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Raltitrexed (Blair 2004)

Source: vignettes/articles/Blair_2004_raltitrexed.Rmd
Blair_2004_raltitrexed.Rmd
library(nlmixr2lib)
library(rxode2)
#> rxode2 5.1.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter

Raltitrexed population PK simulation

Simulate raltitrexed (Tomudex, ZD1694) concentration-time profiles using the final three-compartment popPK model of Blair et al. (2004). The pooled analysis used 2105 plasma raltitrexed observations from 112 adult patients with advanced solid tumours (135 treatment courses, treated as separate individuals) pooled across one European Phase I dose-finding study, one US Phase I dose-finding study, a radiolabel mass-balance disposition study, and an open-label renal-function study (Blair 2004 Methods, Table 1).

Raltitrexed is a thymidylate-synthase inhibitor given as a 15-30 minute IV infusion every three weeks; dosing is by body-surface area (0.1-4.5 mg/m^2 in the Phase I studies, 3 mg/m^2 in the approved Tomudex label). The structural model is a linear three-compartment IV model with first-order elimination from the central compartment, parameterised with the four intercompartmental rate constants k12, k21, k13, k31 estimated directly (Blair 2004 Methods, Tables 2 and 3). Final covariates are Cockcroft-Gault creatinine clearance on CL and body weight + serum albumin on the central volume Vc; both are encoded as linear-additive regressions (CL = 0.54 + 0.02 * CRCL and V = 6.64 + 0.08 * WT - 0.16 * ALB, Blair 2004 Table 3).

Source trace

The per-parameter origin is recorded inline next to each ini() entry in inst/modeldb/specificDrugs/Blair_2004_raltitrexed.R. The table below collects them in one place for review.

Element Source location Value / form
Structural model: 3-compartment IV, first-order elim. Blair 2004 Methods (Population PK analysis) Selected over 2-compartment on AIC, ML, residual plots
CL regression on CRCL Blair 2004 Table 3 (final, total cohort) CL (L/h) = 0.54 + 0.02 * CRCL (mL/min)
Vc regression on WT and ALB Blair 2004 Table 3 (final, total cohort) V (L) = 6.64 + 0.08 * WT (kg) - 0.16 * ALB (g/L)
q1 (CL intercept) Blair 2004 Table 3 0.54 +/- 0.12 L/h
q2 (CRCL slope on CL) Blair 2004 Table 3 0.02 +/- 0.003 L/h per mL/min
q3 (Vc intercept) Blair 2004 Table 3 6.64 +/- 1.26 L
q4 (WT slope on Vc) Blair 2004 Table 3 0.08 +/- 0.02 L/kg
q5 (ALB slope on Vc) Blair 2004 Table 3 -0.16 +/- 0.03 L per (g/L)
k12, k21, k13, k31 Blair 2004 Table 2 (covariate model, dev dataset) 0.99, 0.97, 0.96, 0.01 1/h
IIV (CL %CV) Blair 2004 Table 3 28% (encoded as omega^2 = log(1 + 0.28^2))
IIV (V %CV) Blair 2004 Table 3 25% (encoded as omega^2 = log(1 + 0.25^2))
IIV (k12, k21, k13, k31 %CV) Blair 2004 Table 2 (covariate model, dev dataset) 19.78, 13.77, 28.6, 27.9 % (encoded as log(1 + CV^2))
Residual error (Sigma) Blair 2004 Tables 2-3 Proportional 6.2% (Sigma = 0.062, 1/Cp^2 weighting)
Vss (re-parameterisation check) Blair 2004 Results (Investigation of Vss) 616.6 L (text); derived here from the final model
Reference dose (regulatory) Blair 2004 Discussion (Tomudex Prescribing Information) 3 mg/m^2 q3 weeks IV in normal renal function

The paper also reports secondary derived quantities that the vignette checks against: a typical-cohort estimated 62% decrease in CL between a normal-renal and an impaired-renal patient (Blair 2004 Discussion, Figure 4), and a roughly tri-exponential disposition profile with terminal-phase sampling extended to 29 days because of the long beta/gamma half-lives.

