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Fluconazole (Patel 2011)

Source: vignettes/articles/Patel_2011_fluconazole.Rmd
Patel_2011_fluconazole.Rmd

Model and source

This is a two-compartment IV-infusion popPK model for fluconazole in 10 critically ill anuric adults receiving continuous venovenous hemodiafiltration (CVVHDF). Total fluconazole clearance from the central compartment is partitioned into a CVVHDF-route arm (CL_CVVHDF, encoded as lcl_renal; the dialysis filter performs the renal-mimetic extracorporeal clearance in these anuric patients) and a non-CVVHDF arm (CL_NCVVHDF, encoded as lcl_nonren). The two arms are fitted simultaneously to the plasma concentration-time data and the cumulative amount of fluconazole in the CVVHDF effluent. Dialysis filters in use for more than 48 hours reduce the CVVHDF clearance efficiency to 36.8% of the fresh-filter baseline (FILT_AGE_HI indicator on the CVVHDF arm; Patel 2011 Table 2 ffCL_CVVHDF = 0.368, bootstrap 95% CI 0.326-0.426).

mod_fn  <- readModelDb("Patel_2011_fluconazole")
mod     <- rxode2::rxode2(mod_fn())
mod_typ <- rxode2::rxode2(rxode2::zeroRe(mod_fn()))

Population

The model was developed from 10 critically ill anuric adults enrolled at the Royal Brisbane and Women’s Hospital, Queensland, Australia, over a 28-month window. Age range 51-76 years (median 67); body weight 50-104 kg (median 80); 50% female; APACHE II scores 17-44 (median 29). All 10 patients were anuric and required CVVHDF for renal failure of any cause; all were prescribed IV fluconazole for a suspected fungal infection. Causative organism was Candida albicans in 7 patients, Candida parapsilosis in 1, nonfungal in 1, and not listed in 1. Eight of 10 patients had normal liver function; serum albumin was low in all 10 (range 11-30 g/L), consistent with critical illness.

Each patient received a standard 200 mg dose of IV fluconazole twice daily delivered as a 60-min infusion. Plasma was sampled at 0.5, 1, 2, 3, 4, 6, 8, and 12 h after the dose; CVVHDF effluent was sampled hourly over 12 h. Patients 3, 4, and 8 were sampled on the first day of treatment (initial profile); the other 7 patients were sampled on day 3 or day 5 (steady-state profile). The dialysis prescription was uniform: predilution filtration solution 2 L/h + dialysate 1 L/h = 3 L/h CVVHDF effluent, with fluid input / effluent flow rates controlled at 999 mL/h. Blood was pumped at 200 mL/min through a Hospal AN69HF hemofilter. With the exception of patient 4, all patients had filters in use less than 48 h at the start of CVVHDF treatment.

The same baseline-characteristics summary is available programmatically via readModelDb("Patel_2011_fluconazole")$population.

Source trace

Per-parameter origins are recorded as in-file comments in inst/modeldb/specificDrugs/Patel_2011_fluconazole.R; the table below collects them in one place for review.

