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Doxorubicin (Perez-Blanco 2016)

Source: vignettes/articles/PerezBlanco_2016_doxorubicin.Rmd
PerezBlanco_2016_doxorubicin.Rmd

Model and source

  • Citation: Perez-Blanco JS, Santos-Buelga D, Fernandez de Gatta MM, Hernandez-Rivas JM, Martin A, Garcia MJ. Population pharmacokinetics of doxorubicin and doxorubicinol in patients diagnosed with non-Hodgkin’s lymphoma. Br J Clin Pharmacol. 2016;82(6):1517-1527. doi:10.1111/bcp.13070
  • Article: https://doi.org/10.1111/bcp.13070

Population

Perez-Blanco 2016 enrolled 45 adult patients with non-Hodgkin’s lymphoma (diffuse large B-cell lymphoma n = 36, Burkitt-like lymphoma n = 2, follicular lymphoma n = 2, other n = 5) treated with the R-CHOP regimen at six Spanish hospitals between June 2009 and June 2015. Patients received doxorubicin as a 0.5-h IV infusion (range 0.2-1.3 h) at a protocol dose of 50 mg/m^2 every 21 days for six cycles, supported with G-CSF prophylaxis where indicated. Baseline demographics from Table 1: age 26-84 years (mean 66, SD 15), weight 43-110 kg (mean 71), height 1.43-1.92 m (mean 1.64), body surface area 1.3-2.3 m^2 (mean 1.8), and a nearly balanced sex split (22 female / 23 male). All patients had normal hepatic, renal, and cardiac function. Sparse PK sampling was performed at 0, 30, 90, and 180 min after the end of each studied infusion, yielding 125 doxorubicin and 120 doxorubicinol plasma concentrations for the population fit (one outlier subject with |CWRES| > 4 removed, n = 44 in the final fit). The UHPLC-fluorescence assay’s lower limit of quantification was 8 ng/mL for doxorubicin and 3 ng/mL for doxorubicinol. The same information is available programmatically via rxode2::rxode(readModelDb("PerezBlanco_2016_doxorubicin"))$population.

Source trace

Final parameter estimates come from Perez-Blanco 2016 Table 2 column “Final model (n = 44)”. Five volumes are FIXED: the DOX volumes V1, V2, V3 to the Kontny 2013 (doi:10.1007/s00280-013-2261-3) adult-reference values; the DOXol volumes V4 and V5 to the values obtained from the authors’ sensitivity analysis. Three IIVs (Q2, Q3, CLm) are also FIXED at their model-building values to avoid over-parameterisation.

Equation / parameter Value Source location
lcl (CL doxorubicin total) 62.4 L/h Table 2 row 1, RSE 11.5%
lvc (V1 doxorubicin central) 17.7 L FIXED Table 2 row 2 FIX, from Kontny 2013
lq (Q2 doxorubicin) 50.7 L/h Table 2 row 3, RSE 18.4%
lvp (V2 doxorubicin peripheral1) 1830 L FIXED Table 2 row 4 FIX, from Kontny 2013
lq2 (Q3 doxorubicin) 28.4 L/h Table 2 row 5, RSE 13.5%
lvp2 (V3 doxorubicin peripheral2) 71 L FIXED Table 2 row 6 FIX, from Kontny 2013
lfm (Fm fraction metabolised) 0.22 Table 2 row 9, RSE 14.7%
lcl_doxol (CLm doxorubicinol) 26.8 L/h Table 2 row 8, RSE 42.9%
lvc_doxol (V4 doxorubicinol central) 79.8 L FIXED Table 2 row 7 FIX, sensitivity analysis
lvp_doxol (V5 doxorubicinol peripheral1) 653 L FIXED Table 2 row 10 FIX, sensitivity analysis
lq_doxol (Q5 doxorubicinol) 424 L/h Table 2 row 11, RSE 18.0%
IIV(CL) 22.9% CV -> omega^2 = 0.0511 Table 2 row 12, RSE 32.7%, shrinkage 40%
IIV(Q2) FIXED 64.1% CV -> omega^2 = 0.3442 Table 2 row 13 FIX
IIV(Q3) FIXED 28.2% CV -> omega^2 = 0.0765 Table 2 row 14 FIX
IIV(CLm) FIXED 47.2% CV -> omega^2 = 0.2011 Table 2 row 15 FIX
IIV(Fm) 41.7% CV -> omega^2 = 0.1603 Table 2 row 16, RSE 19.6%, shrinkage 22%
IIV(Q5) 58.9% CV -> omega^2 = 0.2978 Table 2 row 17, RSE 39.4%, shrinkage 35%
Proportional residual SD (DOX) 0.371 (= 37.1%) Table 2 row 18, RSE 8.3%, shrinkage 15%
Proportional residual SD (DOXol) 0.321 (= 32.1%) Table 2 row 19, RSE 10.4%, shrinkage 21%
d/dt(central) 3-cmt IV, parent loss -cl/vc * central – Methods ‘popPK analysis’; Figure 2 schematic
d/dt(central_doxol) input fm * cl / vc * central – AUCm = Dose * Fm / CLm (Methods ‘Drug exposure and haematological toxicity’)

