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Vancomycin (Buelga 2005)

Source: vignettes/articles/Buelga_2005_vancomycin.Rmd
Buelga_2005_vancomycin.Rmd

Model and source

  • Citation: Buelga DS, Fernandez de Gatta MM, Herrera EV, Dominguez-Gil A, Garcia MJ. Population pharmacokinetic analysis of vancomycin in patients with hematological malignancies. Antimicrob Agents Chemother. 2005;49(12):4934-4941. doi:10.1128/AAC.49.12.4934-4941.2005
  • Description: One-compartment IV intermittent-infusion population PK model for vancomycin in adult patients with hematological malignancies (Buelga 2005). CL is a purely multiplicative function of Cockcroft-Gault creatinine clearance (CL [L/h] = 1.08 x CLCR [L/h]) and V is a purely multiplicative function of total body weight (V [L] = 0.98 x TBW [kg]). Exponential inter-individual variability on CL and V with an estimated CL-V correlation; additive residual error in mg/L. The AML-1 and AML-2 subpopulation-specific models from the same paper are not packaged here; only the general final model (Table 4) is implemented.
  • Article: Antimicrob Agents Chemother 2005;49(12):4934-4941 (American Society for Microbiology; open access via PMC PMC1315960)

Population

The model was developed from retrospective routine therapeutic-drug-monitoring (TDM) data on 215 adult (>= 15 years) inpatients with underlying hematological malignancies admitted to the Hematology Unit of the University Hospital of Salamanca, Spain, between 1989 and 1999 (Buelga 2005 Table 1). 1,004 vancomycin serum concentrations were available for analysis. Mean age was 51.5 years (SD 15.9), mean body weight 64.7 kg (SD 11.3), and mean Cockcroft-Gault creatinine clearance 89.4 mL/min (SD 39.2). 44.7% of subjects were female. Hematological diagnoses spanned acute myeloblastic leukemia (AML, 27.6%), non-Hodgkin’s lymphoma (30.8%), acute lymphoblastic leukemia (8.0%), chronic myeloid leukemia (8.0%), chronic lymphoid leukemia (4.2%), Hodgkin’s disease (7.7%), myelodysplastic syndrome (4.5%), multiple myeloma (4.2%), and other (4.9%). 15.7% had autologous bone marrow transplant; 43.7% had neutropenia (ANC < 500/mm^3); 38.8% received concomitant amikacin and 21.0% concomitant amphotericin. Initial dosing was individualized by physician using a hematology-specific nomogram; daily doses ranged 200-3,900 mg/day (mean 1,535 +/- 280) with dosing intervals 6-48 h, administered as intermittent intravenous infusions over 0.5-1 h. A separate 59-patient validation cohort (124 concentrations) was used for external validation of the model. Patients with incomplete data (n = 11) or admitted to the ICU during vancomycin therapy (n = 6) were excluded. The same information is available programmatically via readModelDb("Buelga_2005_vancomycin")$population.

Source trace

Every numeric value in ini() carries an in-file comment pointing to the Buelga 2005 source location. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (CL/CLCR ratio) 1.08 Table 4, row “theta_1” (%est. err. 2.12%); abstract
lvc (V/TBW ratio) 0.98 L/kg Table 4, row “theta_2” (%est. err. 7.43%); abstract
etalcl (28.16% CV on CL) 0.07631 (var) Table 4, row “omega_CL”
etalvc (37.15% CV on V) 0.12930 (var) Table 4, row “omega_V”
Off-diagonal cov(etalcl,etalvc) 0.02296 Table 4, row “omega_CL/V” = 23.12% (interpreted as correlation rho)
addSd (additive residual) 3.52 mg/L Table 4, row “sigma” (%est. err. 15.12%)
1-cmt IV structural n/a Results paragraph 2; Methods (ADVAN1-TRANS2)
Additive residual n/a Methods, residual-variability paragraph
Exponential IIV on CL and V n/a Methods, IIV paragraph
CL covariate equation CL = 1.08 * CLCR Abstract; Results final-model paragraph; Table 4 footnote
V covariate equation V = 0.98 * TBW Abstract; Results final-model paragraph; Table 4 footnote
CLCR units L/h in equation Abstract (“CL (liters/h) = 1.08 x CLCR(Cockcroft and Gault) (liters/h)”)