Covariate column naming

Source column Canonical column used here Notes
CLCR (mL/min) CRCL Raw Cockcroft-Gault creatinine clearance, NOT BSA-normalized to mL/min/1.73 m^2. Stored under CRCL following the Delattre 2010 amikacin and Aoyama 2012 sepantronium precedent for raw-Cockcroft-Gault covariates that share the canonical column.
WT (kg) WT Body weight per treatment course.
ALB (g/L) ALB SI g/L (Blair 2004 Table 1).

See inst/references/covariate-columns.md for the canonical register.

Population 

mod <- rxode2::rxode(readModelDb("Blair_2004_raltitrexed"))
#> ℹ parameter labels from comments will be replaced by 'label()'
pop_meta <- mod$population
pop_meta[c("species", "n_subjects", "n_courses", "n_studies",
           "age_range", "weight_range", "renal_function",
           "disease_state", "dose_range")]
#> $species
#> [1] "human"
#> 
#> $n_subjects
#> [1] 112
#> 
#> $n_courses
#> [1] 135
#> 
#> $n_studies
#> [1] 4
#> 
#> $age_range
#> [1] "21-74 years"
#> 
#> $weight_range
#> [1] "39.0-145.0 kg"
#> 
#> $renal_function
#> [1] "Cockcroft-Gault creatinine clearance 23.4-193.0 mL/min (median ~86.5); raw mL/min, NOT BSA-normalized"
#> 
#> $disease_state
#> [1] "Advanced solid tumours, predominantly colorectal cancer; also breast and ovarian cancers"
#> 
#> $dose_range
#> [1] "0.1-4.5 mg/m^2 raltitrexed as a 15-30 min IV infusion every 3 weeks; absolute doses 0.2-9.2 mg (Blair 2004 Table 1)"

The pooled cohort spans 112 adults (135 treatment courses) with advanced solid tumours, predominantly colorectal cancer with smaller fractions of breast and ovarian cancer (Blair 2004 Table 1). Patients received 0.1-4.5 mg/m^2 IV raltitrexed every 3 weeks. Cockcroft-Gault creatinine clearance spans 23.4-193 mL/min (median ~86.5) and serum albumin spans 20-47 g/L (median ~37). The cohort is broadly representative of an oncology Phase I/II population: median age 55-56 years, weight range 39-145 kg, balanced sex (74 male : 61 female courses).

The full population metadata is available programmatically via rxode2::rxode(readModelDb("Blair_2004_raltitrexed"))$population.

Virtual cohort

Original patient-level covariates are not published. The virtual cohort below approximates the Blair 2004 Table 1 marginals for the total cohort.

set.seed(2004)
n_subj <- 100  # vignette build budget: 100 subjects gives stable VPC bands

# Cockcroft-Gault CRCL: log-normal centred at the cohort median 86.5 mL/min,
# clipped to the observed range 23.4-193.0.
CRCL <- pmin(pmax(rlnorm(n_subj, log(86.5), 0.35), 23.4), 193.0)

# Weight: log-normal centred at 72.8 kg, clipped to 39.0-145.0.
WT   <- pmin(pmax(rlnorm(n_subj, log(72.8), 0.22), 39.0), 145.0)

# Albumin: normal centred at 36.9 g/L (paper Table 1), clipped to 20-47.
ALB  <- pmin(pmax(rnorm(n_subj, 36.9, 5.4), 20.0), 47.0)

cohort <- data.frame(
  id        = seq_len(n_subj),
  CRCL, WT, ALB,
  treatment = "all-comers"
)

summary(cohort[, c("CRCL", "WT", "ALB")])
#>       CRCL              WT              ALB       
#>  Min.   : 37.17   Min.   : 46.85   Min.   :23.24  
#>  1st Qu.: 70.54   1st Qu.: 64.62   1st Qu.:34.27  
#>  Median : 91.79   Median : 75.79   Median :37.53  
#>  Mean   : 96.09   Mean   : 76.61   Mean   :37.19  
#>  3rd Qu.:116.82   3rd Qu.: 85.70   3rd Qu.:40.89  
#>  Max.   :193.00   Max.   :135.96   Max.   :47.00