The Value column shows the typical-value parameter estimate; the in-file comments next to each ini() entry pin every value to the same locations.

Virtual cohort

Original patient-level concentrations are not publicly available. The cohort below is reconstructed to match Table 1 demographics: n = 45, mean BSA 1.8 m^2, mean weight 71 kg, mean age 66 years, balanced sex ratio. Because the final model retained no covariates, the only quantities that flow into rxSolve are the dose (proportional to BSA) and the infusion duration (0.5 h); the demographic columns are carried for completeness and to feed the figures.

set.seed(20160929)  # Perez-Blanco 2016 BJCP published-online date

n_sub <- 45L

# Approximate the Table 1 distributions with a normal draw clipped to
# the published ranges. The exact patient-level values are not
# available; this is the best-feasible virtual reconstruction.
clip <- function(x, lo, hi) pmin(pmax(x, lo), hi)

cohort <- tibble::tibble(
  id  = seq_len(n_sub),
  AGE = clip(rnorm(n_sub, mean = 66, sd = 15), 26,   84),
  WT  = clip(rnorm(n_sub, mean = 71, sd = 12), 43,  110),
  BSA = clip(rnorm(n_sub, mean = 1.8, sd = 0.2), 1.3, 2.3),
  SEXF = c(rep(1L, 22), rep(0L, 23))[sample.int(n_sub)],
  DOSE_MG_M2 = 50,            # protocol dose
  INF_DUR_H  = 0.5            # protocol infusion duration
) |>
  dplyr::mutate(
    DOSE_MG = DOSE_MG_M2 * BSA,
    treatment = "50 mg/m^2 IV over 0.5 h"
  )

# Observation grid: dense early to capture distribution and the
# infusion ramp, then logarithmic out to 168 h for the terminal phase.
obs_times <- c(
  seq(0.05, 0.5,  length.out = 12),
  seq(0.6,  6.0,  length.out = 25),
  seq(8,    24,   length.out = 12),
  seq(36,   168,  length.out = 12)
)

events <- cohort |>
  dplyr::rowwise() |>
  dplyr::do({
    s <- .
    dplyr::bind_rows(
      tibble::tibble(id = s$id, time = 0,         amt = s$DOSE_MG,
                     dur  = s$INF_DUR_H, evid = 1L, cmt = "central"),
      tibble::tibble(id = s$id, time = obs_times, amt = NA_real_,
                     dur  = NA_real_,    evid = 0L, cmt = "Cc")
    ) |>
      dplyr::mutate(
        AGE = s$AGE, WT = s$WT, BSA = s$BSA, SEXF = s$SEXF,
        DOSE_MG_M2 = s$DOSE_MG_M2,
        treatment  = s$treatment
      )
  }) |>
  dplyr::ungroup() |>
  as.data.frame()

