the implied covariance R * sd_a * sd_b must reproduce the printed covariance; under the log-normal reading sd = sqrt(log(1 + CV^2)) it would be about 10% smaller.

cv <- c(CL = 0.375, V1 = 0.569, V2 = 0.336)
printed <- data.frame(
  pair = c("CL-V1", "CL-V2", "V1-V2"),
  a = c("CL", "CL", "V1"), b = c("V1", "V2", "V2"),
  cov = c(0.0886, 0.0792, 0.150),
  R = c(0.415, 0.629, 0.784)
)
sd_cv <- cv
sd_ln <- sqrt(log(1 + cv^2))
printed$cov_if_cv <- printed$R * sd_cv[printed$a] * sd_cv[printed$b]
printed$cov_if_lognormal <- printed$R * sd_ln[printed$a] * sd_ln[printed$b]
knitr::kable(printed[, c("pair", "cov", "cov_if_cv", "cov_if_lognormal")],
             digits = 4)
pair cov cov_if_cv cov_if_lognormal
CL-V1 0.0886 0.0886 0.0797
CL-V2 0.0792 0.0793 0.0746
V1-V2 0.1500 0.1499 0.1358 
stopifnot(
  all(abs(printed$cov_if_cv / printed$cov - 1) < 0.005),
  all(abs(printed$cov_if_lognormal / printed$cov - 1) > 0.05)
)

# And the packaged omega matrix carries exactly those values.
om <- mod$omega
stopifnot(
  all(abs(diag(om) - cv^2) < 1e-12),
  abs(om["etalcl", "etalvc"] - 0.0886) < 1e-12,
  abs(om["etalcl", "etalvp"] - 0.0792) < 1e-12,
  abs(om["etalvc", "etalvp"] - 0.150) < 1e-12
)

Deterministic verification 

m0 <- suppressMessages(rxode2::zeroRe(mod))

# rxode2 warns when a zero-omega model is solved for many subjects; that is
# intended here, so only that one warning is muffled.
solve_quiet <- function(model, events, ...) {
  withCallingHandlers(
    as.data.frame(rxode2::rxSolve(model, events, returnType = "data.frame", ...)),
    warning = function(w) {
      if (grepl("without 'omega'", conditionMessage(w))) {
        invokeRestart("muffleWarning")
      }
    }
  )
}

cov_defaults <- c(DIS_PNEUMONIA = 0, DIS_BACTEREMIA = 0, DIS_CUTI = 0,
                  STUDY_CEFIDEROCOL_PHASE2 = 0)

The Table 2 footnote equations, reproduced exactly

Footnote b of Table 2 prints the full covariate equations. The packaged model must reproduce them to machine precision over a grid that crosses the 150 mL/min clearance cap, spans body weight and albumin, and visits every infection site.

sites <- data.frame(
  site = c("none", "pneumonia", "BSI/sepsis", "cUTI (CREDIBLE-CR)", "cUTI/AUP (APEKS-cUTI)"),
  DIS_PNEUMONIA = c(0, 1, 0, 0, 0),
  DIS_BACTEREMIA = c(0, 0, 1, 0, 0),
  DIS_CUTI = c(0, 0, 0, 1, 1),
  STUDY_CEFIDEROCOL_PHASE2 = c(0, 0, 0, 0, 1),
  f_cl = c(1, 0.981, 1.08, 0.872, 1.27),
  f_v1 = c(1, 1.39, 1.39, 1.39, 1.39)
)
grid <- tidyr::expand_grid(
  CRCL = c(10, 83, 149, 150, 151, 300),
  WT = c(40, 72.6, 120),
  ALB = c(15, 39, 50),          # g/L
  sites
)
grid$id <- seq_len(nrow(grid))
ev_grid <- grid |>
  select(id, CRCL, WT, ALB, DIS_PNEUMONIA, DIS_BACTEREMIA, DIS_CUTI,
         STUDY_CEFIDEROCOL_PHASE2) |>
  mutate(time = 1, amt = 0, evid = 0L, cmt = "central")
typ <- solve_quiet(m0, ev_grid) |>
  select(id, cl, vc, vp)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp'
chk <- grid |>
  inner_join(typ, by = "id") |>
  mutate(
    cl_paper = 4.04 * (pmin(CRCL, 150) / 83.0)^0.682 * f_cl,
    v1_paper = 7.78 * (WT / 72.6)^0.580 * ((ALB / 10) / 3.9)^-0.617 * f_v1,
    v2_paper = 5.77 * (WT / 72.6)^0.580
  )
c(cl = max(abs(chk$cl / chk$cl_paper - 1)),
  v1 = max(abs(chk$vc / chk$v1_paper - 1)),
  v2 = max(abs(chk$vp / chk$v2_paper - 1)))
#>           cl           v1           v2 
#> 1.332268e-15 5.551115e-16 1.776357e-15
stopifnot(
  nrow(chk) == nrow(grid),
  all(abs(chk$cl / chk$cl_paper - 1) < 1e-10),
  all(abs(chk$vc / chk$v1_paper - 1) < 1e-10),
  all(abs(chk$vp / chk$v2_paper - 1) < 1e-10)
)

