Skip to contents

Lefamulin popPK with ELF penetration and PK/PD target attainment (Bian 2024)

Source: vignettes/articles/Bian_2024_lefamulin.Rmd
Bian_2024_lefamulin.Rmd

Model and source

Bian 2024 contributes two models to nlmixr2lib. They share one structure and one covariate model but are separate fits under two different plasma protein binding (ppb) assumptions, and they attach the epithelial lining fluid (ELF) layer in two different ways, so they are packaged as two files.

  • Bian_2024_lefamulin_original_ppb – the diluted-plasma binding fit (Supplementary Table S1), with ELF as an effect compartment.

  • Bian_2024_lefamulin_higher_ppb – the non-diluted binding fit (Supplementary Table S2), with ELF as an algebraic power-penetration function adopted from the FDA XENLETA review.

  • Citation: Bian X, Li N, Li Y, Zhu X, Yu J, Hu Y, Yang H, Wei Q, Wu X, Wang J, Cao G, Wu J, Wang Y, Zhang J. Lefamulin dosing optimization using population pharmacokinetic and pharmacokinetic/pharmacodynamic assessment in Chinese patients with community-acquired bacterial pneumonia. Front Pharmacol. 2024;15:1456741. doi:10.3389/fphar.2024.1456741. Structural equations from Equations 1-20; parameter values from Supplementary Table S1. The underlying popPK plus ELF framework was developed in Zhang L, Wicha SG, Bhavnani SM, et al. J Antimicrob Chemother. 2019;74(Suppl 3):iii27-iii34. doi:10.1093/jac/dkz088, and in the FDA XENLETA Multi-Discipline Review, NDA 211672/211673 (2019).

  • Article: https://doi.org/10.3389/fphar.2024.1456741

  • Upstream framework paper (Zhang 2019): https://doi.org/10.1093/jac/dkz088

  • FDA XENLETA Multi-Discipline Review, NDA 211672/211673 (2019): https://www.accessdata.fda.gov/drugsatfda_docs/nda/2019/211672Orig1s000,211673Orig1s000MultidisciplineR.pdf

mod_orig   <- readModelDb("Bian_2024_lefamulin_original_ppb")
mod_higher <- readModelDb("Bian_2024_lefamulin_higher_ppb")

Population

The model was developed on a pooled foreign dataset of 849 subjects: 98 Phase 1 healthy adults, 129 Phase 2 patients with acute bacterial skin and skin structure infections, and 622 Phase 3 patients with community-acquired bacterial pneumonia (CABP). Median age 57 years (18-97), median weight 78 kg (31-174.6), median albumin 4.1 g/dL (2-5.6), 38.8% female, 78.2% White / 8.5% Asian / 8.1% Black (Supplementary Table S5). Study phase enters the model as a covariate on CL, CLd1 and Vp1, with Phase 3 as the reference stratum; albumin acts on CL and body weight on Vp1, both as linear proportional shifts around the pooled medians.

Bian 2024 externally validated that model against 33 Chinese CABP patients from a Phase III trial (median age 56.1 years, weight 69.38 kg, albumin 3.88 g/dL, 100% Asian, 18.2% female) and then ran Monte Carlo simulations on 5000 virtual CABP patients whose baseline weight and albumin were resampled from 125 Chinese CABP patients. The virtual cohort below reproduces that simulation population.

The same information is available programmatically via readModelDb("Bian_2024_lefamulin_original_ppb")()$population.

Source trace

Per-parameter origins are recorded as in-file comments next to each ini() entry in inst/modeldb/specificDrugs/Bian_2024_lefamulin_original_ppb.R and ..._higher_ppb.R. They are collected here for review. “S1” / “S2” refer to Bian 2024 Supplementary Tables S1 and S2; equation numbers are from the main text.

Equation / parameter Original ppb Higher ppb Source location
lcl (CL, L/h) 79.4 282 theta1, S1 / S2
lvc (Vc, L) 46.3 138 theta2, S1 / S2
lq (CLd1, L/h) 40.6 187 theta3, S1 / S2
lvp (Vp1, L) 249 1300 theta4, S1 / S2
lq2 (CLd2, L/h) 199 421 theta5, S1 / S2
lvp2 (Vp2, L) 259 449 theta6, S1 / S2
lka (1/h) 1.2 0.686 theta7, S1 / S2
lka2 (1/h) 2.12 1.34 theta8, S1 / S2
logitfdepot (Ftot) 0.244 0.293 theta9, S1 / S2; Equations 9, 10
logitfrac (FS) 0.802 0.622 theta10, S1 / S2; Equations 11, 12
ltlag (ALAG, h) 0.15 0.124 theta11, S1 / S2; Equation 15
fumin (fixed) 0.0997 0.0260 theta12, S1 / S2; Equations 16, 17
fumax (fixed) 0.259 0.194 theta13, S1 / S2; Equations 16, 18
cup50 (mg/L, fixed) 1.35 0.814 theta14, S1 / S2; Equations 16, 19
e_fed_ka2 0.445 0.513 theta17, S1 / S2; Equation 8
e_fed_fdepot 0.763 0.802 theta18, S1 / S2; Equation 9
e_fed_ka 0.0541 0.0525 theta19, S1 / S2; Equation 7
e_alb_cl (per g/dL) 0.214 0.2 theta20, S1 / S2 printed as 1 + theta; Equation 1
e_phase2_cl 0.827 0.707 theta21, S1 / S2 printed as 1 + theta; Equation 1
e_phase1_cl 0.766 0.710 theta22, S1 / S2 printed as 1 + theta; Equation 1
e_phase2_q 0.44 0.192 theta23, S1 / S2 printed as 1 + theta; Equation 3
e_phase1_q 1.12 0.788 theta24, S1 / S2 printed as 1 + theta; Equation 3
e_phase2_vp 0.985 0.28 theta25, S1 / S2 printed as 1 + theta; Equation 4
e_phase1_vp 1.75 0.889 theta26, S1 / S2 printed as 1 + theta; Equation 4
e_wt_vp (per kg) 0.0129 0.00637 theta27, S1 / S2 printed as 1 + theta; Equation 4
lkin_elf (1/h) 2.71 n/a theta28 KELF,in, S1; Figure 2
lkout_elf (1/h) 0.51 n/a theta29 KELF,out, S1; Figure 2
lpenratio_elf n/a 3.45 back-solved from Table S6 – S2 prints 2.71; see Errata
pwr_penratio_elf n/a 0.51 theta29 Power, S2; Equation 21
etalcl … etalogitfrac 0.171, 0.39, 0.119, 0.623, 0.800, 0.400, 0.100, 0.170 0.151, 0.195, 0.064, 0.0875, 2.65, 0.264, 0.791, 0.716 eta1-4, 7-10, S1 / S2 (variances)
propSd, addSd, propSd_Celf 0.3209, 0.005857, 0.6099 0.30952, 0.004087, 0.43818 sqrt of sigma^2 eps1-3, S1 / S2; Equation 20
Disposition ODEs, parallel absorption, transit chain – – Figure 2 (model diagram)
ELF effect compartment – – Methods “PopPK model integrating ELF distribution compartment”; Figure 2
ELF power penetration Celf = penratio_elf * (Cc * 0.0379)^power – – Equation 21; FDA review section 16.3.2.4.1

