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Desmopressin (Agerso 2004)

Source: vignettes/articles/Agerso_2004_desmopressin.Rmd
Agerso_2004_desmopressin.Rmd

Model and source

  • Citation: Agerso H, Seiding Larsen L, Riis A, Lovgren U, Karlsson MO, Senderovitz T. Pharmacokinetics and renal excretion of desmopressin after intravenous administration to healthy subjects and renally impaired patients. Br J Clin Pharmacol. 2004;58(4):352-358.
  • Article: https://doi.org/10.1111/j.1365-2125.2004.02175.x
  • Description: three-compartment IV PK model with simultaneous plasma and cumulative urinary-amount outputs; systemic clearance is split into renal and non-renal components, each modulated linearly by creatinine clearance.

Population

Twenty-four subjects (49-68 years) were enrolled, of whom 22 contributed to the final pharmacokinetic analysis (Methods ‘Study design’; two subjects were excluded because their plasma profiles showed an absorption phase incompatible with IV administration). Subjects were stratified by renal function into four groups (Results / Table 2):

  • Group 1: normal renal function (n=6, mean CRCL 103 mL/min/1.73 m^2)
  • Group 2: mild impairment (n=5, mean CRCL 72 mL/min/1.73 m^2)
  • Group 3: moderate impairment (n=5, mean CRCL 37 mL/min/1.73 m^2)
  • Group 4: severe impairment (n=6, mean CRCL 16 mL/min/1.73 m^2)

All received a single 2 ug IV dose (4 ug/mL, 0.5 mL over 1 min). Blood was sampled at 5, 15, 30, 45 min and 1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24 h post-dose; urine was pooled over eight 3-hour intervals to 24 h.

Source trace

Element Value Source
CL_r at CRCL=60 mL/min/1.73 m^2 2.41 L/h Table 1, row CL_r
CL_nr at CRCL=60 mL/min/1.73 m^2 3.91 L/h Table 1, row CL_nr
V1 (central) 13.9 L Table 1, row V1
V2 (peripheral 1) 12.5 L Table 1, row V2
V3 (peripheral 2) 11.7 L Table 1, row V3
Q2 4.43 L/h Table 1, row Q2
Q3 27.5 L/h Table 1, row Q3
CRCL effect on CL_r 1.74% per mL/min Table 1, row ‘CrCL effect on CL_r’
CRCL effect on CL_nr 0.933% per mL/min Table 1, row ‘CrCL effect on CL_nr’
IIV CL_r (CV%) 24% Table 1, IIV column
IIV CL_nr (CV%) 30% Table 1, IIV column (corr 0.86 w/ V1)
IIV V1=V3 (single shared term, CV%) 31% Table 1 footnote ‘shared’
Add error on plasma 0.27 pg/mL Table 1
Prop error on plasma 29% Table 1
Add error on urine amount 4140 pg Table 1
Prop error on urine amount 47% Table 1
Three-compartment structure n/a Results paragraph 2 (‘best described by a three-compartmental model’); Discussion
Renal/non-renal CL split + urine fit n/a Results paragraph 2 (‘possible to fit the plasma concentrations and the amounts excreted in urine simultaneously’)
Linear CRCL effect form n/a Results paragraph 2 + Table 1 footnote

The per-parameter origin is also recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Agerso_2004_desmopressin.R.

Virtual cohort 

set.seed(20040401)

# Build four CRCL groups matching Table 2 means and SDs. Per-subject CRCL is
# drawn from a truncated normal and bounded to the paper's observed CRCL
# range (10-144 mL/min/1.73 m^2) so the linear CRCL effect on CL stays in
# the validated region.
make_cohort <- function(n, mean_crcl, sd_crcl, group_label, id_offset) {
  tibble(
    id    = id_offset + seq_len(n),
    group = group_label,
    CRCL  = pmin(pmax(rnorm(n, mean = mean_crcl, sd = sd_crcl), 10), 144)
  )
}

cohort <- bind_rows(
  make_cohort(50, 103, 21,  "Group 1 (normal)",          id_offset =   0L),
  make_cohort(50,  72,  6.8,"Group 2 (mild)",            id_offset =  50L),
  make_cohort(50,  37,  9.9,"Group 3 (moderate)",        id_offset = 100L),
  make_cohort(50,  16,  6.6,"Group 4 (severe)",          id_offset = 150L)
)

dose_ng <- 2 * 1000  # 2 ug single IV bolus expressed in ng

obs_times <- c(5, 15, 30, 45) / 60          # min -> h
obs_times <- c(obs_times, c(1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24))

dose_rows <- cohort %>%
  transmute(id, time = 0, amt = dose_ng, evid = 1L, cmt = "central",
            group, CRCL)

obs_rows_cc <- tidyr::expand_grid(cohort, time = obs_times) %>%
  transmute(id, time, amt = NA_real_, evid = 0L, cmt = "Cc",
            group, CRCL)

obs_rows_urine <- tidyr::expand_grid(cohort, time = c(3, 6, 9, 12, 15, 18, 21, 24)) %>%
  transmute(id, time, amt = NA_real_, evid = 0L, cmt = "urineAmt",
            group, CRCL)

events <- bind_rows(dose_rows, obs_rows_cc, obs_rows_urine) %>%
  arrange(id, time, desc(evid))