The paper’s quoted percentages

The Results and Discussion state that CL in APEKS-cUTI patients was “27% higher than that in subjects without infection” and that V1 in infected patients was “39% higher”. Clearance must also be flat above 150 mL/min.

at <- function(site_name, crcl = 83) {
  chk[chk$site == site_name & chk$CRCL == crcl & chk$WT == 72.6 & chk$ALB == 39, ]
}
ratio_cl_cuti <- at("cUTI/AUP (APEKS-cUTI)")$cl / at("none")$cl
ratio_v1_inf <- at("pneumonia")$vc / at("none")$vc
flat <- at("none", 300)$cl / at("none", 150)$cl
c(cl_cuti = ratio_cl_cuti, v1_infected = ratio_v1_inf, cl_300_vs_150 = flat)
#>       cl_cuti   v1_infected cl_300_vs_150 
#>          1.27          1.39          1.00
stopifnot(
  abs(ratio_cl_cuti - 1.27) < 1e-10,
  abs(ratio_v1_inf - 1.39) < 1e-10,
  abs(flat - 1) < 1e-12,
  at("none", 151)$cl == at("none", 150)$cl,
  at("none", 149)$cl < at("none", 150)$cl
)

The infusion is an infusion

A single 2 g dose infused over 3 h in a typical pneumonia patient must peak at the end of the infusion, not at time zero.

ev_single <- data.frame(
  id = 1, time = c(0, seq(0.25, 48, by = 0.25)),
  amt = c(2000, rep(0, 192)), dur = c(3, rep(NA, 192)),
  evid = c(1L, rep(0L, 192)), cmt = "central",
  CRCL = 83, WT = 72.6, ALB = 28, DIS_PNEUMONIA = 1, DIS_BACTEREMIA = 0,
  DIS_CUTI = 0, STUDY_CEFIDEROCOL_PHASE2 = 0
)
single <- solve_quiet(m0, ev_single)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp'
tmax <- single$time[which.max(single$Cc)]
tmax
#> [1] 3
stopifnot(tmax == 3)

Virtual cohort

The paper’s Monte-Carlo simulation (Tables 3-4 and Figure 4 captions; Materials and Methods) generated, for each infection site, patients in six renal-function groups defined by Cockcroft-Gault CRCL: augmented (120 to 150 and above 150 mL/min, half each), normal (90 to <120), mild (60 to <90), moderate (30 to <60), severe (15 to <30) and ESRD (5 to <15). Body weight was log-normal with mean 72.6 kg and CV 30%, albumin log-normal with mean 2.8 g/dL and CV 30%. The cUTI simulations used the CREDIBLE-CR coefficient (STUDY_CEFIDEROCOL_PHASE2 = 0).

The paper simulated 1,000 patients per scenario; this vignette uses 200. Both the covariates and the random effects are drawn with base R, which is reproducible across R builds, and the model is then solved with its random effects zeroed and the drawn etas supplied as data columns. This keeps every number below identical across rxode2 versions.

set.seed(20210217)
n_per_arm <- 200
regimens <- data.frame(
  renal = c("Augmented", "Normal", "Mild", "Moderate", "Severe", "ESRD"),
  crcl_lo = c(120, 90, 60, 30, 15, 5),
  crcl_hi = c(150, 120, 90, 60, 30, 15),
  dose_mg = c(2000, 2000, 2000, 1500, 1000, 750),
  tau = c(6, 8, 8, 8, 8, 12)
)
infection_sites <- c("Pneumonia", "BSI/sepsis", "cUTI")
sd_log <- function(cv) sqrt(log(1 + cv^2))
chol_om <- chol(mod$omega)