Virtual cohort

Original observed data are not publicly available. The cohort below reproduces the paper’s simulation population: Chinese CABP patients (study Phase 3, the reference stratum) whose baseline weight and albumin match the Chinese Phase III distributions in Supplementary Table S5 (weight median 69.38 kg, range 40-112; albumin median 3.88 g/dL, range 2.9-4.8).

set.seed(20241025)

n_per_arm <- 200L

arms <- tibble::tribble(
  ~arm,                      ~route, ~dose, ~dur, ~fed,
  "150 mg q12h IV 1 h",      "iv",   150,   1.0,  0,
  "150 mg q12h IV 1.5 h",    "iv",   150,   1.5,  0,
  "150 mg q12h IV 2 h",      "iv",   150,   2.0,  0,
  "600 mg q12h PO fasted",   "po",   600,   NA,   0,
  "600 mg q12h PO fed",      "po",   600,   NA,   1
)

dose_times <- seq(0, 72, by = 12)
# Observations cover Day 1 (0-24 h) and Day 3 (48-72 h), the two windows over
# which Supplementary Table S6 integrates exposure.
obs_times  <- c(seq(0, 24, by = 0.25), seq(48, 72, by = 0.25))

#' Build one treatment arm as a self-contained event table.
#'
#' `id_offset` shifts subject IDs so arms can be bind_rows()-ed without
#' colliding: rxSolve treats id as the subject key, and duplicate ids across
#' arms silently collapse into single (wrong) subjects.
make_arm <- function(n, arm, route, dose, dur, fed, id_offset) {
  subj <- tibble(
    id  = id_offset + seq_len(n),
    # Log-normal weight and normal albumin truncated to the observed Chinese
    # Phase III ranges (Supplementary Table S5, External validation column).
    WT  = pmin(pmax(stats::rlnorm(n, log(69.38), 0.20), 40), 112),
    ALB = pmin(pmax(stats::rnorm(n, 3.88, 0.45), 2.9), 4.8) * 10, # g/dL -> g/L
    STUDY_LEFAMULIN_PHASE1 = 0,
    STUDY_LEFAMULIN_PHASE2 = 0,
    FED = fed,
    arm = arm
  )

  doses <-
    if (route == "iv") {
      tidyr::expand_grid(subj, time = dose_times) |>
        mutate(evid = 1L, amt = dose, cmt = "central", rate = dose / dur)
    } else {
      # An oral dose is presented to BOTH depots; f(depot) and f(depot2) split
      # it into the immediate and delayed fractions (Equations 13, 14).
      bind_rows(
        tidyr::expand_grid(subj, time = dose_times) |>
          mutate(evid = 1L, amt = dose, cmt = "depot",  rate = 0),
        tidyr::expand_grid(subj, time = dose_times) |>
          mutate(evid = 1L, amt = dose, cmt = "depot2", rate = 0)
      )
    }

  obs <- tidyr::expand_grid(subj, time = obs_times) |>
    # Two `~` endpoints means observation rows need a dvid; cmt must stay NA so
    # rxode2 does not auto-inject a compartment slot for an algebraic output.
    mutate(evid = 0L, amt = 0, cmt = NA_character_, rate = 0)

  bind_rows(doses, obs) |>
    mutate(dvid = ifelse(evid == 0L, 1L, NA_integer_)) |>
    arrange(id, time, desc(evid))
}

events <- do.call(
  bind_rows,
  lapply(seq_len(nrow(arms)), function(i) {
    make_arm(
      n = n_per_arm, arm = arms$arm[i], route = arms$route[i],
      dose = arms$dose[i], dur = arms$dur[i], fed = arms$fed[i],
      id_offset = (i - 1L) * n_per_arm
    )
  })
)

# ids must not collide across arms: rxSolve keys subjects by `id` alone, so a
# repeated id would silently merge two regimens into a single (wrong) subject.
stopifnot(max(table(unique(events[, c("id", "arm")])$id)) == 1L)
nrow(events)
#> [1] 203800

Simulation 

sim_orig <- rxode2::rxSolve(
  mod_orig, events,
  keep = c("arm", "WT", "ALB"), returnType = "data.frame"
)
sim_higher <- rxode2::rxSolve(
  mod_higher, events,
  keep = c("arm", "WT", "ALB"), returnType = "data.frame"
)

Typical-value replication of Supplementary Table S6

The paper’s Table S6 reports medians over 5000 virtual patients. As a deterministic cross-check that is independent of cohort sampling noise, the block below solves the typical Chinese CABP patient (weight 69.38 kg, albumin 3.88 g/dL, Phase 3) with every eta set to zero and integrates the Day 3 (48-72 h) window on a fine grid.

etas <- c("etalcl", "etalvc", "etalq", "etalvp", "etalka", "etalka2",
          "etalogitfdepot", "etalogitfrac")

typical_events <- events |>
  # NB the parentheses: `%in%` binds tighter than `*` and `+` in R.
  filter(id %in% ((seq_len(nrow(arms)) - 1L) * n_per_arm + 1L)) |>
  mutate(WT = 69.38, ALB = 38.8)
for (e in etas) typical_events[[e]] <- 0

trapz <- function(t, y) sum(diff(t) * (head(y, -1) + tail(y, -1)) / 2)

typical_exposure <- function(mod, label) {
  s <- rxode2::rxSolve(mod, typical_events, omega = NA, keep = "arm",
                       addDosing = FALSE, returnType = "data.frame")
  s |>
    filter(time >= 48, time <= 72) |>
    group_by(arm) |>
    summarise(
      ppb        = label,
      fAUC_24    = trapz(time, Cu),
      AUC_ELF_24 = trapz(time, Celf),
      .groups    = "drop"
    )
}

typical_tbl <- bind_rows(
  typical_exposure(mod_orig,   "Original ppb"),
  typical_exposure(mod_higher, "Higher ppb")
)
#> Warning: multi-subject simulation without without 'omega'
#> Warning: multi-subject simulation without without 'omega'

published_s6 <- tibble::tribble(
  ~ppb,           ~arm,                     ~paper_fAUC, ~paper_ELF,
  "Original ppb", "150 mg q12h IV 1 h",     3.87,        20.51,
  "Original ppb", "150 mg q12h IV 1.5 h",   3.86,        20.51,
  "Original ppb", "150 mg q12h IV 2 h",     3.86,        20.50,
  "Original ppb", "600 mg q12h PO fasted",  3.71,        19.69,
  "Original ppb", "600 mg q12h PO fed",     2.76,        14.64,
  "Higher ppb",   "150 mg q12h IV 1 h",     1.08,        16.12,
  "Higher ppb",   "150 mg q12h IV 1.5 h",   1.08,        16.32,
  "Higher ppb",   "150 mg q12h IV 2 h",     1.08,        16.48,
  "Higher ppb",   "600 mg q12h PO fasted",  1.26,        18.10,
  "Higher ppb",   "600 mg q12h PO fed",     0.89,        16.49
)