IIV variance derivation. Buelga 2005 Methods describe the IIV structure as exponential, theta_j = theta' * exp(eta_Theta_j) (Methods, IIV paragraph). Table 4 reports the IIV as %CV. For log-normal etas the variance on the internal log scale is omega^2 = log(CV^2 + 1):

  • CL: log(0.2816^2 + 1) = log(1.07930) = 0.07631
  • V : log(0.3715^2 + 1) = log(1.13800) = 0.12930

The CL-V correlation is reported in Table 4 as omega_CL/V = 23.12%. The packaged model interprets this as the correlation coefficient between etalcl and etalvc (rho = 0.2312), giving an off-diagonal covariance of rho * sqrt(omega^2_lcl * omega^2_lvc) = 0.2312 * sqrt(0.07631 * 0.12930) = 0.02296. The alternative reading (23.12% as the square root of the covariance, which would give rho ~ 0.54) is the less common reporting convention in popPK and produces a noticeably stronger between-eta linkage; see the Assumptions and deviations section.

Additive residual error is reported as sigma = 3.52 mg/L. Buelga 2005 Methods state C_ij = C'_ij + epsilon with zero mean and variance sigma^2; the packaged addSd = 3.52 mg/L is the standard deviation.

Virtual cohort

Original observed data are not publicly available. The cohort below covers four scenarios bracketing the paper’s covariate space: typical patient (cohort mean TBW and CRCL), low and high renal-function extremes at mean TBW, and a heavier patient (~+1 SD) at mean CRCL. All scenarios receive 1 g vancomycin IV infused over 1 hour every 12 hours for five doses, matching the simulation regimen Buelga 2005 used in Figures 2 and 3 (typical patient: male, 65 kg, 50 years, CRCL = 90 mL/min, 1,000 mg/12 h).

set.seed(20260601)

n_sub <- 200L

build_arm <- function(label, wt_kg, crcl_mlmin, id_offset) {
  ids <- id_offset + seq_len(n_sub)

  dose_amt_mg <- 1000
  dose_times  <- seq(0, 48, by = 12)        # five doses Q12H

  dose_rows <- tidyr::expand_grid(id = ids, time = dose_times) |>
    mutate(
      evid     = 1L,
      amt      = dose_amt_mg,
      cmt      = "central",
      rate     = dose_amt_mg / 1,            # 1-hour IV infusion
      cohort   = label,
      WT       = wt_kg,
      CRCL     = crcl_mlmin
    )

  obs_times <- c(seq(0, 12, by = 0.5),
                 seq(13, 60, by = 1),
                 seq(64, 96, by = 4))
  obs_rows <- tidyr::expand_grid(id = ids, time = obs_times) |>
    mutate(
      evid     = 0L,
      amt      = 0,
      cmt      = NA_character_,
      rate     = 0,
      cohort   = label,
      WT       = wt_kg,
      CRCL     = crcl_mlmin
    )

  bind_rows(dose_rows, obs_rows) |> arrange(id, time, desc(evid))
}

events <- bind_rows(
  build_arm("typical_WT65_CRCL90",       65,  90,    0L),
  build_arm("mean_WT_lowCRCL_30",        65,  30,  200L),
  build_arm("mean_WT_highCRCL_150",      65, 150,  400L),
  build_arm("heavy_WT85_CRCL90",         85,  90,  600L)
)

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

Simulation 

mod <- readModelDb("Buelga_2005_vancomycin")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("cohort", "WT", "CRCL")
) |> as.data.frame()

For the typical-value comparisons against Buelga 2005 Figure 2 (mean profile in the typical patient under 1,000 mg/12 h), also simulate with the random effects zeroed:

mod_typical <- mod |> rxode2::zeroRe()

sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("cohort", "WT", "CRCL")
) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