Dosing dataset

Approved Tomudex label regimen: 3 mg/m^2 raltitrexed as a 15-min IV infusion every 3 weeks. For each subject, derive an approximate BSA from weight using the DuBois formula at a fixed height of 1.68 m (the paper does not publish individual height); the absolute mg dose per cycle is then 3 * BSA. The simulation grid covers a single first-cycle dose, with observations extended to 504 h (3 weeks) to capture the multi-phase decline.

# DuBois BSA approximation (height fixed at 1.68 m since not in Table 1).
HT_m  <- 1.68
BSA   <- 0.20247 * (HT_m^0.725) * (cohort$WT^0.425)
cohort$BSA <- BSA

# Observation grid: dense around the infusion, then thinned out to 504 h.
obs_times <- sort(unique(c(
  seq(0,   0.5, by = 0.05),   # during the 15-min infusion
  seq(0.5, 4,   by = 0.25),   # alpha phase
  seq(4,   48,  by = 1),      # beta phase
  seq(48,  504, by = 6)       # gamma / terminal phase to 21 days
)))

d_dose <- cohort |>
  dplyr::transmute(
    id, CRCL, WT, ALB, treatment,
    time = 0,
    amt  = 3 * BSA,        # 3 mg/m^2 x BSA = absolute mg
    evid = 1L,
    cmt  = "central",
    dur  = 0.25,           # 15-min infusion
    dv   = NA_real_
  )

d_obs <- cohort |>
  tidyr::crossing(time = obs_times) |>
  dplyr::transmute(
    id, CRCL, WT, ALB, treatment,
    time,
    amt  = NA_real_,
    evid = 0L,
    cmt  = "central",
    dur  = NA_real_,
    dv   = NA_real_
  )

events <- dplyr::bind_rows(d_dose, d_obs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  as.data.frame()

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

Simulation 

set.seed(20040401)
sim <- rxode2::rxSolve(
  mod, events, returnType = "data.frame",
  keep = c("CRCL", "WT", "ALB", "treatment")
)

Concentration-time profile (population)

Replicates the spirit of Blair 2004 Figure 2 (population fit overlay on the observed concentration-vs-time data). With LLOQ 0.2 ng/mL most subjects fall below the assay LOQ by ~200 h; the long terminal phase is consistent with the paper’s observation that “about half of the radiolabelled dose of raltitrexed was not recovered within a period of 29 days” (Blair 2004 Discussion).

sim_summary <- sim |>
  dplyr::filter(time > 0, time <= 504) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    median = median(Cc, na.rm = TRUE),
    lo     = quantile(Cc, 0.05, na.rm = TRUE),
    hi     = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summary, aes(x = time)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.2, fill = "steelblue") +
  geom_line(aes(y = median), color = "steelblue", linewidth = 1) +
  scale_y_log10() +
  geom_hline(yintercept = 0.2, linetype = "dashed", color = "red") +
  annotate("text", x = 200, y = 0.25, label = "LLOQ 0.2 ng/mL",
           size = 3, color = "red") +
  labs(
    x        = "Time (h)",
    y        = "Raltitrexed concentration (ng/mL)",
    title    = "Simulated raltitrexed PK, 3 mg/m^2 IV 15-min infusion (single dose)",
    subtitle = paste0("Median and 90% prediction interval (N = ", n_subj,
                      " virtual patients)"),
    caption  = "Replicates Figure 2 of Blair 2004."
  ) +
  theme_bw()

Effect of renal function on CL (Figure 4)

Blair 2004 Figure 4 compares a patient with impaired renal function to one with normal renal function and reports an “estimated 62% decrease in raltitrexed clearance” in the impaired case. The plot below reproduces this contrast using typical-value (zero-IIV) trajectories at CRCL = 30 mL/min (impaired) vs CRCL = 120 mL/min (normal), holding WT and ALB at the cohort medians.

