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Ganciclovir (Perrottet 2009)

Source: vignettes/articles/Perrottet_2009_ganciclovir.Rmd
Perrottet_2009_ganciclovir.Rmd

Model and source

  • Citation: Perrottet N, Csajka C, Pascual M, Manuel O, Lamoth F, Meylan P, Aubert JD, Venetz JP, Soccal P, Decosterd LA, Biollaz J, Buclin T. Population pharmacokinetics of ganciclovir in solid-organ transplant recipients receiving oral valganciclovir. Antimicrob Agents Chemother. 2009;53(7):3017-3023. doi:10.1128/AAC.00836-08
  • Description: Two-compartment population PK model for ganciclovir (administered as oral valganciclovir prodrug) in adult solid-organ transplant recipients (Perrottet 2009)
  • Article: https://doi.org/10.1128/AAC.00836-08

Population

Perrottet 2009 enrolled 65 adult solid-organ transplant recipients at the University Hospitals of Lausanne and Geneva (November 2005 - January 2008); 437 ganciclovir (GCV) plasma samples were collected, including four full profiles from two kidney recipients (rich data). The cohort was 69% male, with median age 55 years (range 18-70), median body weight 72 kg (range 46-115), median serum creatinine 108 umol/L (range 29-691), and a wide range of renal function (Cockroft-Gault GFR 10-170 mL/min). Graft type distribution: kidney 41 (63%), heart 10 (15%), lung 12 (18%), liver 2 (3%). Dosing was oral valganciclovir (VGC, the L-valyl ester prodrug of GCV) at 450 mg or 900 mg once daily for prophylaxis (renal-function adjusted) or 900 mg twice daily for treatment; two patients received intravenous GCV at 5 mg/kg every 12 h. See Perrottet 2009 Table 1 for the full baseline demographics.

The same information is available programmatically via readModelDb("Perrottet_2009_ganciclovir")$population.

Source trace

Every parameter in the model file carries an inline source-location comment. The table below collects the entries in one place.

Equation / parameter Value Source location
lka (ka) 0.56 1/h Table 3, ka row
lcl (CL slope on GFR, male kidney reference) 1.68 L/h per L/h Table 3, theta_kidney row
e_tx_heart_cl (heart vs kidney multiplier on CL) log(0.86/1.68) Table 3, theta_heart row
e_tx_lungliver_cl (lung-or-liver vs kidney multiplier on CL) log(1.17/1.68) Table 3, theta_lung/liver row
e_sexf_cl (female vs male multiplier on CL) log(1.21) Table 3, theta_female on CL row
lvc (V1 at 70-kg male reference) 24 L Table 3, theta_BW row
e_sexf_vc (female vs male multiplier on V1) log(0.78) Table 3, theta_female on V1 row
lq (Q) 4.1 L/h Table 3, Q row
lvp (V2) 22 L Table 3, V2 row
lfdepot (F, fixed) 0.6 Methods (Structural model): fixed per refs 6, 10, 19, 24
etalcl (IIV CL, variance log(0.26^2 + 1)) 26% CV Table 3, interpatient CL row
etalvc (IIV V1, variance log(0.20^2 + 1)) 20% CV Table 3, interpatient V1 row
Interoccasion variability on CL (documented, not modelled here) 12% CV Table 3, IOV row
propSd (proportional residual error) 21% CV Table 3, sigma_prop row
Two-compartment model with first-order absorption from depot – Methods (Structural model); Results (Population pharmacokinetic analyses)
CL covariate form: CL = theta_graft * GFR_MDRD * theta_female^SEXF – Table 3 footnote (a) and Results (Population pharmacokinetic analyses)
V1 covariate form: V1 = theta_BW * (BW/70) * theta_female^SEXF – Table 3 footnote (a) and Table 2 V1 covariate rows

The four-variable MDRD formula GFR_MDRD = 175 * (Crs/88.4)^-1.154 * age^-0.203 * 0.742^SEXF (Methods) returns mL/min/1.73 m^2; the model de-indexes to L/h inside model() using each subject’s BSA via gfr_lh = CRCL * BSA / 1.73 * 60 / 1000. For BSA = 1.73 m^2 this reduces to CRCL * 0.06.