Item Value Source
Two-compartment IV-infusion disposition with zero-order input structural Patel 2011 Results paragraph 2 (“the time course of fluconazole in plasma was best described by a two-compartment model with combined residual error, BSV on clearance, central volume of distribution, and infusion duration. Input into the central compartment was fitted by zero-order kinetics.”); Figure 1
Additive split CL_total = CL_CVVHDF + CL_NCVVHDF structural Patel 2011 Methods (“CVVHDF model”) and Figure 1
lcl_renal -> CL_CVVHDF = 1.66 L/h 1.66 Patel 2011 Table 2
lcl_nonren -> CL_NCVVHDF = 1.01 L/h 1.01 Patel 2011 Table 2
lvc -> Vc = 31.7 L 31.7 Patel 2011 Table 2
lvp -> Vp = 21.9 L 21.9 Patel 2011 Table 2
lq -> Q = 27.6 L/h 27.6 Patel 2011 Table 2
ldur -> D1 = 0.689 h 0.689 Patel 2011 Table 2
e_filt_age_hi_cl_renal -> ffCL_CVVHDF = 0.368 (multiplicative on CL_CVVHDF when FILT_AGE_HI = 1) 0.368 Patel 2011 Table 2 (bootstrap 95% CI 0.326-0.426); Results (“filters in use > 48 h considerably reduced the efficiency of dialysis to 37% of total fluconazole clearance”); Methods (“CVVHDF model”: Delta-OBJ = -11.46)
Filter-age binary threshold (48 h) and the n = 1 subject above the threshold structural Patel 2011 Methods (“Dosing and sample collection”: “With the exception of patient 4, all patients had filters in use < 48 h at the start of CVVHDF treatment”)
BSV CL_CVVHDF 19.8% CV -> log(1 + 0.198^2) Patel 2011 Table 2
BSV CL_NCVVHDF 77.1% CV -> log(1 + 0.771^2) Patel 2011 Table 2
BSV Vc 22.9% CV -> log(1 + 0.229^2) Patel 2011 Table 2
BSV D1 23.0% CV -> log(1 + 0.230^2) Patel 2011 Table 2
Lognormal BSV interpretation (omega^2 = log(1 + CV^2)) structural Patel 2011 Methods (“Between-subject variability (BSV) was calculated using an exponential variability model and was assumed to follow a lognormal distribution”)
addSd (plasma additive residual SD) 0.239 mg/L Patel 2011 Table 2 (RUVSDP)
propSd (plasma proportional residual SD) 0.0367 (3.67% CV) Patel 2011 Table 2 (RUVCVP)
addSd_urineAmt (cumulative CVVHDF effluent additive residual SD) 2.84 mg (see Errata for the units note) Patel 2011 Table 2 (RUVSDC)
Combined exponential + additive plasma residual structural Patel 2011 Methods (“Residual unexplained variability (RUV) was modeled using a combined exponential and additive random error”)
Additive-only effluent residual structural Patel 2011 Results paragraph 3 (“The residual variability for the amount of fluconazole in the CVVHDF effluent was best described by an additive error model”)
No demographic covariates retained structural Patel 2011 Results paragraph 2 (“After screening all biologically plausible covariates on clearance and volume of distribution, no statistically significant improvements in the base model were found”)

Virtual cohort

Original observed concentrations from the 10 enrolled patients are not publicly available. The simulations below use a 100-subject virtual cohort, dosed at the standard regimen of 200 mg IV q12h delivered as 60-min infusions over five doses (60 h total simulation horizon, which spans the initial-profile day-1 dose through to a steady-state day-3 profile per the paper’s sampling design). Subject-level FILT_AGE_HI is set to 0 for the typical-population scenario (fresh-filter baseline); a matched n = 100 cohort with FILT_AGE_HI = 1 is built for the side-by-side filter-age comparison.

The model has no retained demographic covariates, so the covariate distribution does not affect the simulation; only FILT_AGE_HI matters.

set.seed(20260609)

n_subjects <- 100L
dose_mg    <- 200
tau_h      <- 12        # q12h dosing interval
n_doses    <- 5L        # 5 doses -> 4 complete intervals; steady state by 48-60 h
t_horizon  <- tau_h * n_doses   # 60 h

build_events <- function(filt_age_hi, id_offset) {
  ids <- id_offset + seq_len(n_subjects)
  dose_times <- (seq_len(n_doses) - 1L) * tau_h

  # Dosing rows: rate = -2 invokes the model-defined dur(central) <- dur_inf
  dose_rows <- tidyr::expand_grid(id = ids, time = dose_times) |>
    dplyr::mutate(
      evid        = 1L,
      cmt         = "central",
      amt         = dose_mg,
      rate        = -2,
      FILT_AGE_HI = filt_age_hi
    )

  # Observation grid: dense over each interval to capture infusion peak +
  # post-infusion decline; sparser at end-of-interval troughs.
  obs_times_one_interval <- c(0.25, 0.5, 0.75, 1, 1.25, 1.5, 2, 3, 4, 6, 8, 10, 12)
  obs_times <- sort(unique(c(
    as.numeric(outer(dose_times, obs_times_one_interval, "+")),
    t_horizon
  )))
  obs_times <- obs_times[obs_times <= t_horizon]
  obs_rows <- tidyr::expand_grid(id = ids, time = obs_times) |>
    dplyr::mutate(
      evid        = 0L,
      cmt         = "Cc",
      amt         = 0,
      rate        = 0,
      FILT_AGE_HI = filt_age_hi
    )

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

events_fresh <- build_events(filt_age_hi = 0L, id_offset = 0L)
events_old   <- build_events(filt_age_hi = 1L, id_offset = n_subjects)
events_all   <- dplyr::bind_rows(
  events_fresh |> dplyr::mutate(filter_age = "Fresh (<= 48 h)"),
  events_old   |> dplyr::mutate(filter_age = "Old (> 48 h)")
)