typical_tbl |>
  left_join(published_s6, by = c("ppb", "arm")) |>
  mutate(
    `fAUC % diff` = round(100 * (fAUC_24 / paper_fAUC - 1), 1),
    `ELF % diff`  = round(100 * (AUC_ELF_24 / paper_ELF - 1), 1)
  ) |>
  select(ppb, arm, fAUC_24, paper_fAUC, `fAUC % diff`,
         AUC_ELF_24, paper_ELF, `ELF % diff`) |>
  dplyr::rename(
    "Binding"                    = ppb,
    "Regimen"                    = arm,
    "fAUC0-24 simulated"         = fAUC_24,
    "fAUC0-24 Table S6"          = paper_fAUC,
    "AUC0-24,ELF simulated"      = AUC_ELF_24,
    "AUC0-24,ELF Table S6"       = paper_ELF
  ) |>
  knitr::kable(
    digits  = 2,
    caption = paste(
      "Typical-value Day 3 (48-72 h) exposures in mg*h/L versus the medians",
      "reported in Bian 2024 Supplementary Table S6."
    )
  )
Typical-value Day 3 (48-72 h) exposures in mg*h/L versus the medians reported in Bian 2024 Supplementary Table S6.
Binding Regimen fAUC0-24 simulated fAUC0-24 Table S6 fAUC % diff AUC0-24,ELF simulated AUC0-24,ELF Table S6 ELF % diff
Original ppb 150 mg q12h IV 1 h 3.96 3.87 2.3 21.03 20.51 2.5
Original ppb 150 mg q12h IV 1.5 h 3.96 3.86 2.6 21.03 20.51 2.5
Original ppb 150 mg q12h IV 2 h 3.96 3.86 2.6 21.03 20.50 2.6
Original ppb 600 mg q12h PO fasted 3.87 3.71 4.2 20.52 19.69 4.2
Original ppb 600 mg q12h PO fed 2.93 2.76 6.1 15.54 14.64 6.2
Higher ppb 150 mg q12h IV 1 h 1.11 1.08 2.8 15.78 16.12 -2.1
Higher ppb 150 mg q12h IV 1.5 h 1.11 1.08 2.8 16.00 16.32 -2.0
Higher ppb 150 mg q12h IV 2 h 1.11 1.08 2.7 16.18 16.48 -1.8
Higher ppb 600 mg q12h PO fasted 1.30 1.26 3.3 18.00 18.10 -0.6
Higher ppb 600 mg q12h PO fed 0.99 0.89 11.3 16.80 16.49 1.9

Both fits reproduce Table S6 closely. The original-ppb model runs uniformly a little high (fAUC +2.3% to +6.1%, ELF +2.5% to +6.2%), which is consistent with the typical patient being simulated against a published median over a 5000-patient virtual population. The higher-ppb model is within +2.7% to +3.3% on free plasma for four of five regimens and -2.1% to +1.9% on ELF throughout; its one outlier is the fed oral arm at +11.3% on free plasma, the regimen whose exposure depends most heavily on the food-effect multipliers.

A second, structural check: for the original-ppb model the ELF effect compartment implies an exact steady-state exposure ratio AUC(ELF) / fAUC(plasma) = kin_elf / kout_elf.

ratio_sim   <- typical_tbl$AUC_ELF_24[1] / typical_tbl$fAUC_24[1]
ratio_theor <- 2.71 / 0.51
c(simulated = ratio_sim, `kin_elf / kout_elf` = ratio_theor,
  `Table S6 20.51 / 3.87` = 20.51 / 3.87)
#>             simulated    kin_elf / kout_elf Table S6 20.51 / 3.87 
#>              5.312001              5.313725              5.299742

Zhang 2019 states the same result independently: “the median lefamulin total-drug ELF AUC(0-24):free-drug plasma AUC(0-24) ratio was ~5:1”.

Replicate published figures 

# Replicates Figure 3 of Bian 2024: steady-state (Day 3) total plasma
# concentration-time profiles by administration route, under both binding
# assumptions.
bind_rows(
  sim_orig   |> mutate(ppb = "Original ppb"),
  sim_higher |> mutate(ppb = "Higher ppb")
) |>
  filter(time >= 48, time <= 72) |>
  mutate(time = time - 48) |>
  group_by(ppb, arm, time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  mutate(ppb = factor(ppb, levels = c("Original ppb", "Higher ppb"))) |>
  ggplot(aes(time, Q50, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.15, colour = NA) +
  geom_line() +
  facet_wrap(~ppb) +
  scale_y_log10() +
  labs(x = "Time since the Day 3 dose (h)",
       y = "Total plasma lefamulin (mg/L)",
       colour = NULL, fill = NULL,
       title = "Day 3 total plasma concentration-time profiles",
       caption = "Replicates Figure 3 of Bian 2024.") +
  theme(legend.position = "bottom")

# Replicates Figure S4 of Bian 2024: distribution of Day 3 free-plasma and
# ELF exposures under both binding assumptions.
bind_rows(
  sim_orig   |> mutate(ppb = "Original ppb"),
  sim_higher |> mutate(ppb = "Higher ppb")
) |>
  filter(time >= 48, time <= 72) |>
  group_by(ppb, arm, id) |>
  summarise(
    `fAUC0-24h,plasma` = trapz(time, Cu),
    `AUC0-24h,ELF`     = trapz(time, Celf),
    .groups = "drop"
  ) |>
  tidyr::pivot_longer(c(`fAUC0-24h,plasma`, `AUC0-24h,ELF`),
                      names_to = "metric", values_to = "auc") |>
  mutate(ppb = factor(ppb, levels = c("Original ppb", "Higher ppb"))) |>
  ggplot(aes(arm, auc, fill = ppb)) +
  geom_boxplot(outlier.size = 0.4) +
  facet_wrap(~metric, scales = "free_y") +
  scale_y_log10() +
  coord_flip() +
  labs(x = NULL, y = "Exposure (mg*h/L)", fill = NULL,
       title = "Day 3 exposure distributions",
       caption = "Replicates Figure S4 of Bian 2024.") +
  theme(legend.position = "bottom")

PKNCA validation

The model has three outputs of interest – total plasma (Cc, the measured quantity), free plasma (Cu, the PK/PD driver in plasma) and ELF (Celf) – so PKNCA is run once per output. Day 1 is the 0-24 h interval and Day 3 the 48-72 h interval, matching Supplementary Table S6.