Virtual cohort

The trial-level patient data are not openly available. The virtual cohort below mirrors the demographics in Perrottet 2009 Table 1 (median 72 kg, 69% male, median creatinine 108 umol/L) with two strata that match the paper’s main organ-type contrasts: kidney recipients and heart recipients.

set.seed(20090101)

n_per_organ <- 200L

make_cohort <- function(n, tx_heart, tx_lung, tx_liver, label, id_offset = 0L) {
  female <- rbinom(n, 1L, prob = 0.31)
  wt <- pmax(pmin(rlnorm(n, log(72), 0.20), 115), 46)
  # BSA via Mosteller approximation using a typical height for the sex
  # (172 cm male median, 162 cm female median from Perrottet Table 1
  # 147-192 cm range with median 172 cm overall).
  ht <- ifelse(female == 1L,
               pmax(pmin(rnorm(n, mean = 162, sd = 6), 178), 147),
               pmax(pmin(rnorm(n, mean = 174, sd = 7), 192), 155))
  bsa <- sqrt(ht * wt / 3600)
  # Renal function: skewed toward impaired with a long upper tail
  # (cohort Cockroft-Gault GFR range 10-170 mL/min). Reported median
  # GFR_MDRD is not in the paper directly; we anchor the typical
  # cohort patient at 50 mL/min/1.73 m^2 per the paper's simulation
  # cohort and let the tail extend to 170.
  crcl <- pmax(pmin(rlnorm(n, log(55), 0.50), 170), 10)

  data.frame(
    id        = id_offset + seq_len(n),
    WT        = wt,
    BSA       = bsa,
    CRCL      = crcl,
    SEXF      = female,
    TX_HEART  = tx_heart,
    TX_LUNG   = tx_lung,
    TX_LIVER  = tx_liver,
    cohort    = label
  )
}

cohort <- bind_rows(
  make_cohort(n_per_organ, 0L, 0L, 0L, "kidney", id_offset = 0L),
  make_cohort(n_per_organ, 1L, 0L, 0L, "heart",  id_offset = n_per_organ)
)

# Expand into dose + observation rows: 450 mg oral VGC at time 0,
# observations from 0 to 36 h on a 0.5 h grid.
event_times <- seq(0, 36, by = 0.5)

events <- cohort %>%
  group_by(id) %>%
  do({
    base <- .
    rbind(
      data.frame(
        id    = base$id, time = 0, amt = 450, evid = 1L, cmt = "depot",
        WT = base$WT, BSA = base$BSA, CRCL = base$CRCL,
        SEXF = base$SEXF, TX_HEART = base$TX_HEART,
        TX_LUNG = base$TX_LUNG, TX_LIVER = base$TX_LIVER,
        cohort = base$cohort
      ),
      data.frame(
        id    = base$id, time = event_times, amt = 0, evid = 0L,
        cmt = "central",
        WT = base$WT, BSA = base$BSA, CRCL = base$CRCL,
        SEXF = base$SEXF, TX_HEART = base$TX_HEART,
        TX_LUNG = base$TX_LUNG, TX_LIVER = base$TX_LIVER,
        cohort = base$cohort
      )
    )
  }) %>%
  ungroup() %>%
  as.data.frame()

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

Simulation 

mod <- readModelDb("Perrottet_2009_ganciclovir")
sim <- rxode2::rxSolve(mod, events = events, keep = c("cohort"))
#> ℹ parameter labels from comments will be replaced by 'label()'

For deterministic typical-value replication (no between-subject variability), zero out the random effects:

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

# Typical kidney male, 70 kg, GFR_MDRD = 50 mL/min/1.73 m^2, BSA = 1.73
# (matches the Perrottet 2009 Figure 1F simulation cohort).
typ_events <- data.frame(
  id        = c(1L, 1L),
  time      = c(0, 0),
  amt       = c(450, 0),
  evid      = c(1L, 0L),
  cmt       = c("depot", "central"),
  WT        = 70, BSA = 1.73, CRCL = 50, SEXF = 0L,
  TX_HEART  = 0L, TX_LUNG = 0L, TX_LIVER = 0L
)
typ_events <- bind_rows(
  typ_events[1, , drop = FALSE],
  data.frame(
    id        = 1L,
    time      = seq(0, 48, by = 0.25),
    amt       = 0,
    evid      = 0L,
    cmt       = "central",
    WT = 70, BSA = 1.73, CRCL = 50, SEXF = 0L,
    TX_HEART = 0L, TX_LUNG = 0L, TX_LIVER = 0L
  )
)
sim_typ <- rxode2::rxSolve(mod_typical, events = typ_events)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'

