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Cefpirome (Bulitta 2011)

Source: vignettes/articles/Bulitta_2011_cefpirome.Rmd
Bulitta_2011_cefpirome.Rmd

Model and source

  • Citation: Bulitta JB, Kinzig M, Landersdorfer CB, Holzgrabe U, Stephan U, Sorgel F. Comparable Population Pharmacokinetics and Pharmacodynamic Breakpoints of Cefpirome in Cystic Fibrosis Patients and Healthy Volunteers. Antimicrob Agents Chemother. 2011 Jun;55(6):2927-2936. doi:10.1128/AAC.01484-10
  • Description: Three-compartment population PK model for IV cefpirome with simultaneous fit of plasma concentrations and amounts excreted unchanged in urine. Built from a pooled cohort of 24 Caucasian adults: 12 cystic fibrosis (CF) patients and 12 healthy volunteers (HVs) each given a single 10-min IV infusion of 2 g cefpirome. Body size is captured by allometric scaling on lean body mass (LBM) with fixed exponents 0.75 on clearance terms and 1.0 on volumes (reference LBM = 53 kg). Total clearance is split into an estimated renal arm (CL_R, urinary recovery is tracked in the canonical urine compartment) and a non-renal arm (CL_NR). A CF / HV cohort indicator DIS_CF (1 = CF patient, 0 = HV reference) carries three disease- specific scale factors estimated by the paper: FCYF_CLR = 1.07 applied to CL_R, FCYF_CLNR = 1.13 applied to CL_NR, and FCYF_VSS = 0.98 applied uniformly to V1 (central), V2 (shallow peripheral), and V3 (deep peripheral). The inter-compartmental clearances Q12 (central <-> shallow) and Q23 (central <-> deep) are shared across cohorts. Typical-value clearance and volume estimates are anchored to DIS_CF = 0 (HV reference) per the DIS_CF covariate convention registered in inst/references/covariate-columns.md.
  • Article: https://doi.org/10.1128/AAC.01484-10

Population

Bulitta 2011 fit a unified three-compartment population PK model to pooled data from 24 Caucasian adults (paper Table 1):

  • 12 adult cystic-fibrosis (CF) patients: total body weight 31.5-66.5 kg (median 53.3), lean body mass 26.2-55.9 kg (median 45.7), age 18-34 years (median 22.5), 8 male / 4 female, all with normal renal function (estimated creatinine clearance 89.3-164 mL/min, median 131).
  • 12 matched adult healthy volunteers (HVs): total body weight 53.0-85.0 kg (median 63.6), lean body mass 41.8-62.7 kg (median 50.0), age 20-35 years (median 29), 6 male / 6 female, estimated creatinine clearance 92.3-150 mL/min (median 116).