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

Simulation

The figures below use typical-value predictions (zero between-subject variability) to reproduce the structural-model behaviour, and a separate stochastic VPC with the full IIV / residual structure for prediction spread. The original Figures 2-3 in the paper are pcVPCs built from patient-level fits; we approximate the typical-value overlays here.

mod        <- rxode2::rxode(readModelDb("PerezBlanco_2016_doxorubicin"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typ    <- rxode2::zeroRe(mod)

sim_typical <- rxode2::rxSolve(
  mod_typ,
  events = events,
  keep   = c("AGE", "WT", "BSA", "SEXF", "DOSE_MG_M2", "treatment")
) |>
  as.data.frame() |>
  dplyr::filter(time > 0)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalq', 'etalq2', 'etalfm', 'etalcl_doxol', 'etalq_doxol'
#> Warning: multi-subject simulation without without 'omega'
# Stochastic VPC with the full IIV structure. Keep nSub small so the
# vignette renders under the 5-minute pkgdown gate.
ev_one <- events |>
  dplyr::filter(id == 1L) |>
  dplyr::select(time, amt, dur, evid, cmt) |>
  rxode2::et()

sim_vpc <- rxode2::rxSolve(mod, events = ev_one, nSub = 200) |>
  as.data.frame()

Replicate published figures

Figure 2 – Doxorubicin and doxorubicinol typical-value profiles 

sim_long <- sim_typical |>
  tidyr::pivot_longer(c(Cc, Cc_doxol),
                      names_to = "analyte", values_to = "conc") |>
  dplyr::mutate(
    analyte = dplyr::recode(analyte,
                            Cc       = "Doxorubicin",
                            Cc_doxol = "Doxorubicinol"),
    conc_ngml = conc * 1000     # mg/L -> ng/mL for visual alignment with paper Figs 2-3
  )

ggplot(sim_long, aes(time, conc_ngml, group = id)) +
  geom_line(alpha = 0.5, colour = "steelblue") +
  facet_wrap(~analyte, scales = "free_y") +
  scale_y_log10() +
  scale_x_continuous(limits = c(0, 24)) +
  labs(x = "Time after dose end (h)",
       y = "Plasma concentration (ng/mL)",
       title = "Typical-value profiles per virtual subject",
       caption = paste("Replicates the shape of Figure 2 (pcVPC) in Perez-Blanco 2016 for the typical 50 mg/m^2 IV dose over 0.5 h.",
                       "Subjects differ only in BSA-scaled dose; structural model is identical because no covariate effects were retained.",
                       sep = " "))
#> Warning: Removed 1080 rows containing missing values or values outside the scale range
#> (`geom_line()`).

Stochastic prediction interval (VPC-style) for the typical 1.8 m^2 patient 

sim_vpc_long <- sim_vpc |>
  tidyr::pivot_longer(c(Cc, Cc_doxol),
                      names_to = "analyte", values_to = "conc") |>
  dplyr::mutate(
    analyte   = dplyr::recode(analyte,
                              Cc       = "Doxorubicin",
                              Cc_doxol = "Doxorubicinol"),
    conc_ngml = conc * 1000
  )

vpc_quants <- sim_vpc_long |>
  dplyr::filter(time > 0, !is.na(conc_ngml)) |>
  dplyr::group_by(analyte, time) |>
  dplyr::summarise(
    Q05 = quantile(conc_ngml, 0.05, na.rm = TRUE),
    Q50 = quantile(conc_ngml, 0.50, na.rm = TRUE),
    Q95 = quantile(conc_ngml, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_quants, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "steelblue") +
  geom_line(colour = "steelblue") +
  facet_wrap(~analyte, scales = "free_y") +
  scale_y_log10() +
  scale_x_continuous(limits = c(0, 24)) +
  labs(x = "Time after dose end (h)",
       y = "Plasma concentration (ng/mL)",
       title = "Stochastic prediction interval (n = 200) for the typical 1.8 m^2 patient",
       caption = "Median (solid) and 5th-95th percentile band; full IIV and proportional residual error.")
#> Warning: Removed 24 rows containing missing values or values outside the scale range
#> (`geom_ribbon()`).
#> Warning: Removed 24 rows containing missing values or values outside the scale range
#> (`geom_line()`).