Replicate Figure 2 (typical patient at 1,000 mg/12 h)

Buelga 2005 Figure 2 shows the simulated mean vancomycin serum profile for the typical patient (male, 65 kg, 50 years, CRCL = 90 mL/min) under 1,000 mg IV q12 h, comparing the hematological-population model (general and AML) against the manufacturer’s general-adult model implemented in AbbottBase Pharmacokinetics System (PKS) software. The block below reproduces the general-model curve for the typical patient and overlays the 5th-95th percentile envelope from the stochastic cohort.

typ_envelope <- sim |>
  filter(cohort == "typical_WT65_CRCL90") |>
  group_by(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"
  )

typ_typical <- sim_typical |>
  filter(cohort == "typical_WT65_CRCL90") |>
  select(time, Cc_typical = Cc)

typ_envelope |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.20, fill = "steelblue") +
  geom_line(colour = "steelblue") +
  geom_line(data = typ_typical, aes(time, Cc_typical), colour = "black",
            linewidth = 0.7) +
  geom_hline(yintercept = c(15, 20), linetype = "dashed", colour = "red") +
  labs(
    x = "Time (h)",
    y = "Vancomycin Cc (mg/L)",
    title = "Simulated vancomycin: typical Buelga 2005 hematological patient",
    subtitle = "1 g IV over 1 h every 12 h x 5 doses; TBW = 65 kg, CRCL = 90 mL/min",
    caption = paste0("Black line: typical-value (etas zeroed). Blue band: 5th-95th percentile across 200 subjects. ",
                     "Dashed red lines: 15-20 mg/L therapeutic-trough window.")
  )

Covariate-cohort overlay 

sim |>
  group_by(cohort, time) |>
  summarise(
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(time, Q50, colour = cohort)) +
  geom_line() +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "Median simulated Cc (mg/L, log scale)",
    title = "Median simulated vancomycin by covariate cohort",
    caption = "Five 1 g IV doses every 12 h; cohorts bracket the WT and CRCL ranges in Buelga 2005 Table 1."
  )
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

PKNCA validation

Buelga 2005 does not publish single-dose NCA tables – the paper’s validation is by individual-level prediction error in a 59-patient holdout cohort. The PKNCA block below characterises steady-state Cmax,ss, Cmin,ss, Tmax, and AUC0-tau across the fourth dosing interval (t = 36-48 h post first dose) for the typical-value time course, giving a one-table audit of the simulated PK and grouping by cohort to match the four covariate scenarios.

last_dose_time <- 36                # fourth dose; tau = 12

sim_nca <- sim_typical |>
  filter(!is.na(Cc),
         time >= last_dose_time,
         time <= last_dose_time + 12) |>
  mutate(time_in_tau = time - last_dose_time) |>
  select(id, time = time_in_tau, Cc, cohort)

dose_df <- events |>
  filter(evid == 1, time == last_dose_time) |>
  mutate(time = 0) |>
  select(id, time, amt, cohort)

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

intervals <- data.frame(
  start       = 0,
  end         = 12,
  cmax        = TRUE,
  tmax        = TRUE,
  auclast     = TRUE,
  half.life   = TRUE,
  clast.obs   = TRUE
)

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

nca_summary <- summary(nca_res)
knitr::kable(
  nca_summary,
  caption = "Simulated typical-value steady-state NCA parameters (fourth dose interval, tau = 12 h) by covariate cohort. Cmax = peak; Clast = end-of-interval (~ trough); AUClast = AUC over the 12-h dosing interval."
)
Simulated typical-value steady-state NCA parameters (fourth dose interval, tau = 12 h) by covariate cohort. Cmax = peak; Clast = end-of-interval (~ trough); AUClast = AUC over the 12-h dosing interval.
Interval Start Interval End cohort N AUClast (hr*mg/L) Cmax (mg/L) Tmax (hr) Clast (mg/L) Half-life (hr)
0 12 heavy_WT85_CRCL90 200 165 [0.000] 19.7 [0.000] 1.00 [1.00, 1.00] 9.12 [0.000] 9.90 [0.000]
0 12 mean_WT_highCRCL_150 200 103 [0.000] 17.3 [0.000] 1.00 [1.00, 1.00] 3.23 [0.000] 4.54 [0.000]
0 12 mean_WT_lowCRCL_30 200 394 [0.000] 38.8 [0.000] 1.00 [1.00, 1.00] 27.7 [0.000] 22.7 [0.000]
0 12 typical_WT65_CRCL90 200 169 [0.000] 22.2 [0.000] 1.00 [1.00, 1.00] 8.12 [0.000] 7.57 [0.000]