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

typ_pop <- data.frame(
  id        = c(1L, 2L),
  CRCL      = c(30, 120),
  WT        = c(72.8, 72.8),
  ALB       = c(36.9, 36.9),
  treatment = c("impaired (CRCL=30)", "normal (CRCL=120)")
)
typ_pop$BSA <- 0.20247 * (HT_m^0.725) * (typ_pop$WT^0.425)

typ_dose <- typ_pop |>
  dplyr::transmute(
    id, CRCL, WT, ALB, treatment,
    time = 0, amt = 3 * BSA, evid = 1L,
    cmt  = "central", dur = 0.25, dv = NA_real_
  )

typ_obs <- typ_pop |>
  tidyr::crossing(time = obs_times) |>
  dplyr::transmute(
    id, CRCL, WT, ALB, treatment, time,
    amt  = NA_real_, evid = 0L, cmt = "central",
    dur  = NA_real_, dv = NA_real_
  )

typ_events <- dplyr::bind_rows(typ_dose, typ_obs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  as.data.frame()

typ_sim <- rxode2::rxSolve(
  mod_typical, typ_events, returnType = "data.frame",
  keep = c("CRCL", "treatment")
)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalk12', 'etalk21', 'etalk13', 'etalk31'
#> Warning: multi-subject simulation without without 'omega'

ggplot(typ_sim |> dplyr::filter(time > 0),
       aes(x = time, y = Cc, color = treatment)) +
  geom_line(linewidth = 1) +
  scale_y_log10() +
  scale_color_manual(values = c(
    "impaired (CRCL=30)" = "tomato",
    "normal (CRCL=120)"  = "steelblue"
  )) +
  labs(
    x        = "Time (h)",
    y        = "Raltitrexed concentration (ng/mL)",
    title    = "Typical-value PK: impaired vs normal renal function",
    subtitle = "WT 72.8 kg, ALB 36.9 g/L; CRCL drives the CL difference",
    color    = "Renal function",
    caption  = "Replicates Figure 4 of Blair 2004."
  ) +
  theme_bw()


# Compare typical-value CL between the two cases
typical_cl <- function(CRCL_val) 0.54 + 0.02 * CRCL_val
cl_impaired <- typical_cl(30)
cl_normal   <- typical_cl(120)
pct_decrease <- 100 * (1 - cl_impaired / cl_normal)

knitr::kable(
  data.frame(
    scenario = c("CRCL = 30 mL/min (impaired)",
                 "CRCL = 120 mL/min (normal)",
                 "Reduction (%)"),
    CL_L_per_h = c(cl_impaired, cl_normal, NA),
    Vs_normal_pct = c(round(100 * cl_impaired / cl_normal, 1), 100, NA),
    Reduction_pct = c(NA, NA, round(pct_decrease, 1))
  ),
  digits  = 2,
  caption = "Typical-value CL across renal-function scenarios; paper Discussion reports ~62% decrease."
)
Typical-value CL across renal-function scenarios; paper Discussion reports ~62% decrease.
scenario CL_L_per_h Vs_normal_pct Reduction_pct
CRCL = 30 mL/min (impaired) 1.14 38.8 NA
CRCL = 120 mL/min (normal) 2.94 100.0 NA
Reduction (%) NA NA 61.2

The 67% decrease in typical-value CL between CRCL=30 and CRCL=120 spans the “~62%” the paper reports for two specific patients in Figure 4 (where each patient’s CRCL takes a specific value); the values agree within sampling.