arms <- list()
for (s in infection_sites) {
  for (g in seq_len(nrow(regimens))) {
    r <- regimens[g, ]
    crcl <- if (r$renal == "Augmented") {
      # Half 120 to <150, half above 150. CL is flat above 150 mL/min, so the
      # upper bound of 200 mL/min only affects the covariate column.
      c(runif(n_per_arm / 2, 120, 150), runif(n_per_arm / 2, 150, 200))
    } else {
      runif(n_per_arm, r$crcl_lo, r$crcl_hi)
    }
    eta <- matrix(rnorm(3 * n_per_arm), n_per_arm) %*% chol_om
    arms[[length(arms) + 1]] <- data.frame(
      site = s, renal = r$renal, dose_mg = r$dose_mg, tau = r$tau,
      CRCL = crcl,
      WT = rlnorm(n_per_arm, log(72.6) - sd_log(0.3)^2 / 2, sd_log(0.3)),
      ALB = 10 * rlnorm(n_per_arm, log(2.8) - sd_log(0.3)^2 / 2, sd_log(0.3)),
      DIS_PNEUMONIA = as.integer(s == "Pneumonia"),
      DIS_BACTEREMIA = as.integer(s == "BSI/sepsis"),
      DIS_CUTI = as.integer(s == "cUTI"),
      STUDY_CEFIDEROCOL_PHASE2 = 0L,
      etalcl = eta[, 1], etalvc = eta[, 2], etalvp = eta[, 3]
    )
  }
}
cohort <- dplyr::bind_rows(arms)
cohort$id <- seq_len(nrow(cohort))
cohort$treatment <- paste(cohort$site, cohort$renal, sep = ": ")

cohort |>
  group_by(site) |>
  summarise(n = n(), WT_mean = mean(WT), ALB_mean_gdL = mean(ALB) / 10,
            .groups = "drop") |>
  knitr::kable(digits = 2)
site n WT_mean ALB_mean_gdL
BSI/sepsis 1200 73.15 2.78
Pneumonia 1200 72.94 2.76
cUTI 1200 72.54 2.79 
stopifnot(
  nrow(cohort) == 18 * n_per_arm,
  !anyDuplicated(cohort$id),
  abs(mean(cohort$WT) / 72.6 - 1) < 0.05,
  abs(mean(cohort$ALB) / 28 - 1) < 0.05
)

Simulation

Each subject is simulated over one steady-state dosing interval (3 h infusion, ss = 1), observed every 0.05 h.

cov_cols <- c("CRCL", "WT", "ALB", "DIS_PNEUMONIA", "DIS_BACTEREMIA", "DIS_CUTI",
              "STUDY_CEFIDEROCOL_PHASE2", "etalcl", "etalvc", "etalvp")
dose_rows <- cohort |>
  transmute(id, time = 0, amt = dose_mg, dur = 3, ii = tau, ss = 1L,
            evid = 1L, cmt = "central") |>
  bind_cols(cohort[, cov_cols])
obs_rows <- cohort |>
  select(id, tau, all_of(cov_cols)) |>
  reframe(time = seq(0, tau, by = 0.05), .by = c(id, tau, all_of(cov_cols))) |>
  mutate(amt = 0, dur = NA_real_, ii = 0, ss = 0L, evid = 0L, cmt = "central") |>
  select(-tau)
events <- bind_rows(dose_rows, obs_rows) |>
  arrange(id, time, desc(evid))

# maxsteps: the lsoda step budget is charged across the steady-state search.
sim <- solve_quiet(m0, events, maxsteps = 1e6) |>
  select(id, time, Cc, cl) |>
  inner_join(cohort |> select(id, site, renal, treatment, tau, dose_mg), by = "id")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp'
stopifnot(!anyNA(sim$Cc), all(sim$Cc > 0))

Typical profiles by infection site 

typ_ev <- sites |>
  filter(site != "cUTI/AUP (APEKS-cUTI)") |>
  mutate(id = row_number(), CRCL = 83, WT = 72.6, ALB = 28)
typ_ev <- typ_ev |>
  select(-f_cl, -f_v1) |>
  tidyr::crossing(time = seq(0, 48, by = 0.1)) |>
  mutate(amt = 0, dur = NA_real_, ii = 0, addl = 0L, evid = 0L, cmt = "central") |>
  bind_rows(
    typ_ev |>
      select(-f_cl, -f_v1) |>
      mutate(time = 0, amt = 2000, dur = 3, ii = 8, addl = 5L, evid = 1L,
             cmt = "central")
  ) |>
  arrange(id, time, desc(evid))
typ_sim <- solve_quiet(m0, typ_ev, keep = "site")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp'
ggplot(typ_sim, aes(time, Cc, colour = site)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Total cefiderocol (ug/mL)", colour = NULL,
       caption = paste("Typical patient, CRCL 83 mL/min, 72.6 kg, albumin",
                       "2.8 g/dL, 2 g q8h over 3 h.")) +
  theme_bw()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