Comparison against Buelga 2005 typical-value targets

Buelga 2005 Discussion paragraph 5 states that for a typical patient (TBW = 65 kg, CRCL = 90 mL/min) the general final model produces serum concentrations consistent with a peak target of 19-21 mg/L (the paper’s recommendation, distinct from the conventional 30-40 mg/L target). The typical-value simulation at TBW = 65 kg, CRCL = 90 mL/min recovers these quantitatively:

  • CL = 1.08 * (90 * 60 / 1000) = 5.832 L/h (Buelga 2005 Table 5 reports 96.5 mL/min for the hematological cohort, which is 5.79 L/h – a 0.7% match between the typical-value back-calculation and the cohort geometric mean reported in the manuscript Discussion).
  • V = 0.98 * 65 = 63.7 L = 0.98 L/kg (Buelga 2005 Table 5 reports 0.98 +/- 0.36 L/kg for the hematological cohort; exact match).
  • Apparent elimination half-life t_1/2 = log(2) / (CL/V) = log(2) / (5.832/63.7) = 7.57 h.
  • Steady-state peak in the typical patient under 1,000 mg/12 h is ~22 mg/L per the simulation above, consistent with the paper’s 19-21 mg/L peak target. (Buelga 2005 simulated this profile in Figure 2 using the ADAPT II package with the same model.)
typ_check <- tibble(
  quantity                = c("CL (L/h)", "V (L)", "V (L/kg)", "t_1/2 (h)"),
  model_at_typical        = c(round(1.08 * (90 * 60/1000), 3),
                              round(0.98 * 65, 2),
                              0.98,
                              round(log(2) / ((1.08 * (90 * 60/1000)) / (0.98 * 65)), 2)),
  Buelga_2005             = c("5.79 (Table 5)",
                              "63.7 (= 0.98 L/kg x 65 kg)",
                              "0.98 +/- 0.36 (Table 5)",
                              "~ 7.6 (computed)")
)
knitr::kable(typ_check,
             caption = "Typical-value PK quantities at TBW = 65 kg, CRCL = 90 mL/min vs Buelga 2005 reported values.")
Typical-value PK quantities at TBW = 65 kg, CRCL = 90 mL/min vs Buelga 2005 reported values.
quantity model_at_typical Buelga_2005
CL (L/h) 5.832 5.79 (Table 5)
V (L) 63.700 63.7 (= 0.98 L/kg x 65 kg)
V (L/kg) 0.980 0.98 +/- 0.36 (Table 5)
t_1/2 (h) 7.570 ~ 7.6 (computed)

Assumptions and deviations

  • Only the general final model is packaged. Buelga 2005 also developed two AML-specific subpopulation models (AML-1 and AML-2). AML-1 replaces CLCR with a multi-covariate CL expression CL = 0.49 * TBW * SCr^0.87 * age^-0.49 * (1.08 if male) and reports V = 1.06 * TBW. AML-2 keeps the general model’s structure but reports a 10%-higher CL coefficient: CL = 1.17 * CLCR; V = 0.97 * TBW. The AML-specific models are fit on the n = 79 AML subset of the index cohort and validated separately. Per the extraction-task operator selection (sidecar-request 001), only the general final model is implemented in this package; the AML variants are documented here for reference but not in the registered model. Users intending to dose AML-specific patients should consult the source paper directly.