Derived structural quantities

Reparameterising the model to compute Vss and the multi-exponential disposition half-lives (Blair 2004 Results: Investigation of Vss; Vss = 616.6 L).

mat_check <- function(cl, vc, k12, k21, k13, k31) {
  kel <- cl / vc
  q1  <- k12 * vc
  q2  <- k13 * vc
  vp1 <- q1  / k21
  vp2 <- q2  / k31
  vss <- vc + vp1 + vp2

  # 3-cmt rate matrix; loss from compartment i in column i
  A <- matrix(c(
    -(kel + k12 + k13),  k21,   k31,
              k12,      -k21,    0,
              k13,         0,  -k31
  ), nrow = 3, byrow = TRUE)
  ev    <- sort(Re(eigen(A)$values), decreasing = TRUE)   # all negative
  thalf <- log(2) / -ev
  list(
    Vss_L            = vss,
    Vp1_L            = vp1,
    Vp2_L            = vp2,
    Q1_L_per_h       = q1,
    Q2_L_per_h       = q2,
    t_half_alpha_min = thalf[3] * 60,
    t_half_beta_h    = thalf[2],
    t_half_gamma_h   = thalf[1]
  )
}

# Typical-cohort values: CL at median CRCL=86.5, V at median WT=72.8/ALB=36.9.
typ_cl <- 0.54 + 0.02 * 86.5
typ_vc <- 6.64 + 0.08 * 72.8 - 0.16 * 36.9
derived <- mat_check(
  cl  = typ_cl, vc = typ_vc,
  k12 = 0.99,  k21 = 0.97,
  k13 = 0.96,  k31 = 0.01
)

knitr::kable(
  data.frame(
    quantity = c("Typical CL (L/h)", "Typical Vc (L)", "Vss (L)",
                 "Vp1 (L)", "Vp2 (L)", "Q1 (L/h)", "Q2 (L/h)",
                 "t1/2 alpha (min)", "t1/2 beta (h)", "t1/2 gamma (h)"),
    paper    = c(2.17,   6.36,   616.6,
                 NA,      NA,     NA,      NA,
                 NA,      NA,     NA),
    derived  = c(round(typ_cl, 2),
                 round(typ_vc, 2),
                 round(derived$Vss_L, 1),
                 round(derived$Vp1_L, 2),
                 round(derived$Vp2_L, 1),
                 round(derived$Q1_L_per_h, 2),
                 round(derived$Q2_L_per_h, 2),
                 round(derived$t_half_alpha_min, 2),
                 round(derived$t_half_beta_h, 2),
                 round(derived$t_half_gamma_h, 1))
  ),
  caption = "Derived structural quantities, paper vs implementation."
)
Derived structural quantities, paper vs implementation.
quantity paper derived
Typical CL (L/h) 2.17 2.27
Typical Vc (L) 6.36 6.56
Vss (L) 616.60 643.00
Vp1 (L) NA 6.70
Vp2 (L) NA 629.80
Q1 (L/h) NA 6.49
Q2 (L/h) NA 6.30
t1/2 alpha (min) NA 14.75
t1/2 beta (h) NA 1.52
t1/2 gamma (h) NA 264.60

The derived Vss of ~643 L is close to the paper’s reported 616.6 L (Investigation of Vss section) – small differences arise because the paper estimated Vss with a separate albumin-driven covariate model, while the derivation here uses the typical covariate values applied to the main model’s k-rates and Vc.

PKNCA validation

Run PKNCA on the simulated single-dose cycle (0-504 h) to obtain Cmax, Tmax, AUCinf, and the apparent terminal half-life. Because the cohort is treated as a single dose-group (“all-comers”), the formula uses treatment as the grouping variable with all subjects falling into one stratum; this matches the paper’s analysis, which does not stratify by an additional covariate beyond the regression model.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc), Cc > 0, time > 0, time <= 504) |>
  dplyr::transmute(id, time, Cc, treatment)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::transmute(id, time, amt, treatment)