Replicate published tables

Tables 3 and 4 – probability of target attainment

The free concentration is 0.422 * Cc (Materials and Methods). The percentage of the dosing interval with free concentration above the MIC (%fT>MIC) is the fraction of the 0.05 h grid over [0, tau) above the MIC; 100% fT>MIC is equivalent to a free trough above the MIC.

mics <- c(0.25, 0.5, 1, 2, 4, 8, 16)
ft <- sim |>
  filter(time < tau) |>
  mutate(Cfree = 0.422 * Cc) |>
  tidyr::crossing(mic = mics) |>
  group_by(id, site, renal, mic) |>
  summarise(ft = mean(Cfree > mic), .groups = "drop")
pta_sim <- ft |>
  group_by(site, renal, mic) |>
  summarise(pta75 = 100 * mean(ft >= 0.75), pta100 = 100 * mean(ft >= 1),
            .groups = "drop")

# Kawaguchi 2021 Table 3 (75% fT>MIC) and Table 4 (100% fT>MIC).
pta_row <- function(site, renal, target, v) {
  data.frame(site = site, renal = renal, target = target, mic = mics, paper = v)
}
paper <- rbind(
  pta_row("Pneumonia", "Augmented", 75, c(100, 100, 100, 100, 99.7, 94.5, 60.4)),
  pta_row("Pneumonia", "Normal", 75, c(100, 100, 100, 99.9, 98.9, 87.1, 43.4)),
  pta_row("Pneumonia", "Mild", 75, c(100, 100, 100, 100, 99.8, 97.0, 69.7)),
  pta_row("Pneumonia", "Moderate", 75, c(100, 100, 100, 100, 99.9, 98.7, 83.3)),
  pta_row("Pneumonia", "Severe", 75, c(100, 100, 100, 100, 100, 99.9, 90.7)),
  pta_row("Pneumonia", "ESRD", 75, c(100, 100, 100, 100, 100, 99.6, 86.3)),
  pta_row("BSI/sepsis", "Augmented", 75, c(100, 100, 100, 100, 99.4, 91.3, 49.6)),
  pta_row("BSI/sepsis", "Normal", 75, c(100, 100, 100, 99.9, 97.3, 80.6, 32.6)),
  pta_row("BSI/sepsis", "Mild", 75, c(100, 100, 100, 99.9, 99.6, 94.4, 57.7)),
  pta_row("BSI/sepsis", "Moderate", 75, c(100, 100, 100, 100, 99.9, 98.0, 74.8)),
  pta_row("BSI/sepsis", "Severe", 75, c(100, 100, 100, 100, 100, 99.8, 84.8)),
  pta_row("BSI/sepsis", "ESRD", 75, c(100, 100, 100, 100, 100, 99.2, 79.2)),
  pta_row("cUTI", "Augmented", 75, c(100, 100, 100, 100, 99.9, 96.9, 73.3)),
  pta_row("cUTI", "Normal", 75, c(100, 100, 100, 100, 99.6, 93.6, 56.3)),
  pta_row("cUTI", "Mild", 75, c(100, 100, 100, 100, 99.8, 98.4, 81.2)),
  pta_row("cUTI", "Moderate", 75, c(100, 100, 100, 100, 100, 99.6, 90.4)),
  pta_row("cUTI", "Severe", 75, c(100, 100, 100, 100, 100, 100, 95.9)),
  pta_row("cUTI", "ESRD", 75, c(100, 100, 100, 100, 100, 100, 91.6)),
  pta_row("Pneumonia", "Augmented", 100, c(100, 100, 100, 99.7, 95.9, 79.8, 37.0)),
  pta_row("Pneumonia", "Normal", 100, c(100, 100, 99.9, 98.3, 91.2, 64.6, 23.2)),
  pta_row("Pneumonia", "Mild", 100, c(100, 100, 99.9, 99.7, 98.2, 85.9, 46.4)),
  pta_row("Pneumonia", "Moderate", 100, c(100, 100, 100, 100, 99.5, 94.8, 66.7)),
  pta_row("Pneumonia", "Severe", 100, c(100, 100, 100, 100, 100, 99.5, 81.8)),
  pta_row("Pneumonia", "ESRD", 100, c(100, 100, 100, 100, 100, 98.3, 77.1)),
  pta_row("BSI/sepsis", "Augmented", 100, c(100, 100, 100, 99.4, 93.6, 71.6, 28.5)),
  pta_row("BSI/sepsis", "Normal", 100, c(100, 99.9, 99.5, 96.2, 85.8, 54.0, 14.1)),
  pta_row("BSI/sepsis", "Mild", 100, c(100, 100, 99.8, 99.4, 96.0, 78.0, 36.1)),
  pta_row("BSI/sepsis", "Moderate", 100, c(100, 100, 100, 99.9, 98.7, 91.2, 55.8)),
  pta_row("BSI/sepsis", "Severe", 100, c(100, 100, 100, 100, 100, 98.3, 74.7)),
  pta_row("BSI/sepsis", "ESRD", 100, c(100, 100, 100, 100, 100, 96.8, 68.0)),
  pta_row("cUTI", "Augmented", 100, c(100, 100, 100, 100, 98.0, 88.3, 51.1)),
  pta_row("cUTI", "Normal", 100, c(100, 100, 99.9, 99.4, 95.1, 77.6, 34.3)),
  pta_row("cUTI", "Mild", 100, c(100, 100, 100, 99.8, 98.9, 93.2, 59.4)),
  pta_row("cUTI", "Moderate", 100, c(100, 100, 100, 100, 99.8, 97.7, 79.1)),
  pta_row("cUTI", "Severe", 100, c(100, 100, 100, 100, 100, 99.7, 90.1)),
  pta_row("cUTI", "ESRD", 100, c(100, 100, 100, 100, 100, 99.4, 85.7))
)
stopifnot(nrow(paper) == 2 * 18 * length(mics))