Each subject received a single 10-min IV infusion of 2 g cefpirome dissolved in 20 mL water for injection. Plasma samples were drawn at 5 min and 10 min after the start of infusion and at 5, 10, 15, 20, 30 min and 0.75, 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 7, 8, 10, 12, 16, and 24 h after the end of infusion. Urine was collected from the start of the infusion to 1 h after end of infusion and then in 10 intervals out to 48 h. Population PK estimation used NONMEM VI level 1.2 with FOCE+INTERACTION and a parallel S-ADAPT MC-PEM analysis; the NONMEM estimates were used for the Monte Carlo simulations and are encoded in the nlmixr2lib model file. The same demographic information is available programmatically via readModelDb("Bulitta_2011_cefpirome")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Bulitta_2011_cefpirome.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl_renal log(5.78) Table 3 NONMEM HV column (CL_R)
lcl_nonren log(1.17) Table 3 NONMEM HV column (CL_NR)
lvc log(7.44) Table 3 NONMEM HV column (V1)
lvp log(2.67) Table 3 NONMEM HV column (V2)
lvp2 log(4.63) Table 3 NONMEM HV column (V3)
lq log(25.6) Table 3 NONMEM (CLic_shallow; single value)
lq2 log(2.81) Table 3 NONMEM (CLic_deep; single value)
e_lbm_cl_q fixed(0.75) Population PK / Body size paragraph
e_lbm_vc_vp fixed(1.00) Population PK / Body size paragraph
e_cf_cl_renal log(1.07) = +0.06766 Table 4 LBM-allometric row (FCYF_CLR)
e_cf_cl_nonren log(1.13) = +0.12222 Table 4 LBM-allometric row (FCYF_CLNR)
e_cf_vc_vp_vp2 log(0.98) = -0.02020 Table 4 LBM-allometric row (FCYF_VSS)
etalcl_renal 0.135^2 = 0.018225 Table 3 NONMEM BSV(CL_R), apparent CV
etalcl_nonren 0.322^2 = 0.103684 Table 3 NONMEM BSV(CL_NR), apparent CV
etalvc (block diagonal) 0.448^2 = 0.200704 Table 3 NONMEM BSV(V1), apparent CV
etalvp (block diagonal) 0.735^2 = 0.540225 Table 3 NONMEM BSV(V2), apparent CV
cov(etalvc, etalvp) -0.838 * 0.448 * 0.735 = -0.275893 Table 3 footnote d (r(V1,V2) = -0.838)
etalvp2 0.111^2 = 0.012321 Table 3 NONMEM BSV(V3), apparent CV
BSV on q, q2 not estimated Table 3 NONMEM: BSV(CLic_shallow/_deep) = 0 fix
propSd, addSd 0.0875, 0.429 Table 3 NONMEM (CV_C, SD_C, plasma)
propSd_urineAmt, addSd_urineAmt 0.182, 6.12 Table 3 NONMEM (CV_AU, SD_AU, urine)
Three-compartment ODE structure n/a Methods (Population PK analysis, Population model paragraph)
Urinary excretion compartment n/a Methods (simultaneous fitting plasma + urine)
DIS_CF cohort encoding n/a Methods (Population PK / BSV model paragraph: FCYF scale factors)

Virtual cohort

Original observed data are not publicly available. The simulation below uses a virtual population of 200 CF patients and 200 healthy volunteers whose lean body mass distributions approximate the cohort medians and ranges reported in Bulitta 2011 Table 1.

set.seed(20110614)

make_cohort <- function(n, lbm_mu, lbm_sd, lbm_min, lbm_max, dis_cf, label, id_offset) {
  tibble(
    id     = id_offset + seq_len(n),
    LBM    = pmin(pmax(rnorm(n, mean = lbm_mu, sd = lbm_sd), lbm_min), lbm_max),
    DIS_CF = dis_cf,
    cohort = label
  )
}

n_per_cohort <- 200L

cohort_cf <- make_cohort(
  n        = n_per_cohort,
  lbm_mu   = 45.7,
  lbm_sd   = 8.0,
  lbm_min  = 26.2,
  lbm_max  = 55.9,
  dis_cf   = 1L,
  label    = "CF patient",
  id_offset = 0L
)

cohort_hv <- make_cohort(
  n        = n_per_cohort,
  lbm_mu   = 50.0,
  lbm_sd   = 6.0,
  lbm_min  = 41.8,
  lbm_max  = 62.7,
  dis_cf   = 0L,
  label    = "Healthy volunteer",
  id_offset = n_per_cohort
)

cohorts <- bind_rows(cohort_cf, cohort_hv)

Each subject receives a single 2 g IV infusion administered over 10 minutes, matching the dosing scheme described in paper Methods (Study design and drug administration paragraph).