# Disjoint-id sanity check across the two cohorts.
stopifnot(!anyDuplicated(unique(events_all[, c("id", "time", "evid")])))

Simulation 

sim <- rxode2::rxSolve(
  mod,
  events = events_all,
  keep   = c("FILT_AGE_HI", "filter_age")
) |>
  as.data.frame() |>
  dplyr::filter(time > 0)

Typical-value (no IIV, no residual) simulation for the deterministic overlays:

sim_typ <- rxode2::rxSolve(
  mod_typ,
  events = events_all,
  keep   = c("FILT_AGE_HI", "filter_age")
) |>
  as.data.frame() |>
  dplyr::filter(time > 0)
#> ℹ omega/sigma items treated as zero: 'etalcl_renal', 'etalcl_nonren', 'etalvc', 'etaldur'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 2 – plasma and CVVHDF-effluent VPC at the fresh-filter baseline

Patel 2011 Figure 2 shows the visual predictive check of fluconazole in plasma (panels A, C) and in the CVVHDF effluent (panels B, D), with the top row covering the initial-profile day-1 cohort and the bottom row the steady-state profile. The chunk below renders an analogous VPC at the fresh-filter baseline (FILT_AGE_HI = 0), with median and 5th/95th-percentile envelopes across the 100-subject virtual cohort.

vpc_df <- sim |>
  dplyr::filter(filter_age == "Fresh (<= 48 h)") |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    Q05_plasma = stats::quantile(Cc,       0.05, na.rm = TRUE),
    Q50_plasma = stats::quantile(Cc,       0.50, na.rm = TRUE),
    Q95_plasma = stats::quantile(Cc,       0.95, na.rm = TRUE),
    Q05_efflux = stats::quantile(urineAmt, 0.05, na.rm = TRUE),
    Q50_efflux = stats::quantile(urineAmt, 0.50, na.rm = TRUE),
    Q95_efflux = stats::quantile(urineAmt, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

vpc_long <- dplyr::bind_rows(
  vpc_df |>
    dplyr::transmute(time, panel = "A: plasma Cc (mg/L)",
                     Q05 = Q05_plasma, Q50 = Q50_plasma, Q95 = Q95_plasma),
  vpc_df |>
    dplyr::transmute(time, panel = "B: cumulative effluent urineAmt (mg)",
                     Q05 = Q05_efflux, Q50 = Q50_efflux, Q95 = Q95_efflux)
)

ggplot(vpc_long, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "steelblue") +
  geom_line(colour = "steelblue4", size = 0.7) +
  facet_wrap(~ panel, nrow = 1, scales = "free_y") +
  labs(
    x = "Time after first dose (h)",
    y = NULL,
    title = "Figure 2 -- simulated VPC at the fresh-filter baseline",
    caption = paste0(
      "Replicates Figure 2 of Patel 2011 (plasma and CVVHDF effluent). ",
      "Lines: 50th percentile across ", n_subjects, " virtual subjects; ",
      "ribbon: 5th-95th percentile. Standard 200 mg IV q12h x 5 doses, ",
      "FILT_AGE_HI = 0."
    )
  )
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.
#> This warning is displayed once per session.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

Filter-age effect (Patel 2011 Table 2 ffCL_CVVHDF = 0.368)

The same 100-subject cohort is also simulated with FILT_AGE_HI = 1 (filter in use > 48 h), in which the CVVHDF clearance arm is reduced to 36.8% of its fresh-filter value. The expected qualitative effect is a higher steady-state plasma Cc (because the CVVHDF-route elimination is slower) and a lower cumulative effluent urineAmt (because less drug is extracted into the effluent per unit time).

filt_summary <- sim_typ |>
  dplyr::group_by(time, filter_age) |>
  dplyr::summarise(
    Cc       = mean(Cc,       na.rm = TRUE),
    urineAmt = mean(urineAmt, na.rm = TRUE),
    .groups  = "drop"
  )

filt_long <- dplyr::bind_rows(
  filt_summary |>
    dplyr::transmute(time, filter_age,
                     panel = "Plasma Cc (mg/L)", value = Cc),
  filt_summary |>
    dplyr::transmute(time, filter_age,
                     panel = "Cumulative effluent urineAmt (mg)", value = urineAmt)
)

ggplot(filt_long, aes(time, value, colour = filter_age)) +
  geom_line(size = 0.8) +
  facet_wrap(~ panel, nrow = 1, scales = "free_y") +
  labs(
    x      = "Time after first dose (h)",
    y      = NULL,
    colour = "Filter age",
    title  = "Effect of dialysis-filter age on fluconazole CVVHDF exposure",
    caption = paste0(
      "Typical-value (no IIV) trajectories at FILT_AGE_HI = 0 vs 1; ",
      "standard 200 mg IV q12h x 5 doses. ",
      "ffCL_CVVHDF = 0.368 multiplies CL_CVVHDF only when FILT_AGE_HI = 1."
    )
  ) +
  theme(legend.position = "bottom")