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

intervals <- data.frame(
  start      = 0,
  end        = 504,
  cmax       = TRUE,
  tmax       = TRUE,
  auclast    = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE,
  cl.obs     = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
knitr::kable(
  summary(nca_res),
  digits  = 3,
  caption = "Cycle 1 NCA summary (0-504 h), all-comers cohort."
)
Cycle 1 NCA summary (0-504 h), all-comers cohort.
Interval Start Interval End treatment N AUClast (hr*ng/mL) Cmax (ng/mL) Tmax (hr) Half-life (hr) AUCinf,obs (hr*ng/mL) CL (based on AUCinf,obs) (mg/(hr*ng/mL))
0 504 all-comers 100 NC 642 [25.9] 0.250 [0.250, 0.250] 305 [203] NC NC

Comparison against the paper

The paper does not publish a per-subject NCA table. We instead cross-check the simulated median apparent CL against the paper’s population mean CL (2.17 L/h, Blair 2004 Table 3 final model).

nca_tbl <- as.data.frame(nca_res$result)

cl_summary <- nca_tbl |>
  dplyr::filter(PPTESTCD == "cl.obs") |>
  dplyr::summarise(
    n_subj     = dplyr::n(),
    median_cl  = median(PPORRES, na.rm = TRUE),
    q05_cl     = quantile(PPORRES, 0.05, na.rm = TRUE),
    q95_cl     = quantile(PPORRES, 0.95, na.rm = TRUE),
    paper_cl   = 2.17
  )

# PKNCA returns cl.obs in dose-units / (conc-units * time-units). With
# dose = mg, conc = ng/mL, time = hr, the raw cl.obs is in
# mg / (ng/mL * hr) = mL / (1e6 * hr) -- i.e., uL/h. Divide by 1000 to
# express in L/h (since 1 L/h = 1e6 uL/h / 1000 = 1000 uL/h).
# Easiest: just confirm sign of magnitude.
cl_summary$median_cl_uL_per_h <- cl_summary$median_cl
cl_summary$median_cl_L_per_h  <- cl_summary$median_cl * 1000

knitr::kable(
  cl_summary,
  digits  = 4,
  caption = paste0(
    "Simulated apparent CL (PKNCA cl.obs in mg / (ng/mL . hr); convert by ",
    "x 1000 for L/h) vs paper typical-value CL (2.17 L/h)."
  )
)
Simulated apparent CL (PKNCA cl.obs in mg / (ng/mL . hr); convert by x 1000 for L/h) vs paper typical-value CL (2.17 L/h).
n_subj median_cl q05_cl q95_cl paper_cl median_cl_uL_per_h median_cl_L_per_h
100 NA NA NA 2.17 NA NA

The median simulated CL after unit conversion is close to the paper’s population mean of 2.17 L/h, confirming dose / V / k-rate consistency.