Replicate published figures 

# Replicates Figure 1F of Perrottet 2009: GCV profile in 36 kidney
# transplant recipients under VGC 450 mg QD with the typical-value
# population prediction and 90% prediction interval.
vpc <- sim %>%
  filter(cohort == "kidney") %>%
  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"
  )

ggplot(vpc, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.20, fill = "steelblue") +
  geom_line(colour = "steelblue", linewidth = 0.8) +
  geom_line(data = sim_typ, aes(time, Cc), colour = "black", linewidth = 0.7,
            linetype = "dashed") +
  scale_y_log10(limits = c(0.05, 20)) +
  labs(
    x = "Time after dose (h)",
    y = "Plasma GCV (mg/L)",
    title = "GCV plasma concentration after oral VGC 450 mg QD (kidney recipients)",
    caption = "Solid line + ribbon: simulated median and 90% prediction interval (n = 200, kidney recipients).\nDashed line: typical-value prediction (70-kg male, GFR_MDRD = 50 mL/min/1.73 m^2). Replicates Figure 1F of Perrottet 2009."
  )
#> Warning in scale_y_log10(limits = c(0.05, 20)): log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> Warning: Removed 32 rows containing missing values or values outside the scale range
#> (`geom_ribbon()`).

# Side-by-side typical CL by graft type and sex (matches Table 3
# theta_graft and theta_female on CL).
typ_grid <- expand.grid(
  cohort  = c("kidney", "heart", "lung_or_liver"),
  SEXF    = c(0L, 1L)
) %>%
  mutate(
    TX_HEART  = as.integer(cohort == "heart"),
    TX_LUNG   = as.integer(cohort == "lung_or_liver"),
    TX_LIVER  = 0L,
    id        = seq_len(n()),
    WT = 70, BSA = 1.73, CRCL = 50
  )

# One row per id, both a dose and an observation at t = 0
typ_grid_events <- bind_rows(
  typ_grid %>% mutate(time = 0, amt = 450, evid = 1L, cmt = "depot"),
  typ_grid %>% mutate(time = 0.001, amt = 0, evid = 0L, cmt = "central")
) %>%
  arrange(id, time)

cov_sim <- rxode2::rxSolve(mod_typical, events = typ_grid_events,
                           keep = c("cohort", "SEXF"))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

cov_sim %>%
  group_by(id) %>%
  slice(1) %>%
  ungroup() %>%
  transmute(
    Graft = factor(cohort, levels = c("kidney", "heart", "lung_or_liver")),
    Sex   = ifelse(SEXF == 1L, "female", "male"),
    `CL (L/h)`   = round(cl, 3),
    `V1 (L)`     = round(vc, 3)
  ) %>%
  arrange(Graft, Sex) %>%
  knitr::kable(caption =
    "Typical CL and V1 by graft type and sex for a 70-kg patient with GFR_MDRD = 50 mL/min/1.73 m^2 (BSA = 1.73 m^2). The lung_or_liver row applies to either a lung or a liver recipient (pooled per Perrottet 2009).")
Typical CL and V1 by graft type and sex for a 70-kg patient with GFR_MDRD = 50 mL/min/1.73 m^2 (BSA = 1.73 m^2). The lung_or_liver row applies to either a lung or a liver recipient (pooled per Perrottet 2009).
Graft Sex CL (L/h) V1 (L)
kidney female 6.098 18.72
kidney male 5.040 24.00
heart female 3.122 18.72
heart male 2.580 24.00
lung_or_liver female 4.247 18.72
lung_or_liver male 3.510 24.00

PKNCA validation 

sim_nca <- sim %>%
  filter(!is.na(Cc), Cc > 0) %>%
  select(id, time, Cc, cohort) %>%
  as.data.frame()

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id)

dose_df <- events %>%
  filter(evid == 1L) %>%
  select(id, time, amt, cohort) %>%
  as.data.frame()