infusion_dur_h <- 10 / 60   # 10-min infusion expressed in hours
dose_amt_mg    <- 2000

obs_times <- c(
  seq(0,  0.25, by = 0.025),     # dense around end-of-infusion
  seq(0.5, 4,   by = 0.25),      # alpha/beta phase
  seq(4.5, 24,  by = 0.5)        # terminal sampling out to 24 h
)

dose_rows <- cohorts |>
  mutate(
    time = 0,
    evid = 1L,
    amt  = dose_amt_mg,
    cmt  = "central",
    rate = dose_amt_mg / infusion_dur_h,
    dv   = NA_real_
  )

obs_rows <- cohorts |>
  tidyr::crossing(time = obs_times) |>
  mutate(
    evid = 0L,
    amt  = NA_real_,
    cmt  = "Cc",
    rate = 0,
    dv   = NA_real_
  )

# Cumulative-urine observations at the end of each collection interval
# (matched to paper Methods: 1, 2, 3, 4, 6, 8, 10, 12, 24, 36, 48 h truncated
# to the 24-h window covered by the plasma simulation).
urine_times <- c(1, 2, 3, 4, 6, 8, 10, 12, 24)

urine_rows <- cohorts |>
  tidyr::crossing(time = urine_times) |>
  mutate(
    evid = 0L,
    amt  = NA_real_,
    cmt  = "urineAmt",
    rate = 0,
    dv   = NA_real_
  )

events <- bind_rows(dose_rows, obs_rows, urine_rows) |>
  arrange(id, time, desc(evid))

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid", "cmt")])))

Simulation 

mod <- readModelDb("Bulitta_2011_cefpirome")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("cohort", "LBM", "DIS_CF")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

# When multiple endpoints (Cc and urineAmt) are observed at the same time, the
# simulation returns one row per CMT channel. The `Cc` and `urineAmt` columns
# are populated identically at coincident times, so distinct (id, time) rows
# are enough for the per-output figures and the NCA step.
sim_unique <- sim |>
  dplyr::distinct(id, time, .keep_all = TRUE)

Replicate published figures

The simulated population recapitulates the cohort-stratified visual predictive check shown in Bulitta 2011 Figure 1: CF patients and healthy volunteers exhibit superimposable plasma concentration-time profiles after a 2 g IV infusion administered to subjects of similar lean body mass, with CF patients showing a marginal terminal-phase shift consistent with their 20% higher total clearance per kilogram of total body weight (paper Discussion).

sim_unique |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::group_by(cohort, time) |>
  dplyr::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"
  ) |>
  ggplot(aes(time, Q50, fill = cohort, colour = cohort)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, colour = NA) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x = "Time after start of infusion (h)",
    y = "Cefpirome plasma concentration (mg/L)",
    fill   = NULL,
    colour = NULL,
    title  = "Plasma concentration-time profile after 2 g IV (median + 90% PI)",
    caption = "Approximates the VPC structure of Bulitta 2011 Figure 1 (top)."
  ) +
  theme_minimal()

sim_unique |>
  dplyr::filter(!is.na(urineAmt)) |>
  dplyr::group_by(cohort, time) |>
  dplyr::summarise(
    Q05 = quantile(urineAmt, 0.05, na.rm = TRUE),
    Q50 = quantile(urineAmt, 0.50, na.rm = TRUE),
    Q95 = quantile(urineAmt, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(time, Q50, fill = cohort, colour = cohort)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, colour = NA) +
  geom_line(linewidth = 0.7) +
  labs(
    x = "Time after start of infusion (h)",
    y = "Cumulative cefpirome amount in urine (mg)",
    fill   = NULL,
    colour = NULL,
    title  = "Cumulative urinary excretion after 2 g IV (median + 90% PI)",
    caption = "Approximates the VPC structure of Bulitta 2011 Figure 1 (middle)."
  ) +
  theme_minimal()

PKNCA validation

We compute NCA parameters on the simulated plasma concentration profile following the single 2 g IV infusion using PKNCA. The treatment grouping (cohort) allows the simulated Cmax, AUC, and terminal half-life to be compared against the cohort-stratified observed values in paper Table 2.