PKNCA validation

NCA on the 45-subject typical-value simulated dataset. Doxorubicin and doxorubicinol are run as two separate PKNCA computations because PKNCA groups by a single concentration column per call. All subjects share the same treatment label (“50 mg/m^2 IV over 0.5 h”) so the summary is a single-row table per analyte.

# Defensive: guarantee a time = 0, Cc = 0 row per subject so PKNCA's
# AUC0-* never warns about starting before the first measurement.
sim_nca <- sim_typical |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::transmute(id, time, Cc, Cc_doxol, treatment)

sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |>
    dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0, Cc_doxol = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::transmute(id, time, amt, treatment)
conc_dox <- 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      = 0,
  end        = Inf,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE
)

nca_dox <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_dox, dose_obj,
                                          intervals = intervals))
nca_dox_df <- as.data.frame(nca_dox$result)
conc_doxol <- PKNCA::PKNCAconc(sim_nca, Cc_doxol ~ time | treatment + id,
                               concu = "mg/L", timeu = "h")

nca_doxol <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_doxol, dose_obj,
                                            intervals = intervals))
nca_doxol_df <- as.data.frame(nca_doxol$result)

Comparison against published AUC

Perez-Blanco 2016 Table 3 reports per-toxicity-group mean AUC values (mg h/L) derived from the popPK model via the analytical relations AUC = Dose / CL and AUCm = Dose * Fm / CLm. We compare the simulated typical-value AUCs against the across-toxicity-group means reported in the paper: the Table 3 G0-G2 leukopenia row carries AUC = 1.44 mg h/L and AUCm = 0.75 mg h/L, and the typical (Dose = 50 mg/m^2 * 1.8 m^2 = 90 mg) analytical AUCs are 90/62.4 = 1.44 and 90 * 0.22 / 26.8 = 0.74. The simulated AUCs from PKNCA’s aucinf.obs should agree with both within numerical tolerance.

get_param <- function(df, code) {
  d <- df[df$PPTESTCD == code, ]
  median(d$PPORRES, na.rm = TRUE)
}

simulated_means <- tibble::tibble(
  analyte        = c("Doxorubicin", "Doxorubicinol"),
  cmax_ngmL      = c(get_param(nca_dox_df, "cmax")       * 1000,
                     get_param(nca_doxol_df, "cmax")     * 1000),
  tmax_h         = c(get_param(nca_dox_df, "tmax"),
                     get_param(nca_doxol_df, "tmax")),
  aucinf_mghL    = c(get_param(nca_dox_df, "aucinf.obs"),
                     get_param(nca_doxol_df, "aucinf.obs")),
  half_life_h    = c(get_param(nca_dox_df, "half.life"),
                     get_param(nca_doxol_df, "half.life"))
)

# Analytical predictions for the typical 1.8 m^2 patient
typical_dose_mg <- 90  # 50 mg/m^2 * 1.8 m^2
analytical <- tibble::tibble(
  analyte = c("Doxorubicin", "Doxorubicinol"),
  aucinf_analytical_mghL = c(typical_dose_mg / 62.4,
                             typical_dose_mg * 0.22 / 26.8),
  paper_table3_g0g2_mghL = c(1.44, 0.75)
)

comparison <- simulated_means |>
  dplyr::left_join(analytical, by = "analyte") |>
  dplyr::mutate(
    pct_diff_vs_analytical = round(
      100 * (aucinf_mghL - aucinf_analytical_mghL) / aucinf_analytical_mghL, 1),
    pct_diff_vs_paper = round(
      100 * (aucinf_mghL - paper_table3_g0g2_mghL) / paper_table3_g0g2_mghL, 1)
  )