#' Run PKNCA over the Day 1 and Day 3 windows for one concentration column.
nca_for <- function(sim_df, conc_col, dose_df) {
  sim_nca <- sim_df |>
    dplyr::rename(Cc_use = dplyr::all_of(conc_col)) |>
    dplyr::filter(!is.na(Cc_use)) |>
    dplyr::select(id, time, Cc = Cc_use, arm)

  # Guarantee a time-zero row per (arm, id); pre-dose concentration is 0.
  sim_nca <- dplyr::bind_rows(
    sim_nca,
    sim_nca |> dplyr::distinct(id, arm) |> dplyr::mutate(time = 0, Cc = 0)
  ) |>
    dplyr::distinct(arm, id, time, .keep_all = TRUE) |>
    dplyr::arrange(id, time)

  conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | arm + id,
                               concu = "mg/L", timeu = "h")
  dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | arm + id, doseu = "mg")

  intervals <- data.frame(
    start   = c(0, 48),
    end     = c(24, 72),
    cmax    = TRUE,
    tmax    = TRUE,
    auclast = TRUE
  )

  PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
}

# One dose record per subject per time (the oral arms present the dose to two
# depots, which would otherwise double-count).
dose_df <- events |>
  dplyr::filter(evid == 1, cmt != "depot2") |>
  dplyr::select(id, time, amt, arm)

nca <- list(
  orig_Cc     = nca_for(sim_orig,   "Cc",   dose_df),
  orig_Cu     = nca_for(sim_orig,   "Cu",   dose_df),
  orig_Celf   = nca_for(sim_orig,   "Celf", dose_df),
  higher_Cc   = nca_for(sim_higher, "Cc",   dose_df),
  higher_Cu   = nca_for(sim_higher, "Cu",   dose_df),
  higher_Celf = nca_for(sim_higher, "Celf", dose_df)
)

Comparison against the published exposures

ncaComparisonTable() aggregates the simulated per-subject values to the median within each arm, which is the statistic Supplementary Table S6 reports.

#' Pull the Day 1 or Day 3 auclast rows out of a PKNCAresults object.
day_auc <- function(res, window_start) {
  as.data.frame(res$result) |>
    filter(PPTESTCD == "auclast", start == window_start) |>
    select(arm, id, PPTESTCD, PPORRES)
}

nca_units <- c(auclast = "mg*h/L", cmax = "mg/L", tmax = "h")

ref_long <- published_s6 |>
  tidyr::pivot_longer(c(paper_fAUC, paper_ELF),
                      names_to = "output", values_to = "auclast") |>
  mutate(output = ifelse(output == "paper_fAUC", "Free plasma", "ELF"))

cmp <- bind_rows(
  nlmixr2lib::ncaComparisonTable(
    simulated = day_auc(nca$orig_Cu, 48),
    reference = ref_long |>
      filter(ppb == "Original ppb", output == "Free plasma") |>
      select(arm, auclast),
    by = "arm", units = nca_units, tolerance_pct = 20
  ) |> mutate(Binding = "Original ppb", Output = "Free plasma", .before = 1),
  nlmixr2lib::ncaComparisonTable(
    simulated = day_auc(nca$orig_Celf, 48),
    reference = ref_long |>
      filter(ppb == "Original ppb", output == "ELF") |>
      select(arm, auclast),
    by = "arm", units = nca_units, tolerance_pct = 20
  ) |> mutate(Binding = "Original ppb", Output = "ELF", .before = 1),
  nlmixr2lib::ncaComparisonTable(
    simulated = day_auc(nca$higher_Cu, 48),
    reference = ref_long |>
      filter(ppb == "Higher ppb", output == "Free plasma") |>
      select(arm, auclast),
    by = "arm", units = nca_units, tolerance_pct = 20
  ) |> mutate(Binding = "Higher ppb", Output = "Free plasma", .before = 1),
  nlmixr2lib::ncaComparisonTable(
    simulated = day_auc(nca$higher_Celf, 48),
    reference = ref_long |>
      filter(ppb == "Higher ppb", output == "ELF") |>
      select(arm, auclast),
    by = "arm", units = nca_units, tolerance_pct = 20
  ) |> mutate(Binding = "Higher ppb", Output = "ELF", .before = 1)
)

knitr::kable(
  cmp,
  digits  = 3,
  caption = paste(
    "Simulated versus published Day 3 (48-72 h) exposures,",
    "Bian 2024 Supplementary Table S6.",
    "* marks rows differing from the reference by more than 20%."
  )
)
Simulated versus published Day 3 (48-72 h) exposures, Bian 2024 Supplementary Table S6. * marks rows differing from the reference by more than 20%.
Binding Output NCA parameter arm Reference Simulated % diff
Original ppb Free plasma AUClast (mg*h/L) 150 mg q12h IV 1 h 3.87 3.85 -0.6%
Original ppb Free plasma AUClast (mg*h/L) 150 mg q12h IV 1.5 h 3.86 3.57 -7.6%
Original ppb Free plasma AUClast (mg*h/L) 150 mg q12h IV 2 h 3.86 3.86 -0.1%
Original ppb Free plasma AUClast (mg*h/L) 600 mg q12h PO fasted 3.71 3.94 +6.1%
Original ppb Free plasma AUClast (mg*h/L) 600 mg q12h PO fed 2.76 2.86 +3.5%
Original ppb ELF AUClast (mg*h/L) 150 mg q12h IV 1 h 20.5 20.5 -0.3%
Original ppb ELF AUClast (mg*h/L) 150 mg q12h IV 1.5 h 20.5 19 -7.5%
Original ppb ELF AUClast (mg*h/L) 150 mg q12h IV 2 h 20.5 20.5 -0.0%
Original ppb ELF AUClast (mg*h/L) 600 mg q12h PO fasted 19.7 20.9 +6.0%
Original ppb ELF AUClast (mg*h/L) 600 mg q12h PO fed 14.6 15.1 +3.3%
Higher ppb Free plasma AUClast (mg*h/L) 150 mg q12h IV 1 h 1.08 1.09 +1.2%
Higher ppb Free plasma AUClast (mg*h/L) 150 mg q12h IV 1.5 h 1.08 1.11 +2.8%
Higher ppb Free plasma AUClast (mg*h/L) 150 mg q12h IV 2 h 1.08 1.11 +3.0%
Higher ppb Free plasma AUClast (mg*h/L) 600 mg q12h PO fasted 1.26 1.41 +12.2%
Higher ppb Free plasma AUClast (mg*h/L) 600 mg q12h PO fed 0.89 0.858 -3.5%
Higher ppb ELF AUClast (mg*h/L) 150 mg q12h IV 1 h 16.1 15.8 -2.3%
Higher ppb ELF AUClast (mg*h/L) 150 mg q12h IV 1.5 h 16.3 16 -1.8%
Higher ppb ELF AUClast (mg*h/L) 150 mg q12h IV 2 h 16.5 16.3 -1.3%
Higher ppb ELF AUClast (mg*h/L) 600 mg q12h PO fasted 18.1 18.5 +2.4%
Higher ppb ELF AUClast (mg*h/L) 600 mg q12h PO fed 16.5 15.8 -4.4%

Total-plasma Cmax and Tmax at steady state are not tabulated in the paper, but Figure 3 shows the observed Chinese Phase III scatter; the simulated medians below sit inside it.

bind_rows(
  as.data.frame(nca$orig_Cc$result)   |> mutate(ppb = "Original ppb"),
  as.data.frame(nca$higher_Cc$result) |> mutate(ppb = "Higher ppb")
) |>
  filter(PPTESTCD %in% c("cmax", "tmax"), start == 48) |>
  group_by(ppb, arm, PPTESTCD) |>
  summarise(median = median(PPORRES, na.rm = TRUE), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = median) |>
  dplyr::rename("Binding" = ppb, "Regimen" = arm,
                "Cmax,ss total plasma (mg/L)" = cmax,
                "Tmax,ss (h)" = tmax) |>
  knitr::kable(digits = 2,
               caption = "Simulated Day 3 total-plasma Cmax and Tmax medians.")
Simulated Day 3 total-plasma Cmax and Tmax medians.
Binding Regimen Cmax,ss total plasma (mg/L) Tmax,ss (h)
Higher ppb 150 mg q12h IV 1 h 3.31 13.00
Higher ppb 150 mg q12h IV 1.5 h 2.90 13.50
Higher ppb 150 mg q12h IV 2 h 2.61 14.00
Higher ppb 600 mg q12h PO fasted 2.33 14.00
Higher ppb 600 mg q12h PO fed 1.27 17.25
Original ppb 150 mg q12h IV 1 h 3.55 13.00
Original ppb 150 mg q12h IV 1.5 h 2.94 13.50
Original ppb 150 mg q12h IV 2 h 2.68 14.00
Original ppb 600 mg q12h PO fasted 2.26 13.75
Original ppb 600 mg q12h PO fed 1.31 16.25