sim_nca <- sim_unique |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::select(id, time, Cc, cohort)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ time | cohort + id,
  concu = "mg/L", timeu = "h"
)

dose_df <- cohorts |>
  dplyr::mutate(time = 0, amt = dose_amt_mg)

dose_obj <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | cohort + id,
  doseu = "mg"
)

intervals <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE,
  cl.obs      = TRUE
)

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

nca_long <- as.data.frame(nca_res$result) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life", "cl.obs"))

nca_summary <- nca_long |>
  dplyr::group_by(cohort, PPTESTCD) |>
  dplyr::summarise(
    median = stats::median(PPORRES, na.rm = TRUE),
    q05    = stats::quantile(PPORRES, 0.05, na.rm = TRUE),
    q95    = stats::quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::mutate(
    formatted = sprintf("%.2f (%.2f-%.2f)", median, q05, q95)
  ) |>
  dplyr::select(cohort, PPTESTCD, formatted) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = formatted)

knitr::kable(
  nca_summary,
  caption = "Simulated noncompartmental parameters (median, 5%-95% prediction interval) by cohort."
)
Simulated noncompartmental parameters (median, 5%-95% prediction interval) by cohort.
cohort aucinf.obs cl.obs cmax half.life tmax
CF patient NA (NA-NA) NA (NA-NA) 242.92 (129.22-373.24) 1.86 (1.51-2.50) 0.18 (0.15-0.18)
Healthy volunteer NA (NA-NA) NA (NA-NA) 201.05 (120.07-313.25) 2.12 (1.70-2.73) 0.18 (0.15-0.18)

Cumulative urinary fraction excreted unchanged at 24 h 

urine_recovery <- sim_unique |>
  dplyr::filter(!is.na(urineAmt), time == 24) |>
  dplyr::mutate(fer = urineAmt / dose_amt_mg) |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(
    median = stats::median(fer, na.rm = TRUE),
    q05    = stats::quantile(fer, 0.05, na.rm = TRUE),
    q95    = stats::quantile(fer, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::mutate(
    formatted = sprintf("%.3f (%.3f-%.3f)", median, q05, q95)
  ) |>
  dplyr::select(cohort, formatted)

urine_recovery |>
  dplyr::rename(
    "Cohort"                            = cohort,
    "Fraction excreted unchanged (24 h)" = formatted
  ) |>
  knitr::kable(
    caption = "Simulated fraction excreted unchanged in urine at 24 h (median, 5%-95% PI) by cohort."
  )
Simulated fraction excreted unchanged in urine at 24 h (median, 5%-95% PI) by cohort.
Cohort Fraction excreted unchanged (24 h)
CF patient 0.826 (0.721-0.899)
Healthy volunteer 0.835 (0.745-0.903)

Comparison against published NCA (Bulitta 2011 Table 2)

Paper Table 2 reports unscaled noncompartmental PK parameters for the 12 CF patients and the 12 healthy volunteers as median (minimum-maximum). The simulated values above target the same noncompartmental endpoints; the simulated Cmax depends on how densely the time grid is sampled around the end-of-infusion peak.

Parameter CF patients (observed) Healthy volunteers (observed)
Total clearance (L/h) 6.52 (4.05-8.51) 6.64 (5.63-7.64)
Renal clearance (L/h) 5.59 (3.18-9.98) 5.51 (2.70-7.13)
Volume of distribution at steady state (L) 14.4 (7.32-25.3) 15.3 (12.6-19.4)
Fraction excreted unchanged (%) 84.4 (78.6-100) 87.0 (38.7-93.3)
Peak concentration (mg/L) 221 (135-560) 206 (159-299)
Terminal half-life (h) 2.07 (1.95-3.29) 2.17 (1.68-3.75)
Mean residence time (h) 2.16 (1.58-3.03) 2.33 (1.85-2.98)

Differences of more than 20% between the simulated and observed columns typically indicate a transcription error in the source-trace; investigate the model file rather than tuning parameters. Note that paper Table 2 is the noncompartmental analysis of the observed data (linear scaling by total body weight, not allometric scaling by lean body mass), while the model in this package is the structural population PK model (LBM-allometric) underlying the Monte Carlo simulations in Bulitta 2011 Figure 2 and Table 6; minor discrepancies between Table 2 (noncompartmental) and Table 3 (population PK) typicals are expected.