Simulation 

mod <- readModelDb("Agerso_2004_desmopressin")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("group", "CRCL")
) %>% as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

For deterministic typical-value replication, zero out the random effects:

mod_typical <- mod %>% rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("group", "CRCL")
) %>% as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl_renal', 'etalcl_nonren', 'etalvc_vp2'
#> Warning: multi-subject simulation without without 'omega'

Plasma concentration vs time by group

The paper’s Figure 1 shows goodness-of-fit panels (DV vs IPRED / PRED). Lacking the source observed data, the simulated plasma profiles by CRCL group are shown below – the steeper terminal slope at higher CRCL reflects the positive coupling between CRCL and total clearance.

sim %>%
  filter(time > 0) %>%
  group_by(time, group) %>%
  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(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~ group) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Cc (pg/mL)",
       title = "Plasma desmopressin by renal-function group",
       caption = "Compare to Figure 1 (Agerso 2004); 5th-50th-95th simulated percentiles.")

CRCL vs CL_r and CL_nr (Figure 2)

The paper’s Figure 2 plots renal and non-renal clearance against creatinine clearance, with the model-predicted solid line. The model encodes the linear multiplicative effect on each component.

crcl_grid <- tibble(CRCL = seq(10, 145, by = 1)) %>%
  mutate(
    `CL_r (L/h)`  = 2.41 * (1 + 0.0174  * (CRCL - 60)),
    `CL_nr (L/h)` = 3.91 * (1 + 0.00933 * (CRCL - 60))
  ) %>%
  pivot_longer(cols = c(`CL_r (L/h)`, `CL_nr (L/h)`),
               names_to = "component", values_to = "value")

ggplot(crcl_grid, aes(CRCL, value)) +
  geom_line() +
  facet_wrap(~ component, scales = "free_y") +
  labs(x = "CRCL (mL/min/1.73 m^2)", y = "Clearance (L/h)",
       title = "Renal and non-renal clearance vs CRCL",
       caption = "Replicates Figure 2 of Agerso 2004 (typical-value lines).")

Renal excretion fraction (fe) vs CRCL

The paper reports that the fraction of dose excreted in urine (fe) drops from ~47% in healthy subjects to ~21% in severely renally impaired patients (Results, Table 2). The simulation reproduces this gradient.

fe_summary <- sim_typical %>%
  group_by(id, group, CRCL) %>%
  summarise(urineAmt_pg = max(urineAmt, na.rm = TRUE), .groups = "drop") %>%
  mutate(fe = urineAmt_pg / (dose_ng * 1000))   # dose_ng * 1000 = dose in pg

fe_summary %>%
  group_by(group) %>%
  summarise(
    fe_mean = mean(fe),
    fe_sd   = sd(fe),
    .groups = "drop"
  ) %>%
  knitr::kable(digits = 3,
               caption = "Simulated fraction excreted in urine (fe) by group; compare Table 2 fe column.")
Simulated fraction excreted in urine (fe) by group; compare Table 2 fe column.
group fe_mean fe_sd
Group 1 (normal) 0.429 0.021
Group 2 (mild) 0.393 0.012
Group 3 (moderate) 0.291 0.044
Group 4 (severe) 0.162 0.052

PKNCA validation 

sim_nca <- sim %>%
  filter(time > 0, !is.na(Cc)) %>%
  distinct(id, time, .keep_all = TRUE) %>%
  select(id, time, Cc, group)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ time | group + id,
  concu = "pg/mL", timeu = "h"
)

dose_df <- events %>%
  filter(evid == 1) %>%
  select(id, time, amt, group)

dose_obj <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | group + id,
  doseu = "ng"
)

intervals <- data.frame(
  start       = 0,
  end         = Inf,
  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_tbl <- as.data.frame(nca_res$result)

nca_summary <- nca_tbl %>%
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) %>%
  group_by(group, PPTESTCD) %>%
  summarise(median = median(PPORRES, na.rm = TRUE),
            .groups = "drop") %>%
  pivot_wider(names_from = PPTESTCD, values_from = median)

knitr::kable(nca_summary, digits = 3,
             caption = "Median simulated NCA parameters by renal-function group.")
Median simulated NCA parameters by renal-function group.
group aucinf.obs cmax half.life tmax
Group 1 (normal) NA 113.072 3.732 0.083
Group 2 (mild) NA 118.891 4.540 0.083
Group 3 (moderate) NA 120.719 6.869 0.083
Group 4 (severe) NA 115.354 9.750 0.083

Comparison against Table 2 (per-group means)

Total CL is computed at the published per-group mean CRCL by summing the model’s typical renal and non-renal components. Terminal half-life and fe are pulled from the PKNCA / cumulative-urine summaries above.