PK/PD target attainment

The PK/PD index for lefamulin is fAUC(0-24h)/MIC in plasma and AUC(0-24h),ELF/MIC in ELF (Supplementary Table S4, from a neutropenic mouse lung-infection model). The block below computes probability of target attainment (PTA) from the per-subject Day 3 exposures and compares it against Supplementary Table S7.

targets <- tibble::tribble(
  ~organism,        ~matrix,       ~effect,  ~target,
  "S. pneumoniae",  "Plasma",      "1-log",  1.37,
  "S. pneumoniae",  "Plasma",      "2-log",  2.15,
  "S. pneumoniae",  "ELF",         "1-log",  14,
  "S. pneumoniae",  "ELF",         "2-log",  22,
  "S. aureus",      "Plasma",      "1-log",  2.13,
  "S. aureus",      "Plasma",      "2-log",  6.24,
  "S. aureus",      "ELF",         "1-log",  21.7,
  "S. aureus",      "ELF",         "2-log",  63.9
)

mic_grid <- c(0.015, 0.03, 0.06, 0.125, 0.25, 0.5, 1)

subject_auc <- bind_rows(
  day_auc(nca$orig_Cu,     48) |> mutate(ppb = "Original ppb", matrix = "Plasma"),
  day_auc(nca$orig_Celf,   48) |> mutate(ppb = "Original ppb", matrix = "ELF"),
  day_auc(nca$higher_Cu,   48) |> mutate(ppb = "Higher ppb",   matrix = "Plasma"),
  day_auc(nca$higher_Celf, 48) |> mutate(ppb = "Higher ppb",   matrix = "ELF")
) |>
  # The three IV arms are pooled by the paper into a single "150 mg iv 1/1.5/2 h"
  # row of Table S7, which their near-identical AUCs justify.
  mutate(regimen = case_when(
    grepl("^150 mg", arm) ~ "150 mg iv 1/1.5/2 h",
    grepl("fasted", arm)  ~ "600 mg oral fasted",
    TRUE                  ~ "600 mg oral fed"
  ))

pta <- subject_auc |>
  inner_join(targets, by = "matrix", relationship = "many-to-many") |>
  tidyr::expand_grid(mic = mic_grid) |>
  group_by(ppb, regimen, organism, matrix, effect, target, mic) |>
  summarise(PTA = 100 * mean(PPORRES / mic >= target), .groups = "drop")
published_s7 <- tibble::tribble(
  ~ppb,           ~regimen,               ~matrix,  ~effect, ~mic,  ~paper_PTA,
  # Table S7A, S. pneumoniae, original ppb
  "Original ppb", "150 mg iv 1/1.5/2 h",  "Plasma", "1-log", 0.5,   100,
  "Original ppb", "150 mg iv 1/1.5/2 h",  "Plasma", "1-log", 1,     99,
  "Original ppb", "150 mg iv 1/1.5/2 h",  "Plasma", "2-log", 1,     88,
  "Original ppb", "150 mg iv 1/1.5/2 h",  "ELF",    "1-log", 0.5,   99,
  "Original ppb", "150 mg iv 1/1.5/2 h",  "ELF",    "1-log", 1,     77,
  "Original ppb", "150 mg iv 1/1.5/2 h",  "ELF",    "2-log", 0.5,   90,
  "Original ppb", "150 mg iv 1/1.5/2 h",  "ELF",    "2-log", 1,     39,
  "Original ppb", "600 mg oral fasted",   "Plasma", "1-log", 1,     98,
  "Original ppb", "600 mg oral fasted",   "Plasma", "2-log", 1,     87,
  "Original ppb", "600 mg oral fasted",   "ELF",    "1-log", 1,     75,
  "Original ppb", "600 mg oral fasted",   "ELF",    "2-log", 1,     40,
  "Original ppb", "600 mg oral fed",      "Plasma", "1-log", 1,     92,
  "Original ppb", "600 mg oral fed",      "Plasma", "2-log", 1,     69,
  "Original ppb", "600 mg oral fed",      "ELF",    "1-log", 1,     52,
  "Original ppb", "600 mg oral fed",      "ELF",    "2-log", 1,     18,
  # Table S7B, S. pneumoniae, higher ppb
  "Higher ppb",   "150 mg iv 1/1.5/2 h",  "Plasma", "1-log", 0.5,   84,
  "Higher ppb",   "150 mg iv 1/1.5/2 h",  "Plasma", "2-log", 0.25,  94,
  "Higher ppb",   "150 mg iv 1/1.5/2 h",  "Plasma", "2-log", 0.5,   48,
  "Higher ppb",   "150 mg iv 1/1.5/2 h",  "ELF",    "1-log", 0.5,   100,
  "Higher ppb",   "150 mg iv 1/1.5/2 h",  "ELF",    "2-log", 0.5,   94,
  "Higher ppb",   "600 mg oral fasted",   "Plasma", "1-log", 0.5,   76,
  "Higher ppb",   "600 mg oral fasted",   "Plasma", "2-log", 0.5,   54,
  "Higher ppb",   "600 mg oral fasted",   "ELF",    "2-log", 0.5,   95,
  "Higher ppb",   "600 mg oral fed",      "Plasma", "1-log", 0.5,   61,
  "Higher ppb",   "600 mg oral fed",      "Plasma", "2-log", 0.5,   39,
  "Higher ppb",   "600 mg oral fed",      "ELF",    "2-log", 0.5,   88
)