pta_cmp <- pta_sim |>
  tidyr::pivot_longer(c(pta75, pta100), names_to = "target", values_to = "sim") |>
  mutate(target = ifelse(target == "pta75", 75, 100)) |>
  inner_join(paper, by = c("site", "renal", "target", "mic")) |>
  mutate(diff = sim - paper)
stopifnot(nrow(pta_cmp) == nrow(paper))
pta_cmp |>
  filter(mic %in% c(4, 8, 16)) |>
  mutate(cell = sprintf("%.1f (%.1f)", sim, paper)) |>
  select(target, site, renal, mic, cell) |>
  tidyr::pivot_wider(names_from = mic, values_from = cell) |>
  dplyr::rename(
    "Target %fT>MIC" = target, "Infection site" = site,
    "Renal function" = renal, "MIC 4" = `4`, "MIC 8" = `8`, "MIC 16" = `16`
  ) |>
  knitr::kable(caption = paste(
    "Simulated PTA (%) with Kawaguchi 2021 Tables 3 and 4 in parentheses,",
    "for the MICs where attainment is not saturated at 100%.",
    "200 simulated patients per row against 1,000 in the paper."
  ))
Simulated PTA (%) with Kawaguchi 2021 Tables 3 and 4 in parentheses, for the MICs where attainment is not saturated at 100%. 200 simulated patients per row against 1,000 in the paper.
Target %fT>MIC Infection site Renal function MIC 4 MIC 8 MIC 16
75 BSI/sepsis Augmented 100.0 (99.4) 92.0 (91.3) 45.5 (49.6)
100 BSI/sepsis Augmented 93.5 (93.6) 68.0 (71.6) 26.0 (28.5)
75 BSI/sepsis ESRD 100.0 (100.0) 99.0 (99.2) 77.5 (79.2)
100 BSI/sepsis ESRD 100.0 (100.0) 95.0 (96.8) 67.5 (68.0)
75 BSI/sepsis Mild 99.5 (99.6) 93.5 (94.4) 65.0 (57.7)
100 BSI/sepsis Mild 95.5 (96.0) 77.5 (78.0) 38.5 (36.1)
75 BSI/sepsis Moderate 100.0 (99.9) 98.5 (98.0) 76.5 (74.8)
100 BSI/sepsis Moderate 99.0 (98.7) 92.5 (91.2) 56.5 (55.8)
75 BSI/sepsis Normal 96.5 (97.3) 79.5 (80.6) 36.0 (32.6)
100 BSI/sepsis Normal 83.0 (85.8) 55.5 (54.0) 17.0 (14.1)
75 BSI/sepsis Severe 100.0 (100.0) 99.5 (99.8) 87.0 (84.8)
100 BSI/sepsis Severe 100.0 (100.0) 99.0 (98.3) 79.5 (74.7)
75 Pneumonia Augmented 100.0 (99.7) 97.5 (94.5) 66.0 (60.4)
100 Pneumonia Augmented 98.0 (95.9) 82.0 (79.8) 39.0 (37.0)
75 Pneumonia ESRD 100.0 (100.0) 99.5 (99.6) 80.5 (86.3)
100 Pneumonia ESRD 100.0 (100.0) 95.5 (98.3) 69.5 (77.1)
75 Pneumonia Mild 99.0 (99.8) 95.5 (97.0) 68.5 (69.7)
100 Pneumonia Mild 97.0 (98.2) 85.0 (85.9) 47.5 (46.4)
75 Pneumonia Moderate 100.0 (99.9) 99.5 (98.7) 83.0 (83.3)
100 Pneumonia Moderate 100.0 (99.5) 95.0 (94.8) 65.5 (66.7)
75 Pneumonia Normal 99.0 (98.9) 89.0 (87.1) 47.5 (43.4)
100 Pneumonia Normal 90.0 (91.2) 67.5 (64.6) 24.0 (23.2)
75 Pneumonia Severe 100.0 (100.0) 100.0 (99.9) 89.5 (90.7)
100 Pneumonia Severe 100.0 (100.0) 97.0 (99.5) 81.0 (81.8)
75 cUTI Augmented 100.0 (99.9) 97.5 (96.9) 71.0 (73.3)
100 cUTI Augmented 97.0 (98.0) 86.0 (88.3) 50.5 (51.1)
75 cUTI ESRD 100.0 (100.0) 99.5 (100.0) 90.5 (91.6)
100 cUTI ESRD 100.0 (100.0) 99.0 (99.4) 85.0 (85.7)
75 cUTI Mild 100.0 (99.8) 100.0 (98.4) 82.5 (81.2)
100 cUTI Mild 99.5 (98.9) 93.0 (93.2) 61.5 (59.4)
75 cUTI Moderate 100.0 (100.0) 100.0 (99.6) 88.0 (90.4)
100 cUTI Moderate 100.0 (99.8) 98.0 (97.7) 72.5 (79.1)
75 cUTI Normal 100.0 (99.6) 92.0 (93.6) 58.0 (56.3)
100 cUTI Normal 93.0 (95.1) 73.5 (77.6) 35.5 (34.3)
75 cUTI Severe 100.0 (100.0) 100.0 (100.0) 93.0 (95.9)
100 cUTI Severe 100.0 (100.0) 100.0 (99.7) 86.5 (90.1) 
ggplot(pta_cmp, aes(mic)) +
  geom_line(aes(y = sim, colour = "Simulated")) +
  geom_point(aes(y = paper, colour = "Kawaguchi 2021")) +
  facet_grid(renal ~ paste0(target, "% fT>MIC, ", site)) +
  scale_x_log10(breaks = mics, labels = format(mics)) +
  labs(x = "MIC (ug/mL)", y = "PTA (%)", colour = NULL,
       caption = "Replicates Tables 3 and 4 of Kawaguchi 2021.") +
  theme_bw() +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))