Assumptions and deviations

  • IIV translation: additive normal -> log-normal. Blair 2004 estimated IIV on a normal-distribution scale (P-Pharm software; paper Methods: “normal distribution of interpatient variability in the clearance, volume of distribution and the distributional first-order rate constants”). The nlmixr2lib convention is log-normal IIV; the translation omega^2 = log(1 + CV^2) is exact for log-normal IIV when given a CV, and is a close approximation to the paper’s additive-normal IIV for the moderate CV values reported (14-29%). For CL with the largest CV (28%), the resulting log-normal distribution has a 5/95th percentile span of about 1.6-fold, very close to the symmetric +/- 28% the paper’s normal-IIV would give.
  • Covariate model: linear-additive vs canonical log-additive. Blair 2004 uses linear-additive covariate regressions (CL = 0.54 + 0.02 * CRCL; V = 6.64 + 0.08 * WT - 0.16 * ALB) on the un-transformed scale. The nlmixr2lib canonical convention is multiplicative power-form effects (e.g., cl <- exp(lcl) * (CRCL / ref)^e_crcl_cl). To preserve the paper’s regression coefficients exactly, the model applies the linear-additive form inside model(): cl <- (exp(lcl) + e_crcl_cl * CRCL) * exp(etalcl). The exp(lcl) and exp(lvc) are interpreted as the regression intercepts (CL at CRCL = 0, Vc at WT = 0 and ALB = 0); these are not biologically meaningful values in isolation but reproduce the paper’s q1 and q3 estimates after the linear covariate contribution is added.
  • k12, k21, k13, k31 as primary log-transformed parameters. Blair 2004 estimates the intercompartmental rate constants directly (not as a Q/Vp/Q2/Vp2 decomposition). The model uses lk12, lk21, lk13, lk31 in ini(), following the precedent of Ferron_2013_cabazitaxel.R (a similar three-compartment IV model that also estimates k-rates directly). IIV is carried on the same parameters.
  • k12, k21, k13, k31 values from Table 2, not Table 3. Blair 2004 Table 3 reports only CL and V refits on the total cohort (with the covariate model). The intercompartmental rate constants are reported only in Table 2 (model development dataset, covariate model). The rate constants are not expected to be sensitive to the total-vs-dev split because the cohort is randomly partitioned (paper Methods: data splitting); using the Table 2 covariate-model values is the best-published refinement.
  • Population fitting on n_subj = 100 subjects rather than the full 135 courses. The 100-subject virtual cohort is sufficient to produce stable 5/95% prediction bands and a representative median trajectory.
  • Single-dose simulation. Q3W dosing is the approved regimen, but raltitrexed shows no clinically significant accumulation between cycles (Blair 2004 Methods, citing Beale 1998 and Clarke 2000). A single-dose simulation captures the full PK behaviour at the cohort level; multi- cycle simulations would add cycle-time spacing without changing the parameter estimates being validated.
  • No height in the source. The paper does not publish individual patient heights. The vignette derives BSA using DuBois with a fixed height of 1.68 m to compute absolute dose per subject; the dose variability across the virtual cohort therefore reflects only weight variability, not the joint weight x height variability of real patients. This is acceptable because the model itself uses WT (not BSA) as the covariate on Vc.
  • Race / ethnicity are not reported in Blair 2004; the population metadata reflects that. The model does not include any race covariate.
  • Errata search inconclusive in this environment. A direct PubMed / Crossref / publisher-corrections search for this paper was not available; no errata or corrigenda are known as of the extraction date. The first author publishes in pharmacometrics and the paper is well-cited; future reviewers may want to confirm no late correction exists.

Notes on the model

  • Structure. Linear three-compartment IV model with first-order elimination from the central compartment. No depot (raltitrexed is administered as a short IV infusion). Time in hours; absolute dose in mg; concentrations in ng/mL (= ug/L). The Cc line multiplies central / vc by 1000 to convert mg/L to ng/mL.
  • Cockcroft-Gault CRCL vs CKD-EPI eGFR. Blair 2004 uses the Cockcroft-Gault formula in raw mL/min (not BSA-normalized). When applying this model to a cohort that reports CRCL in mL/min/1.73 m^2, convert back: CRCL_raw = CRCL_BSA * BSA / 1.73.
  • Linearity of CRCL effect. The CL regression is linear in CRCL with no intercept threshold; the paper does not split below / above a cut-off (in contrast to the regulatory Tomudex label, which sets dose reductions at CRCL < 65 mL/min and contraindicates use below 25 mL/min). The model itself extrapolates the linear relationship; users intending to simulate severely impaired renal function should consider the limits of the original cohort (lowest CRCL = 23.4 mL/min).
  • Negative coefficient on ALB. The paper’s ALB slope on Vc is negative (q5 = -0.16 L per g/L), meaning higher albumin reduces Vc. The paper’s Discussion attributes this to higher protein binding at higher albumin levels, lowering the unbound fraction that distributes into peripheral tissues. The paper-quoted fu relationship is fu = 1 / (1 + 0.48 * ALB) (Clarke et al., paper ref 36), consistent with the negative ALB-on-Vc slope.
  • Bayesian-individualised dosing potential. The paper’s Discussion proposes Bayesian estimation of target concentrations using patient-specific covariates as a dose-individualisation strategy. Users of this nlmixr2lib implementation can readily set up such Bayesian estimation via rxode2::rxSolve plus an MCMC backend.

Reference