pta |>
  filter(organism == "S. pneumoniae") |>
  inner_join(published_s7, by = c("ppb", "regimen", "matrix", "effect", "mic")) |>
  mutate(PTA = round(PTA), `abs. diff` = abs(PTA - paper_PTA)) |>
  select(ppb, regimen, matrix, effect, mic, PTA, paper_PTA, `abs. diff`) |>
  dplyr::rename(
    "Binding"          = ppb,
    "Regimen"          = regimen,
    "Matrix"           = matrix,
    "PK/PD target"     = effect,
    "MIC (mg/L)"       = mic,
    "PTA (%) simulated" = PTA,
    "PTA (%) Table S7"  = paper_PTA
  ) |>
  knitr::kable(
    caption = paste(
      "Simulated versus published probability of target attainment for",
      "S. pneumoniae (Bian 2024 Supplementary Table S7), restricted to the",
      "MICs where the published PTA is below 100% and therefore informative."
    )
  )
Simulated versus published probability of target attainment for S. pneumoniae (Bian 2024 Supplementary Table S7), restricted to the MICs where the published PTA is below 100% and therefore informative.
Binding Regimen Matrix PK/PD target MIC (mg/L) PTA (%) simulated PTA (%) Table S7 abs. diff
Higher ppb 150 mg iv 1/1.5/2 h ELF 1-log 0.50 100 100 0
Higher ppb 150 mg iv 1/1.5/2 h ELF 2-log 0.50 96 94 2
Higher ppb 150 mg iv 1/1.5/2 h Plasma 1-log 0.50 90 84 6
Higher ppb 150 mg iv 1/1.5/2 h Plasma 2-log 0.25 97 94 3
Higher ppb 150 mg iv 1/1.5/2 h Plasma 2-log 0.50 54 48 6
Higher ppb 600 mg oral fasted ELF 2-log 0.50 96 95 1
Higher ppb 600 mg oral fasted Plasma 1-log 0.50 80 76 4
Higher ppb 600 mg oral fasted Plasma 2-log 0.50 62 54 8
Higher ppb 600 mg oral fed ELF 2-log 0.50 87 88 1
Higher ppb 600 mg oral fed Plasma 1-log 0.50 64 61 3
Higher ppb 600 mg oral fed Plasma 2-log 0.50 36 39 3
Original ppb 150 mg iv 1/1.5/2 h ELF 1-log 0.50 99 99 0
Original ppb 150 mg iv 1/1.5/2 h ELF 1-log 1.00 81 77 4
Original ppb 150 mg iv 1/1.5/2 h ELF 2-log 0.50 94 90 4
Original ppb 150 mg iv 1/1.5/2 h ELF 2-log 1.00 42 39 3
Original ppb 150 mg iv 1/1.5/2 h Plasma 1-log 0.50 100 100 0
Original ppb 150 mg iv 1/1.5/2 h Plasma 1-log 1.00 99 99 0
Original ppb 150 mg iv 1/1.5/2 h Plasma 2-log 1.00 92 88 4
Original ppb 600 mg oral fasted ELF 1-log 1.00 78 75 3
Original ppb 600 mg oral fasted ELF 2-log 1.00 46 40 6
Original ppb 600 mg oral fasted Plasma 1-log 1.00 98 98 0
Original ppb 600 mg oral fasted Plasma 2-log 1.00 87 87 0
Original ppb 600 mg oral fed ELF 1-log 1.00 56 52 4
Original ppb 600 mg oral fed ELF 2-log 1.00 19 18 1
Original ppb 600 mg oral fed Plasma 1-log 1.00 92 92 0
Original ppb 600 mg oral fed Plasma 2-log 1.00 72 69 3

The PK/PD breakpoint is the highest MIC at which PTA remains at least 90% (Supplementary Table S8).

bp_sim <- pta |>
  filter(PTA >= 90) |>
  group_by(ppb, regimen, organism, matrix, effect) |>
  summarise(breakpoint = max(mic), .groups = "drop")

published_s8 <- tibble::tribble(
  ~ppb,           ~regimen,              ~organism,       ~matrix,  ~effect, ~paper_bp,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. pneumoniae", "Plasma", "1-log", 1,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. pneumoniae", "Plasma", "2-log", 0.5,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. pneumoniae", "ELF",    "1-log", 0.5,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. pneumoniae", "ELF",    "2-log", 0.5,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. aureus",     "Plasma", "1-log", 0.5,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. aureus",     "Plasma", "2-log", 0.25,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. aureus",     "ELF",    "1-log", 0.5,
  "Original ppb", "150 mg iv 1/1.5/2 h", "S. aureus",     "ELF",    "2-log", 0.125,
  "Original ppb", "600 mg oral fasted",  "S. pneumoniae", "Plasma", "1-log", 1,
  "Original ppb", "600 mg oral fasted",  "S. pneumoniae", "Plasma", "2-log", 0.5,
  "Original ppb", "600 mg oral fasted",  "S. pneumoniae", "ELF",    "1-log", 0.5,
  "Original ppb", "600 mg oral fasted",  "S. pneumoniae", "ELF",    "2-log", 0.25,
  "Original ppb", "600 mg oral fasted",  "S. aureus",     "Plasma", "1-log", 0.5,
  "Original ppb", "600 mg oral fasted",  "S. aureus",     "Plasma", "2-log", 0.25,
  "Original ppb", "600 mg oral fasted",  "S. aureus",     "ELF",    "1-log", 0.25,
  "Original ppb", "600 mg oral fasted",  "S. aureus",     "ELF",    "2-log", 0.125,
  "Original ppb", "600 mg oral fed",     "S. pneumoniae", "Plasma", "1-log", 1,
  "Original ppb", "600 mg oral fed",     "S. pneumoniae", "Plasma", "2-log", 0.5,
  "Original ppb", "600 mg oral fed",     "S. pneumoniae", "ELF",    "1-log", 0.5,
  "Original ppb", "600 mg oral fed",     "S. pneumoniae", "ELF",    "2-log", 0.25,
  "Original ppb", "600 mg oral fed",     "S. aureus",     "Plasma", "1-log", 0.5,
  "Original ppb", "600 mg oral fed",     "S. aureus",     "Plasma", "2-log", 0.125,
  "Original ppb", "600 mg oral fed",     "S. aureus",     "ELF",    "1-log", 0.25,
  "Original ppb", "600 mg oral fed",     "S. aureus",     "ELF",    "2-log", 0.06,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. pneumoniae", "Plasma", "1-log", 0.25,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. pneumoniae", "Plasma", "2-log", 0.25,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. pneumoniae", "ELF",    "1-log", 0.5,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. pneumoniae", "ELF",    "2-log", 0.5,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. aureus",     "Plasma", "1-log", 0.25,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. aureus",     "Plasma", "2-log", 0.06,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. aureus",     "ELF",    "1-log", 0.5,
  "Higher ppb",   "150 mg iv 1/1.5/2 h", "S. aureus",     "ELF",    "2-log", 0.125,
  "Higher ppb",   "600 mg oral fasted",  "S. pneumoniae", "Plasma", "1-log", 0.25,
  "Higher ppb",   "600 mg oral fasted",  "S. pneumoniae", "Plasma", "2-log", 0.125,
  "Higher ppb",   "600 mg oral fasted",  "S. pneumoniae", "ELF",    "1-log", 0.5,
  "Higher ppb",   "600 mg oral fasted",  "S. pneumoniae", "ELF",    "2-log", 0.5,
  "Higher ppb",   "600 mg oral fasted",  "S. aureus",     "Plasma", "1-log", 0.125,
  "Higher ppb",   "600 mg oral fasted",  "S. aureus",     "Plasma", "2-log", 0.06,
  "Higher ppb",   "600 mg oral fasted",  "S. aureus",     "ELF",    "1-log", 0.5,
  "Higher ppb",   "600 mg oral fasted",  "S. aureus",     "ELF",    "2-log", 0.125,
  "Higher ppb",   "600 mg oral fed",     "S. pneumoniae", "Plasma", "1-log", 0.125,
  "Higher ppb",   "600 mg oral fed",     "S. pneumoniae", "Plasma", "2-log", 0.125,
  "Higher ppb",   "600 mg oral fed",     "S. pneumoniae", "ELF",    "1-log", 0.5,
  "Higher ppb",   "600 mg oral fed",     "S. pneumoniae", "ELF",    "2-log", 0.25,
  "Higher ppb",   "600 mg oral fed",     "S. aureus",     "Plasma", "1-log", 0.125,
  "Higher ppb",   "600 mg oral fed",     "S. aureus",     "Plasma", "2-log", 0.03,
  "Higher ppb",   "600 mg oral fed",     "S. aureus",     "ELF",    "1-log", 0.25,
  "Higher ppb",   "600 mg oral fed",     "S. aureus",     "ELF",    "2-log", 0.125
)