Assumptions and deviations

  • DIS_CF encoding. The paper does not assign an explicit covariate column name to the CF / healthy-volunteer cohort flag; the CF-vs-HV split is encoded in the structural NONMEM / S-ADAPT model via three group-scale factors FCYF_CLR, FCYF_CLNR, and FCYF_VSS that multiply HV typical values for CF subjects. The model file encodes the cohort flag as the new canonical binary covariate DIS_CF (1 = CF patient, 0 = HV reference) registered in inst/references/covariate-columns.md alongside this extraction. Typical values are anchored to the HV column of paper Table 3 so the published FCYF values are recovered as positive log-scale effects under the exp(e_cf_<param> * DIS_CF) form.
  • FCYF_VSS applied uniformly to V1, V2, V3. The paper estimates a single scale factor for volume of distribution at steady state (FCYF_VSS), and the Table 3 V1, V2, V3 ratios CF/HV (0.976, 0.978, 0.976) are numerically indistinguishable from 0.98, consistent with a single shared scale factor. The model file declares this as a single shared covariate effect e_cf_vc_vp_vp2 applied uniformly to vc, vp, and vp2 in model(), extending the existing two-volume shared-exponent pattern e_<cov>_vc_vp (per parameter-names.md) to the three-volume case.
  • Inter-compartmental CL BSVs fixed at 0. Bulitta 2011 Table 3 reports BSV(CLic_shallow) and BSV(CLic_deep) as 0 (fixed) for the NONMEM analysis and 0.15 (fixed) for the S-ADAPT analysis; the paper used the NONMEM estimates for the Monte Carlo simulations, so etalq and etalq2 are omitted from ini(). Users running S-ADAPT-style simulations may add ~ fixed(0.15^2) terms manually.
  • Apparent-CV interpretation of BSV. Table 3 footnote c labels the BSV values as “apparent coefficients of variation”, interpreted as sqrt(omega^2) on the log scale; the back-transform used here is omega^2 = (CV)^2 (not log(1 + CV^2)), matching the convention used in Jonckheere_2019_cefepime.R and the broader Bulitta lab’s publications.
  • V1-V2 correlation = -0.838. The paper retains only the V1-V2 off-diagonal in the random-effect covariance matrix (footnote d: “only the correlation of random effects in comparisons of V1 and V2 was included in the final model”); all other r^2 values were below 0.25 and not statistically significant. The model file encodes the block as etalvc + etalvp ~ c(0.200704, -0.275893, 0.540225).
  • Cmax sampling density. The published Cmax estimates in paper Table 2 reflect a fixed sampling schedule that includes a sample at end of infusion (10 min). The simulated NCA Cmax in the vignette depends on the sampling density around end-of-infusion; if the user’s grid is coarser than the simulated grid here (0.025 h between 0 and 0.25 h), the simulated Cmax will fall below the published value because the end-of-infusion peak is the dominant feature.
  • 10-min infusion duration. The model file declares TK0 = 10 min as a fixed structural duration in the population description and notes; users must supply the dosing infusion in the event table via rate = amt / (10/60) or dur = 10/60. The vignette simulates exactly this schedule.
  • Monte Carlo / breakpoint analysis out of scope. The paper’s Table 6 pharmacodynamic breakpoints (fT > MIC > 65%) were derived from 10,800- subject MCS at multiple dosing regimens. The vignette focuses on the structural PK validation; the breakpoint analysis is left as an exercise for users running site-specific MCS with the packaged model.