PKNCA validation

For an IV q12h dosing regimen at steady state, the canonical NCA quantity of greatest clinical interest in this paper is the within-interval AUC (AUC0-tau), which determines the fAUC0-24 / MIC ratio that drives fluconazole efficacy. Below, AUC0-tau is computed over the steady-state 48-60 h interval (the fifth dose interval) via PKNCA, separately for each filter-age cohort.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc), time >= 48, time <= 60) |>
  dplyr::select(id, time, Cc, treatment = filter_age)

dose_df <- events_all |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, treatment = filter_age)

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

intervals <- data.frame(
  start   = 48,
  end     = 60,
  cmax    = TRUE,
  cmin    = TRUE,
  cav     = TRUE,
  auclast = TRUE
)

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

Comparison against the derived steady-state AUC0-tau

Under linear kinetics and steady state, the within-interval AUC0-tau = Dose / CL_total. The Patel 2011 Table 2 typical-value clearances give:

  • Fresh filter (FILT_AGE_HI = 0): CL_total = 1.66 + 1.01 = 2.67 L/h, so AUC0-tau = 200 / 2.67 = 74.9 mg.h/L per 12 h interval (which extrapolates to a steady-state fAUC0-24 of approximately 0.78 * 2 * 74.9 = 116.8 mg.h/L of unbound drug under the paper’s 22%-protein-binding assumption for critically ill patients).
  • Old filter (FILT_AGE_HI = 1): CL_total = 1.66 * 0.368 + 1.01 = 1.62 L/h, so AUC0-tau = 200 / 1.62 = 123.5 mg.h/L per 12 h interval – the CVVHDF arm slows down, so fluconazole accumulates and the within-interval AUC grows by approximately 65%.
res_tbl <- as.data.frame(nca_res$result)

simulated_summary <- res_tbl |>
  dplyr::filter(PPTESTCD %in% c("cmax", "cmin", "cav", "auclast")) |>
  dplyr::group_by(treatment, 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"
  )

published_auc <- tibble::tibble(
  treatment = c("Fresh (<= 48 h)", "Old (> 48 h)"),
  derived_AUC0_tau_mg_h_L = c(200 / 2.67, 200 / (1.66 * 0.368 + 1.01))
)

knitr::kable(
  simulated_summary,
  digits  = 2,
  caption = paste("Simulated steady-state NCA parameters (48-60 h dosing",
                  "interval) by filter-age cohort. PPTESTCD: cmax, cmin,",
                  "cav, auclast. Compare auclast against the derived",
                  "Dose / CL_total in the table below.")
)
Simulated steady-state NCA parameters (48-60 h dosing interval) by filter-age cohort. PPTESTCD: cmax, cmin, cav, auclast. Compare auclast against the derived Dose / CL_total in the table below.
treatment PPTESTCD median q05 q95
Fresh (<= 48 h) auclast 68.41 38.73 93.31
Fresh (<= 48 h) cav 5.70 3.23 7.78
Fresh (<= 48 h) cmax 8.41 6.03 11.23
Fresh (<= 48 h) cmin 4.01 1.85 5.84
Old (> 48 h) auclast 100.85 48.21 146.54
Old (> 48 h) cav 8.40 4.02 12.21
Old (> 48 h) cmax 10.92 7.13 14.92
Old (> 48 h) cmin 6.36 2.48 9.41 

knitr::kable(
  published_auc,
  digits  = 1,
  caption = "Derived steady-state AUC0-tau (mg.h/L) from Patel 2011 Table 2 typical-value clearances."
)
Derived steady-state AUC0-tau (mg.h/L) from Patel 2011 Table 2 typical-value clearances.
treatment derived_AUC0_tau_mg_h_L
Fresh (<= 48 h) 74.9
Old (> 48 h) 123.4