bp_cmp <- published_s8 |>
  left_join(bp_sim, by = c("ppb", "regimen", "organism", "matrix", "effect")) |>
  mutate(agree = ifelse(!is.na(breakpoint) & breakpoint == paper_bp, "", "*"))

bp_cmp |>
  select(ppb, regimen, organism, matrix, effect, breakpoint, paper_bp, agree) |>
  dplyr::rename(
    "Binding"                    = ppb,
    "Regimen"                    = regimen,
    "Organism"                   = organism,
    "Matrix"                     = matrix,
    "PK/PD target"               = effect,
    "Breakpoint (mg/L) simulated" = breakpoint,
    "Breakpoint (mg/L) Table S8"  = paper_bp,
    " "                           = agree
  ) |>
  knitr::kable(
    caption = paste(
      "Simulated versus published PK/PD breakpoints (highest MIC with",
      "PTA >= 90%), Bian 2024 Supplementary Table S8.",
      "* marks a disagreement, which at this MIC grid means one two-fold step."
    )
  )
Simulated versus published PK/PD breakpoints (highest MIC with PTA >= 90%), Bian 2024 Supplementary Table S8. * marks a disagreement, which at this MIC grid means one two-fold step.
Binding Regimen Organism Matrix PK/PD target Breakpoint (mg/L) simulated Breakpoint (mg/L) Table S8
Original ppb 150 mg iv 1/1.5/2 h S. pneumoniae Plasma 1-log 1.000 1.000
Original ppb 150 mg iv 1/1.5/2 h S. pneumoniae Plasma 2-log 1.000 0.500 *
Original ppb 150 mg iv 1/1.5/2 h S. pneumoniae ELF 1-log 0.500 0.500
Original ppb 150 mg iv 1/1.5/2 h S. pneumoniae ELF 2-log 0.500 0.500
Original ppb 150 mg iv 1/1.5/2 h S. aureus Plasma 1-log 1.000 0.500 *
Original ppb 150 mg iv 1/1.5/2 h S. aureus Plasma 2-log 0.250 0.250
Original ppb 150 mg iv 1/1.5/2 h S. aureus ELF 1-log 0.500 0.500
Original ppb 150 mg iv 1/1.5/2 h S. aureus ELF 2-log 0.125 0.125
Original ppb 600 mg oral fasted S. pneumoniae Plasma 1-log 1.000 1.000
Original ppb 600 mg oral fasted S. pneumoniae Plasma 2-log 0.500 0.500
Original ppb 600 mg oral fasted S. pneumoniae ELF 1-log 0.500 0.500
Original ppb 600 mg oral fasted S. pneumoniae ELF 2-log 0.500 0.250 *
Original ppb 600 mg oral fasted S. aureus Plasma 1-log 0.500 0.500
Original ppb 600 mg oral fasted S. aureus Plasma 2-log 0.250 0.250
Original ppb 600 mg oral fasted S. aureus ELF 1-log 0.500 0.250 *
Original ppb 600 mg oral fasted S. aureus ELF 2-log 0.125 0.125
Original ppb 600 mg oral fed S. pneumoniae Plasma 1-log 1.000 1.000
Original ppb 600 mg oral fed S. pneumoniae Plasma 2-log 0.500 0.500
Original ppb 600 mg oral fed S. pneumoniae ELF 1-log 0.500 0.500
Original ppb 600 mg oral fed S. pneumoniae ELF 2-log 0.250 0.250
Original ppb 600 mg oral fed S. aureus Plasma 1-log 0.500 0.500
Original ppb 600 mg oral fed S. aureus Plasma 2-log 0.125 0.125
Original ppb 600 mg oral fed S. aureus ELF 1-log 0.250 0.250
Original ppb 600 mg oral fed S. aureus ELF 2-log 0.060 0.060
Higher ppb 150 mg iv 1/1.5/2 h S. pneumoniae Plasma 1-log 0.500 0.250 *
Higher ppb 150 mg iv 1/1.5/2 h S. pneumoniae Plasma 2-log 0.250 0.250
Higher ppb 150 mg iv 1/1.5/2 h S. pneumoniae ELF 1-log 0.500 0.500
Higher ppb 150 mg iv 1/1.5/2 h S. pneumoniae ELF 2-log 0.500 0.500
Higher ppb 150 mg iv 1/1.5/2 h S. aureus Plasma 1-log 0.250 0.250
Higher ppb 150 mg iv 1/1.5/2 h S. aureus Plasma 2-log 0.060 0.060
Higher ppb 150 mg iv 1/1.5/2 h S. aureus ELF 1-log 0.500 0.500
Higher ppb 150 mg iv 1/1.5/2 h S. aureus ELF 2-log 0.125 0.125
Higher ppb 600 mg oral fasted S. pneumoniae Plasma 1-log 0.250 0.250
Higher ppb 600 mg oral fasted S. pneumoniae Plasma 2-log 0.125 0.125
Higher ppb 600 mg oral fasted S. pneumoniae ELF 1-log 0.500 0.500
Higher ppb 600 mg oral fasted S. pneumoniae ELF 2-log 0.500 0.500
Higher ppb 600 mg oral fasted S. aureus Plasma 1-log 0.125 0.125
Higher ppb 600 mg oral fasted S. aureus Plasma 2-log 0.060 0.060
Higher ppb 600 mg oral fasted S. aureus ELF 1-log 0.500 0.500
Higher ppb 600 mg oral fasted S. aureus ELF 2-log 0.125 0.125
Higher ppb 600 mg oral fed S. pneumoniae Plasma 1-log 0.125 0.125
Higher ppb 600 mg oral fed S. pneumoniae Plasma 2-log 0.125 0.125
Higher ppb 600 mg oral fed S. pneumoniae ELF 1-log 0.500 0.500
Higher ppb 600 mg oral fed S. pneumoniae ELF 2-log 0.250 0.250
Higher ppb 600 mg oral fed S. aureus Plasma 1-log 0.125 0.125
Higher ppb 600 mg oral fed S. aureus Plasma 2-log 0.030 0.030
Higher ppb 600 mg oral fed S. aureus ELF 1-log 0.250 0.250
Higher ppb 600 mg oral fed S. aureus ELF 2-log 0.125 0.125 
c(
  n_compared      = nrow(bp_cmp),
  n_exact         = sum(bp_cmp$agree == ""),
  pct_exact       = round(100 * mean(bp_cmp$agree == ""), 1),
  n_within_2fold  = sum(!is.na(bp_cmp$breakpoint) &
                          abs(log2(bp_cmp$breakpoint / bp_cmp$paper_bp)) <= 1)
)
#>     n_compared        n_exact      pct_exact n_within_2fold 
#>           48.0           43.0           89.6           48.0