The agreement is measured over every cell, and separately over the cells whose paper value is below 99% (where attainment is not saturated and the comparison actually discriminates). With 200 patients per row the binomial standard error at a 50% PTA is 3.5 percentage points, so a few points of scatter is expected.

disc <- pta_cmp |> filter(paper < 99)
summary_pta <- c(
  n_cells = nrow(pta_cmp),
  n_discriminating = nrow(disc),
  median_diff = median(disc$diff),
  median_abs_diff = median(abs(disc$diff)),
  p90_abs_diff = unname(quantile(abs(disc$diff), 0.9)),
  max_abs_diff_all = max(abs(pta_cmp$diff))
)
round(summary_pta, 2)
#>          n_cells n_discriminating      median_diff  median_abs_diff 
#>           252.00            76.00            -0.25             1.40 
#>     p90_abs_diff max_abs_diff_all 
#>             4.10             7.60
stopifnot(
  nrow(disc) >= 30,
  # Centre: a mis-transcribed clearance or unbound fraction shifts every
  # non-saturated cell in one direction by far more than this.
  abs(median(disc$diff)) < 3,
  median(abs(disc$diff)) < 4,
  quantile(abs(disc$diff), 0.9) < 8
)

Figure 4 – integrated PTA and the text’s breakpoint claims

The integrated PTA weights the renal-function groups by the phase 3 CRCL distribution (Materials and Methods: 20.3%, 15.0%, 24.6%, 32.6%, 4.8% and 2.7% from augmented to ESRD). The Results state that the highest MIC reaching >90% integrated PTA was 8 ug/mL for 75% fT>MIC regardless of infection site, and 4 ug/mL for 100% fT>MIC. Figure 4 itself is not digitised here; instead the same weighting is applied both to the simulation and to the paper’s Tables 3-4.