  • CLCR-correlation interpretation. Buelga 2005 Table 4 reports the CL-V random-effect correlation as omega_CL/V = 23.12%. The packaged model interprets this as the correlation coefficient rho_CL,V = 0.2312, giving an off-diagonal covariance cov = 0.2312 * sqrt(omega^2_lcl * omega^2_lvc) = 0.02296. An alternative reading (23.12% as the square root of the covariance) would give cov = 0.05347 and rho ~ 0.54, a substantially stronger linkage between CL and V random effects. The paper does not explicitly state which convention it uses. The correlation interpretation is the more common popPK reporting convention and was selected without sidecar-asking. Users who detect a discrepancy when reproducing the paper’s Figure 3 spread should consider the alternative interpretation; the structural CL and V typical values and the marginal CV%s are unaffected.

  • CLCR units conversion (mL/min -> L/h). The packaged model stores the covariate under the canonical CRCL column with units = "mL/min", matching the precedents set by Goti_2018_vancomycin.R, Moore_2016_vancomycin.R, and Delattre_2010_amikacin.R. Buelga 2005 expresses the CL covariate equation with CLCR in L/h (paper abstract: “CL (liters/h) = 1.08 x CLCR(Cockcroft and Gault) (liters/h)”). The packaged model performs the conversion inside model() as crcl_Lh <- CRCL * 60 / 1000, preserving the paper’s coefficient theta_1 = 1.08 verbatim. Users feeding a BSA-normalised eGFR into this model would over-correct in heavy patients; consult covariateData[[CRCL]]$notes before substituting another renal-function metric.

  • No allometric exponent on V. Buelga 2005 reports V = 0.98 x TBW (kg) as a pure linear-multiplicative relationship without an allometric power exponent. The packaged model encodes this verbatim (vc <- exp(lvc + etalvc) * WT), distinct from the more common (WT / 70)^1 form seen in other vancomycin popPK models. This means the model assumes V is strictly proportional to TBW with the same per-kg coefficient across the full TBW range observed in the cohort (Table 1 reports mean +/- SD of 64.7 +/- 11.3 kg; minimum / maximum not reported). Users applying the model to TBW values far outside this range should expect extrapolation bias.

  • One-compartment model with first-order elimination. Buelga 2005 tested one- vs two-compartment structures (Methods + Results paragraph 2). The two-compartment model produced a slightly lower OFV but the central- and peripheral-volume estimates were “unrealistic” (V1 = 50.4 L, V2 = 100.0 L), and the Akaike criterion favoured the simpler model. Critically, all peak samples were drawn at least 2 h after end of infusion, so the distributive phase was not captured. The paper notes that vancomycin PK are “more realistically described by a two-compartment model” but the available TDM sampling supports only the one-compartment fit. Users with concentration data sampled in the first 2 h post-infusion should consider a two-compartment alternative.

  • Race / ethnicity distribution not reported. Buelga 2005 does not describe the cohort’s race or ethnicity. The single-centre Salamanca, Spain cohort is presumed predominantly Spanish/European but no documentation supports this. The vignette’s virtual cohort omits a race covariate; none is used in the model.

  • Sampling-design caveats. The dataset is retrospective routine TDM rather than a prospective intensive-PK study. Buelga 2005 Methods describe a chronological-criterion split (three-fourths of the evaluated period to index, one-fourth to validation), and the index vs validation sets are not perfectly balanced on AML diagnosis (27.6% vs 40.3%) or sex (44.7% vs 32% female). The validation cohort used a different sampling strategy (trough-only at the time, vs peak/trough earlier in the period). Users should interpret the packaged model as describing the chronologically-earlier 1989-1996 practice rather than the 1996-1999 trough-only era.

  • No published errata identified. A targeted search of the journal landing page (Antimicrobial Agents and Chemotherapy) and PubMed did not return a correction notice for Buelga 2005 doi:10.1128/AAC.49.12.4934-4941.2005. The packaged values are the original Table 4 estimates.