Assumptions and deviations

  • The supplement tabulates (1 + theta), not theta, for every covariate effect. Supplementary Tables S1 and S2 print rows such as “The effect of albumin on CL = 1.214”, while Equation 1 writes CL = [1 + theta20 * (ALB - 4.1)] * CLPHASE * theta1. The model files encode the tabulated value minus 1. Reading the tabulated numbers as theta directly makes CL negative at the observed albumin minimum of 2.0 g/dL (1 + 1.214 * (2 - 4.1) = -1.55) and Vp1 negative at 31 kg; the multiplier reading is confirmed by the four- and five-significant-figure weight rows (1.0129 and 1.00637), by the upstream Zhang 2019 Phase-1-only estimates (40.6 * 2.12 = 86.1 vs Zhang’s CLd1 = 86.6 L/h), and by the paper’s own prose that CABP exposure is “approximately 1.73-fold greater” than in adults without pneumonia, matching the 1.766 Phase 1 CL multiplier.
  • penratio_elf = 3.45 is back-solved, not paper-tabulated. Supplementary Table S2 prints LPR = 2.71 and Power = 0.51 for the higher-ppb ELF model. Those two numbers are byte-identical to Table S1’s KELF,in = 2.71 and KELF,out = 0.51, and the pair appears to have been copied across from the original-ppb table. Celf is directly proportional to LPR, so the two readings differ by exactly the factor 2.71 / 3.45 = 0.786. With the power held at the tabulated 0.51, LPR = 2.71 undershoots the paper’s own higher-ppb ELF exposures for the IV 1 h, oral fasted and oral fed regimens (Table S6: 16.12, 18.10 and 16.49 mg*h/L) by 23.1%, 21.9% and 20.0% respectively, whereas 3.45 lands within -2.1% to +1.9% across all five simulated regimens (typical-value table above). Encoding the back-solved value rather than the printed one is an explicit operator ruling that overrides the usual “values from the paper” rule; it is annotated inline at the ini() entry as well as here. A reader who prefers the printed value can recover it with params = c(lpenratio_elf = log(2.71)).
  • Three transit compartments. Figure 2 draws the delayed absorption route as Depot2 -Ka2-> Abs1 -Ka2-> ... -Ka2-> Abs3 -Ka2-> Plasma, eliding the intermediate compartment behind a dotted line; the chain length is not stated in the text or the supplement. A three-compartment chain (transit1, transit2, transit3) matches the literal Abs1 / Abs3 labelling. The choice is exposure-neutral – steady-state AUC is invariant to the chain length because it depends only on Ftot – but it does shift Cmax and Tmax on the oral arms.
  • theta3 and theta4 are missing from Equations 3 and 4 as printed. Both equations set a quantity with units (L/hr, L) equal to a product of bare multipliers. Supplementary Tables S1 and S2 supply the missing typical values (CLd1 40.6 / 187 L/h, Vp1 249 / 1300 L), and the Zhang 2019 cross-check above confirms the reconstruction.
  • Fed-state thetas are multipliers. Table S1 labels theta17 and theta19 with “(1/hr)” units, which would make them absolute fed absorption rate constants, but Equations 7-9 write each as theta * FAST + theta * theta_fed * FEDD, i.e. a multiplier on the fasted value. The equation form is used. For ka the two readings are numerically almost indistinguishable (1.2 * 0.0541 = 0.065 vs 0.0541), but for ka2 they differ two-fold; steady-state AUC is unaffected either way because food enters exposure only through theta18.
  • kin_elf / kout_elf are not wrapped in fixed(). Bian 2024’s Methods say the two ELF rate constants “are derived from the previously established model”, which is equally true of every other parameter in the file – Bian adopted the whole foreign model and externally validated it. Supplementary Table S1 annotates “Fixed” on exactly theta12, theta13 and theta14 (the binding trio) and on nothing else, so that annotation is followed literally. The upstream Zhang 2019 Table 2 supports it: K_in and K_out carry %RSE of 17.0 and 27.5, i.e. they were estimated there, and the word “fixed” in that row refers to their inter-individual variability (31.6% CV, fixed), which Bian’s Table S1 does not carry and which is therefore not encoded here. Zhang 2019 also independently confirms the binding trio (Fu_min 0.0997, Fu_max 0.259, Cup50 1.35 mg/L) and uses the symbol Cup50 verbatim.
  • eta5 and eta6 are omitted. Equations 5 and 6 carry exp(eta5) on CLd2 and exp(eta5) * exp(eta6) on Vp2, but neither variance appears in the Supplementary Table S1 or S2 IIV blocks, so both were not estimated. They are dropped rather than encoded as a zero-variance omega diagonal, which would make the omega matrix singular and break simulation.
  • Table S2’s additive residual row repeats its variance. It prints “0.0000167 (0. 0000167 mg/L)”, where the matching Table S1 row converts (0.0000343 -> 0.00586 mg/L). The square root, 0.00409 mg/L, is used.
  • The plasma observation is total drug. Every clearance and volume is free-drug referenced (Zhang 2019 Table 2 footnote), so central / vc is the unbound concentration and the measured total concentration is recovered as Cu / fu. The identity fAUC = Dose / CL holds exactly in both fits (300 mg/day / 79.4 L/h = 3.78 and / 282 L/h = 1.06 mg*h/L, against Table S6’s 3.87 and 1.08), which is what confirms the free-drug referencing.
  • The 0.0379 constant inside Equation 21 is hardcoded. It is the FDA reviewer’s fixed linear unbound fraction, used only to convert total plasma to free plasma inside the ELF link function, and is deliberately not the saturable fu of the same model. The paper’s rendering of Equation 21 loses the bracket; the FDA review states it unambiguously as C_ELF = LPR(1 mg/L) * [C_P(t) * 0.0379]^power.
  • Simulation population. The paper resampled baseline weight and albumin from 125 Chinese CABP patients; those patient-level data are not published, so the cohort here draws a log-normal weight and a normal albumin truncated to the Chinese Phase III ranges of Supplementary Table S5. Race, sex and age are not covariates in the model and are not simulated.
  • Cohort size. 200 subjects per arm against the paper’s 5000, per the library’s simulation cap. Each arm draws its own subjects and its own etas, so arm-to-arm sampling noise is visible in the stochastic tables even where the underlying exposure is identical: the three IV arms should have the same AUC (they differ only in infusion duration), yet the simulated 1.5 h arm lands 7.6% below its 1 h and 2 h siblings. The deterministic typical-value table is free of this and is the stricter check. Against Table S7 the simulated PTA cells agree to within 8 percentage points (median 3), and 43 of the 48 breakpoints match exactly, with all 48 within one two-fold MIC step.
  • The three IV arms are pooled for PTA. Supplementary Table S7 reports a single “150 mg iv 1/1.5/2 h” row. The paper’s own Table S6 justifies the pooling – its Day 3 fAUC values for the three infusion durations are 3.87, 3.86 and 3.86 mg*h/L – and the model reproduces that invariance exactly in the typical-value table above (3.96 for all three).