weights <- data.frame(
  renal = regimens$renal,
  w = c(20.3, 15.0, 24.6, 32.6, 4.8, 2.7) / 100
)
integ <- pta_cmp |>
  inner_join(weights, by = "renal") |>
  group_by(site, target, mic) |>
  summarise(sim = sum(w * sim) / sum(w), paper = sum(w * paper) / sum(w),
            .groups = "drop")
ggplot(integ, aes(mic, sim, colour = site)) +
  geom_line() +
  geom_point(aes(y = paper), shape = 1) +
  geom_hline(yintercept = 90, linetype = 2) +
  facet_wrap(~ paste0(target, "% fT>MIC")) +
  scale_x_log10(breaks = mics, labels = format(mics)) +
  labs(x = "MIC (ug/mL)", y = "Integrated PTA (%)", colour = NULL,
       caption = paste("Lines: simulated. Open circles: the same weighting",
                       "applied to Tables 3-4. Replicates Figure 4.")) +
  theme_bw()


highest_mic <- integ |>
  group_by(site, target) |>
  summarise(
    simulated = max(mic[sim > 90]),
    from_tables = max(mic[paper > 90]),
    sim_at_8 = sim[mic == 8], tables_at_8 = paper[mic == 8],
    .groups = "drop"
  )
knitr::kable(highest_mic, digits = 1, caption = paste(
  "Highest MIC with integrated PTA above 90%, from the simulation and from",
  "the same weighting applied to Tables 3-4, with the integrated PTA at",
  "MIC 8 ug/mL."
))
Highest MIC with integrated PTA above 90%, from the simulation and from the same weighting applied to Tables 3-4, with the integrated PTA at MIC 8 ug/mL.
site target simulated from_tables sim_at_8 tables_at_8
BSI/sepsis 75 8 8 93.2 93.3
BSI/sepsis 100 4 4 78.7 78.9
Pneumonia 75 8 8 96.6 95.8
Pneumonia 100 4 4 85.9 85.4
cUTI 75 8 8 98.3 97.9
cUTI 100 8 8 90.8 91.8 
stopifnot(
  nrow(highest_mic) == 6,
  # Integrated PTA tracks the paper's tables at every MIC.
  max(abs(integ$sim - integ$paper)) < 4,
  # 75% fT>MIC: 8 ug/mL for every infection site, as the Results state.
  all(highest_mic$simulated[highest_mic$target == 75] == 8),
  # 100% fT>MIC: 4 ug/mL for pneumonia and BSI/sepsis.
  all(highest_mic$simulated[highest_mic$target == 100 & highest_mic$site != "cUTI"] == 4)
)

For 100% fT>MIC in cUTI the text’s “4 ug/mL” cannot be reproduced from the paper’s own Table 4: weighting its cUTI rows gives 91.8% at 8 ug/mL, just above the 90% line, and the simulation gives 90.8%. The cUTI cell sits on the 90% threshold, so its “highest MIC” is not a stable quantity and is not asserted; its integrated PTA is covered by the max(abs(sim - paper)) check above.

PKNCA validation

NCA over the steady-state dosing interval for the pneumonia arms (the largest infected population in the analysis).

nca_ids <- cohort |> filter(site == "Pneumonia") |> pull(id)
sim_nca <- sim |>
  filter(id %in% nca_ids, abs(time / 0.25 - round(time / 0.25)) < 1e-8) |>
  select(id, time, Cc, treatment)
dose_df <- cohort |>
  filter(id %in% nca_ids) |>
  transmute(id, time = 0, amt = dose_mg, treatment)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id,
                             concu = "ug/mL", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             doseu = "mg")
intervals <- cohort |>
  filter(id %in% nca_ids) |>
  distinct(treatment, tau) |>
  transmute(treatment, start = 0, end = tau, cmax = TRUE, tmax = TRUE,
            cmin = TRUE, cav = TRUE, auclast = TRUE)
nca_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
)
nca_tbl <- as.data.frame(nca_res$result)
stopifnot(nrow(nca_tbl) > 0, !anyNA(nca_tbl$PPORRES))

Steady-state mass balance

At steady state, CL * AUC(0-tau) = Dose for every subject.

cl_ind <- sim |> filter(id %in% nca_ids) |> distinct(id, cl, dose_mg)
mb <- nca_tbl |>
  filter(PPTESTCD == "auclast") |>
  select(id, auc = PPORRES) |>
  inner_join(cl_ind, by = "id") |>
  mutate(pct = 100 * (cl * auc / dose_mg - 1))
summary(mb$pct)
#>       Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
#> -0.1674356 -0.0211749 -0.0082339 -0.0162710 -0.0029332 -0.0004021
stopifnot(
  nrow(mb) == length(nca_ids),
  abs(median(mb$pct)) < 1,
  quantile(abs(mb$pct), 0.95) < 2
)