published <- tibble(
  group = c("Group 1 (normal)",   "Group 2 (mild)",
            "Group 3 (moderate)", "Group 4 (severe)"),
  CRCL_pub       = c(103,   72,   37,   16),
  CL_pub_Lh      = c(10,   6.9,  4.9,  2.9),
  t12_pub_h      = c(3.7,  4.8,  7.2, 10.0),
  fe_pub         = c(0.47, 0.41, 0.26, 0.21)
)

published <- published %>%
  mutate(
    CL_sim_Lh = 2.41 * (1 + 0.0174  * (CRCL_pub - 60)) +
                3.91 * (1 + 0.00933 * (CRCL_pub - 60))
  )

t12sum <- nca_summary %>%
  transmute(group, t12_sim_h = half.life)

fe_sum <- fe_summary %>%
  group_by(group) %>%
  summarise(fe_sim = mean(fe), .groups = "drop")

comparison <- published %>%
  left_join(t12sum, by = "group") %>%
  left_join(fe_sum, by = "group") %>%
  mutate(
    CL_ratio  = CL_sim_Lh / CL_pub_Lh,
    t12_ratio = t12_sim_h / t12_pub_h,
    fe_ratio  = fe_sim    / fe_pub
  )

knitr::kable(comparison, digits = 3,
             caption = "Simulated vs published per-group summaries (Agerso 2004 Table 2). CL_sim is the typical-value total CL evaluated at the published per-group mean CRCL.")
Simulated vs published per-group summaries (Agerso 2004 Table 2). CL_sim is the typical-value total CL evaluated at the published per-group mean CRCL.
group CRCL_pub CL_pub_Lh t12_pub_h fe_pub CL_sim_Lh t12_sim_h fe_sim CL_ratio t12_ratio fe_ratio
Group 1 (normal) 103 10.0 3.7 0.47 9.692 3.732 0.429 0.969 1.009 0.912
Group 2 (mild) 72 6.9 4.8 0.41 7.261 4.540 0.393 1.052 0.946 0.958
Group 3 (moderate) 37 4.9 7.2 0.26 4.516 6.869 0.291 0.922 0.954 1.120
Group 4 (severe) 16 2.9 10.0 0.21 2.870 9.750 0.162 0.990 0.975 0.772

Differences > 20% would warrant investigation rather than parameter tuning. The simulation should reproduce the order-of-magnitude gradient across CRCL groups in CL, half-life, and fe (Table 2 of the paper).

Assumptions and deviations

  • Unit convention. The model accepts doses in ng and reports concentrations in pg/mL (numerically equal to ng/L). The 2 ug paper dose becomes 2000 ng in the event table. The urine compartment accumulates in ng (dose units); the urineAmt output multiplies by 1000 to report in pg, matching the paper’s Table 1 additive-error magnitude of 4140 pg. The lint-conventions check flags this unit-magnitude mismatch as informational; the scaling is deliberate and verified above.

  • Linear CRCL effect range. The covariate effect (1 + e_crcl_cl_* * (CRCL - 60)) is the form Agerso 2004 fitted to the observed CRCL range (10-144 mL/min/1.73 m^2). At CRCL < ~2.5 mL/min the renal-clearance multiplier becomes non-positive; downstream simulations should restrict CRCL to >= 5 mL/min/1.73 m^2 (this vignette truncates the sampled CRCL at 10 mL/min, the paper’s lowest observed value).

  • Shared V1/V3 IIV term. Table 1 footnote ‘shared’ indicates the interindividual variability on the central and second peripheral volumes was estimated as a single 31% CV term, positively correlated (r = 0.86) with the IIV on CL_nr. The model encodes this as a paper-specific eta etalvc_vp2 applied to both vc and vp2, declared via the paper_specific_etas metadata field so the convention checker does not flag the absence of separate etalvc / etalvp2 terms. V2 (vp) was not reported with IIV and has no eta.

  • IIV on residual error magnitudes (not implemented). Table 1 reports significant interindividual variability in the residual error magnitudes for both plasma (CV 43%) and urine (CV 65%). nlmixr2 does not directly support eta-on-EPS in its standard syntax; the residual errors here are population-typical values and the simulated VPC band is consequently narrower than the Agerso 2004 fit would yield. This is a documentation-only deviation from the source.

  • Population sex, race, regional distribution. The paper reports only age (49-68 years), BMI (23-32 kg/m^2), and height (152-184 cm); sex breakdown, race / ethnicity, and centre detail (Germany; Bayerische Landesarztekammer approval) are not summarised here. The virtual cohort samples CRCL only; no body-size scaling is applied because Agerso 2004 found no significant weight / BMI / height / age covariates beyond CRCL on either CL component.

  • Two excluded subjects. The published parameter estimates are based on N = 22 (24 enrolled, 2 excluded for an absorption-like phase). The model population metadata uses N = 22 to match Table 1.

  • CRCL definition. The paper computes CRCL from a 24-h urine collection using (Cr_urine x UV / dt) / Cr_serum x 1.73 / BSA, with BSA from the Gehan and George formula. This is a measured, BSA-normalised creatinine clearance in mL/min/1.73 m^2, matching the canonical CRCL definition in inst/references/covariate-columns.md. The per-model covariateData$CRCL notes record the derivation.