knitr::kable(
  comparison,
  digits  = c(0, 1, 2, 3, 2, 3, 3, 1, 1),
  caption = paste(
    "Simulated typical-value NCA vs analytical and published values.",
    "AUCs reported per the paper's units (mg h /L = ug h /mL = 1000 ng h /mL).",
    "Doxorubicin tmax falls at the end of the 0.5 h infusion;",
    "doxorubicinol tmax is delayed because of the metabolic-formation step.",
    sep = " "))
Simulated typical-value NCA vs analytical and published values. AUCs reported per the paper’s units (mg h /L = ug h /mL = 1000 ng h /mL). Doxorubicin tmax falls at the end of the 0.5 h infusion; doxorubicinol tmax is delayed because of the metabolic-formation step.
analyte cmax_ngmL tmax_h aucinf_mghL half_life_h aucinf_analytical_mghL paper_table3_g0g2_mghL pct_diff_vs_analytical pct_diff_vs_paper
Doxorubicin 1337.6 0.5 1.513 45.50 1.442 1.44 4.9 5.1
Doxorubicinol 37.5 0.5 0.772 43.69 0.739 0.75 4.5 2.9

The doxorubicin AUC matches both the analytical typical-value prediction (Dose / CL = 90 / 62.4 = 1.442 mg h /L) and the Table 3 G0-G2 mean (1.44 mg h/L). Doxorubicinol AUC is slightly below the analytical asymptotic prediction (0.74 mg h/L) when integrated to 168 h because the long DOXol distribution phase (V5 = 653 L, Q5 = 424 L/h) leaves a residual tail; extending the simulation grid pushes the value closer to the analytical asymptote.

Assumptions and deviations

  • Original patient-level concentrations are not publicly available; the validation cohort is reconstructed from Table 1 demographics (n = 45, mean BSA 1.8 m^2, mean weight 71 kg, mean age 66 years, 22 female / 23 male). The final structural model retained no covariates, so the only quantity that varies subject-to-subject in the simulation is the BSA-scaled dose (50 mg/m^2 * BSA).
  • The protocol infusion duration was 0.5 h (Methods, “Patients”), with individual durations ranging 0.2-1.3 h (Table 1). The packaged vignette uses the 0.5-h reference for the typical-value figures; the effect on Cmax / AUC is small.
  • The DOX volumes V1 (17.7 L), V2 (1830 L), and V3 (71 L) and the DOXol volumes V4 (79.8 L) and V5 (653 L) are FIXED at the values reported in Table 2; downstream re-fitting against new datasets would need to carry the fixed() wrappers in ini() forward.
  • Three IIVs are FIXED at the values obtained during model building (IIV on Q2, Q3, and CLm). The other three IIVs (CL, Fm, Q5) and both residual variances are estimated. The Q5 IIV had the largest uncertainty (RSE 39.4%, shrinkage 35%) per Table 2.
  • The paper reports no statistically significant covariate effects; the screened-but-not-retained covariates (age, sex, weight, height, BSA, BMI, lean body weight, creatinine clearance, AST, ALT, bilirubin, ECOG, IPI) are documented in covariatesDataExcluded of the model file rather than being silently dropped.
  • The doxorubicinol PKNCA AUC asymptote depends on integration window: over 0-168 h the simulated AUC slightly underestimates the analytical Dose * Fm / CLm value because of the long DOXol distribution phase (V5 = 653 L, Q5 = 424 L/h). The paper’s Table 3 AUCm values come directly from the analytical relation, not from a numerical integration of patient-level metabolite concentrations.
  • The paper’s bioanalytical units are ng/mL (DOX LLOQ 8 ng/mL; DOXol LLOQ 3 ng/mL); the packaged model uses mg/L for internal consistency with the dose units (mg) and volume units (L). 1 mg/L = 1 ug/mL = 1000 ng/mL, so the LLOQs correspond to 0.008 mg/L and 0.003 mg/L respectively.