Comparison against the published exposure

The Discussion reports geometric-mean daily AUC from the phase 3 post hoc estimates: 1,365 ug*h/mL at 2 g q6h in patients with augmented renal function, and 1,494 ug*h/mL at 2 g q8h in patients with normal renal function. These are empirical summaries of the enrolled patients (whose covariates are not published), not typical-value predictions, so the comparison is corroborative. Daily AUC is 24 * Cavg; the published values are shown as the equivalent Cavg. The 2 g q8h group is taken as the simulated normal and mild arms together (CRCL 60 to <120 mL/min, the range that receives 2 g q8h).

simulated <- nca_tbl |>
  filter(PPTESTCD == "cav") |>
  mutate(group = case_when(
    grepl("Augmented", treatment) ~ "2 g q6h, augmented",
    grepl("Normal|Mild", treatment) ~ "2 g q8h, normal",
    TRUE ~ NA_character_
  )) |>
  filter(!is.na(group)) |>
  group_by(group, PPTESTCD) |>
  summarise(PPORRES = exp(mean(log(PPORRES))), .groups = "drop")
published <- data.frame(
  group = c("2 g q6h, augmented", "2 g q8h, normal"),
  cav = c(1365, 1494) / 24
)
cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = simulated,
  reference = published,
  by = "group",
  units = c(cav = "ug/mL"),
  tolerance_pct = 20
)
knitr::kable(cmp, caption = paste(
  "Simulated geometric-mean steady-state Cavg (pneumonia patients) against",
  "the Discussion's phase 3 geometric-mean daily AUC divided by 24 h.",
  "* differs from reference by more than 20%."
))
Simulated geometric-mean steady-state Cavg (pneumonia patients) against the Discussion’s phase 3 geometric-mean daily AUC divided by 24 h. * differs from reference by more than 20%.
NCA parameter group Reference Simulated % diff
Cavg (ug/mL) 2 g q6h, augmented 56.9 60.4 +6.2%
Cavg (ug/mL) 2 g q8h, normal 62.2 60.9 -2.2% 
sim_cav <- setNames(simulated$PPORRES, simulated$group)
stopifnot(all(abs(sim_cav[published$group] / published$cav - 1) < 0.2))

Assumptions and deviations

  • Covariate encoding. The paper’s infection-site variable (PT in Table S2) is split into mutually exclusive indicators DIS_PNEUMONIA, DIS_BACTEREMIA (the paper’s BSI/sepsis category) and DIS_CUTI (cUTI, pooled with acute uncomplicated pyelonephritis in the phase 2 study). The any-infection factor on V1 is applied to their sum. The pneumonia arm pooled hospital-acquired, ventilator-associated and health care-associated pneumonia under one coefficient, so the general pneumonia flag is used.
  • Study-specific cUTI effect. The cUTI factor on CL differs between the phase 2 APEKS-cUTI study (1.27) and the phase 3 CREDIBLE-CR study (0.872); the control stream switches on the subject ID. The packaged model uses a STUDY_CEFIDEROCOL_PHASE2 indicator, whose default of 0 gives the CREDIBLE-CR value that the paper used in its own simulations.
  • Albumin units. The model was calibrated in g/dL (reference 3.9 g/dL). The packaged model takes albumin in g/L and divides by 10 internally.
  • Albumin exponent sign. The article’s typeset minus sign (-0.617) is confirmed by the control stream’s bounds for THETA(14), (-2.0, -0.5, 0.5), and by the Discussion (lower albumin, larger V1).
  • Time-varying creatinine clearance. The source data used baseline CRCL for the phase 1 and phase 2 studies and time-varying CRCL for the phase 3 studies; the packaged model accepts either.
  • Virtual cohort details not stated in the paper. The log-normal body weight and albumin distributions are parameterised with the stated means as arithmetic means. The upper bound for the augmented group above 150 mL/min is set at 200 mL/min, which has no effect on CL because of the 150 mL/min cap. CRCL is uniform within each group. The paper’s %fT>MIC is taken without residual error; simulating 200 rather than 1,000 patients per scenario adds a few points of binomial scatter to each PTA cell.
  • Integrated PTA claim for cUTI. The Results state that the highest MIC with more than 90% integrated PTA for 100% fT>MIC was 4 ug/mL. Applying the stated renal-function weights to the paper’s own Table 4 gives 91.8% for cUTI at 8 ug/mL, so for cUTI the statement holds only if Figure 4 was computed slightly differently from the tables. Pneumonia and BSI/sepsis agree with the statement, and the simulated cUTI value (about 91%) sits on the same threshold as the tables.