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

intervals <- data.frame(
  start       = 0,
  end         = 24,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

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

nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
             caption = "Simulated NCA parameters (median [5th, 95th percentile]) by graft cohort after a single 450 mg oral VGC dose.")
Simulated NCA parameters (median [5th, 95th percentile]) by graft cohort after a single 450 mg oral VGC dose.
start end cohort N cmax tmax half.life aucinf.obs
0 24 heart 200 5.79 [21.8] 2.50 [1.50, 3.50] 13.9 [6.75] NC
0 24 kidney 200 4.83 [26.9] 2.00 [1.00, 3.50] 7.92 [3.02] NC

Comparison against published values

Perrottet 2009 reports an absorption half-life t_1/2a = ln(2)/ka = 1.2 h and a median elimination half-life t_1/2_beta = 8 h (range 5-68 h) in the discussion of the final-model derived parameters. The cohort shows a wide range because the cohort spans a wide range of renal function (GFR 10-170 mL/min).

Quantity Perrottet 2009 (reported) Simulated (kidney cohort, this vignette)
Absorption half-life t_1/2a 1.2 h 1.24 h (derived from ka = 0.56 1/h)
Elimination half-life t_1/2_beta 8 h (median, range 5-68) See PKNCA table above (half.life column)

The published paper does not report Cmax / AUC point estimates by graft type, so the PKNCA table above is the most-granular available comparison. The typical kidney recipient at the simulation reference condition has CL = 1.68 x 3 L/h = 5.04 L/h, which combined with the fixed F = 0.6 gives AUC_inf = 450 * 0.6 / 5.04 = 53.6 mg*h/L – in the right order of magnitude for the simulated cohort given the spread of CRCL values in the virtual population.

Assumptions and deviations

  • Bioavailability F = 0.6 fixed. Perrottet 2009 fixed F based on prior studies (refs 6, 10, 19, 24) because GCV was administered intravenously in only two patients in the present cohort. The fixed value is used here without modification. F is encoded as lfdepot <- fixed(log(0.6)) so a downstream user can see the fix and replace it for a study with explicit IV/PO bioavailability data.

  • Interoccasion variability (IOV) on CL = 12% CV documented but not modelled as a separate eta. Perrottet 2009 retained an IOV term on CL accounting for three operationally defined post-transplant occasions (up to month 1, up to month 2, up to month 6 or more). This nlmixr2lib model exposes the interpatient component (etalcl ~ 0.06544 = 26% CV per Table 3) but does not carry the IOV decomposition because IOV requires a per-event occasion index that is dataset-specific. A user wanting the full Perrottet 2009 within-subject variability can add a second etalcl_iov ~ 0.01441 (= log(0.12^2 + 1)) keyed on occasion in a downstream extension.

  • MDRD-eGFR de-indexing inside model(). The four-variable MDRD formula returns GFR in mL/min/1.73 m^2; the canonical CRCL covariate carries those units. The model de-indexes to L/h via the patient’s BSA: gfr_lh = CRCL * BSA / 1.73 * 60 / 1000. The Perrottet 2009 simulation cohort uses BSA = 1.73 m^2, so the conversion reduces to CRCL * 0.06 for that reference patient. Datasets that supply only CRCL should also supply BSA; if BSA is missing, setting BSA = 1.73 m^2 recovers the simplified form.

  • Graft type encoded as three binary indicators (TX_HEART, TX_LUNG, TX_LIVER). Perrottet 2009 pools lung and liver under a single CL slope; the model applies a shared multiplicative effect via (TX_LUNG + TX_LIVER). Future models that estimate distinct lung-vs-liver effects should reuse the same indicators with separate e_tx_lung_cl / e_tx_liver_cl coefficients.

  • Virtual cohort demographics. Body weight, height, and renal function for the virtual cohort were sampled from log-normal distributions anchored to the cohort medians in Perrottet 2009 Table 1 (WT 72 kg, HT 172 cm, GFR centered slightly below the median to capture the cohort’s predominantly impaired-renal function). BSA was computed from the Mosteller formula (sqrt(HT * WT / 3600)). These cohort-level choices are vignette-only – the model file does not depend on them.