Assumptions and deviations

  • Effluent residual-unit convention. Patel 2011 Table 2 lists the CVVHDF residual error RUVSDC with units “mg/liters” while the paper’s Methods (CVVHDF model paragraph) describes the fit as being on “cumulative amounts of fluconazole in the CVVHDF effluent”. The packaged model treats the structural state urine as a cumulative amount (mg) and applies the published 2.84 magnitude as an additive residual on that mass scale, consistent with the Krekels 2015 paracetamol (urineP / urinePG / urinePS cumulative-amount with addSd_urineP residual in mg) and Taubert 2018 finafloxacin (urineAmt) urine-compartment precedents. The “mg/liters” label in Table 2 most likely reflects the effluent assay’s calibration scale (standard curves prepared at 2.0-200 mg/L) rather than the structural state’s unit. Downstream users running NCA on the cumulative-effluent state can divide by the prescribed CVVHDF effluent rate (3 L/h per Patel 2011 Methods) to convert to an instantaneous effluent concentration if desired.
  • CVVHDF dialysis prescription is hard-coded into CL_CVVHDF. Patel 2011 fits CL_CVVHDF under a uniform dialysis prescription (2 L/h predilution filtration + 1 L/h dialysate = 3 L/h effluent, 200 mL/min blood flow, Hospal AN69HF hemofilter, 999 mL/h fluid input / effluent flow rates). The published CL_CVVHDF point estimate therefore embeds this specific prescription; users simulating other dialysate flow rates, predilution proportions, or hemofilter types should scale CL_CVVHDF accordingly or refit the model against their own data.
  • No demographic covariates were retained. Patel 2011 screened age, total body weight, sex, and APACHE II score with stepwise forwards / backwards inclusion at Delta-OBJ >= 3.84 (p < 0.05) and retained none. The packaged model therefore has no allometric scaling or demographic effects on CL, Vc, Q, or Vp – a notable deviation from popPK practice in larger cohorts, justified by the small enrolled sample (n = 10) and the homogeneity of the underlying dialysis prescription.
  • FILT_AGE_HI is informed by n = 1 patient above the 48 h threshold. Only patient 4 had a hemofilter in use > 48 h at the start of CVVHDF treatment. The bootstrap 95% CI on e_filt_age_hi_cl_renal (0.326 to 0.426) is informed by that single subject combined with the dense plasma + effluent sampling over the 12 h profile. Patel 2011 Discussion paragraph 4 cautions that “caution must be applied, since only 1 patient received CVVHDF treatment with a 48-h filter. Further data are required to confirm the long-term effects of filter age on fluconazole clearance.” Simulations using FILT_AGE_HI = 1 therefore extrapolate outside the cohort and should be interpreted with appropriate uncertainty.
  • Lognormal BSV interpretation (omega^2 = log(1 + CV^2)). Patel 2011 Methods state that BSV “was calculated using an exponential variability model and was assumed to follow a lognormal distribution”. The packaged model back-transforms the published CV% via omega^2 = log(1 + CV^2) (the canonical lognormal-arithmetic-CV relationship). This is distinct from the omega^2 = CV^2 interpretation used in some NONMEM tables (where CV% is the standard deviation of the log-scale eta expressed as a percentage), and is consistent with the explicit lognormal language in the Patel 2011 Methods.
  • No reported correlation between etas. Patel 2011 Table 2 reports only diagonal BSV magnitudes for CL_CVVHDF, CL_NCVVHDF, Vc, and D1; no off-diagonal correlation coefficients are reported, so the packaged model treats all four etas as independent.
  • NONMEM “exponential” residual maps to prop() in nlmixr2. Patel 2011 Methods describe the plasma RUV as “a combined exponential and additive random error”. The NONMEM exponential residual encodes a log-additive error on the observation, which corresponds to a proportional residual on the linear concentration scale in nlmixr2 to first order in eps (the standard Cc ~ add(addSd) + prop(propSd) combination). Patel 2011 Table 2 reports propSd as a CV% (3.67%); this is read as the linear-scale CV magnitude and entered as propSd = 0.0367. See .claude/skills/extract-literature-model/references/verification-checklist.md section D for the canonical NONMEM-to-nlmixr2 residual mapping.
  • The healthy-subject comparator (reference 31) is documented but not packaged. Patel 2011 Figure 3C overlays the CVVHDF PTA against a healthy-subject parameter set drawn from a separate publication (Brammer and Tarbit 1987, reference 31 of Patel 2011), with CL_total = 1.18 L/h, Vss = 55.7 L, one-compartment disposition. That upstream parameter set is NOT encoded here; the packaged model is the CVVHDF model only. Users who wish to compare CVVHDF dosing against normal-renal-function dosing should reproduce the Brammer and Tarbit parameters separately.