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Emfilermin (Goggin 2004)

Source: vignettes/articles/Goggin_2004_emfilermin.Rmd
Goggin_2004_emfilermin.Rmd

Model and source

  • Citation: Goggin T, Nguyen QTX, Munafo A. Population pharmacokinetic modelling of Emfilermin (recombinant human leukaemia inhibitory factor, r-hLIF) in healthy postmenopausal women and in infertile patients undergoing in vitro fertilization and embryo transfer. Br J Clin Pharmacol. 2004;57(4):412-418. doi:10.1111/j.1365-2125.2003.02064.x
  • Description: One-compartment population PK model for subcutaneous emfilermin (recombinant human leukaemia inhibitory factor, r-hLIF) in healthy postmenopausal women and in infertile women undergoing in vitro fertilization and embryo transfer (IVF-ET) (Goggin 2004). Absorption is zero-order (D1 = 0.84 h, invariant, no IIV) directly into the central compartment, followed by first-order elimination. Apparent clearance CL/F is decreased by 35% in IVF-ET patients (typical 37 L/h) relative to healthy postmenopausal women (typical 57 L/h). Apparent volume V/F is linear in body weight on the natural scale: V/F = 235 L at the median 62 kg, increasing or decreasing by 6.7 L/kg (~29% per 10 kg) – an absolute-linear covariate form, not log-multiplicative. Inter-individual variability is log-normal on CL/F (17% CV) and V/F (28% CV); inter-occasion variability is log-normal on V/F (23% CV) across three protocol-defined occasions (first dosing day = 1, intermediate dosing days = 2, last dosing day = 3). Residual error is proportional (20% CV). Studied weight range was 48-83 kg; the linear V/F-WT term is extrapolation-unsafe below ~27 kg where the typical V/F would become negative.
  • Article: https://doi.org/10.1111/j.1365-2125.2003.02064.x

Population

The model was developed from 64 women across three trials of subcutaneous emfilermin (recombinant human leukaemia inhibitory factor, r-hLIF):

  • Study 1 (n = 14): single-dose phase I in healthy postmenopausal women on Cyclo-progynova / Progynova / Utrogestan hormone replacement therapy; subjects received a single 100 ug or 250 ug SC dose on day 22 of the second HRT cycle.
  • Study 2 (n = 11): repeated-dose phase I in healthy postmenopausal women on the same HRT backbone; 150 ug SC BID for 7 days.
  • Study 3 (n = 39): proof-of-concept in premenopausal women with recurrent implantation failure undergoing in vitro fertilization or intracytoplasmic sperm injection and embryo transfer (IVF-ET) after nafarelin pituitary down-regulation, recombinant FSH ovarian stimulation, and recombinant hCG triggering; 150 ug SC BID for 7 days starting on the day of embryo transfer.

After excluding subject 113 (study 1, suspected dosing error; only three measurable concentrations) and subject 116 (study 2, haemolyzed samples), the analysis dataset comprised 342 r-hLIF concentrations from 64 subjects (226 from postmenopausal women, 116 from IVF-ET patients). Below-LoQ samples (LoQ = 50 pg/mL) were treated as missing. Subject characteristics by study are in Goggin 2004 Table 1 (median weights 63 / 63 / 61 kg; median ages 58 / 58 / 34 years; weight range 48-83 kg across the pooled cohort).

The same information is available programmatically via readModelDb("Goggin_2004_emfilermin")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Goggin_2004_emfilermin.R. The table below collects them in one place for review.

Equation / parameter Value Source location
Structural model: one-compartment with zero-order SC input n/a Results paragraph 1 (“a one-compartment disposition model with a zero order input”); Methods Step 1; Discussion paragraph 1
CL/F (PM-typical, healthy postmenopausal reference) 57.0 L/h Table 4 row “CL/F”
V/F (typical at WT = 62 kg) 235 L Table 4 row “V/F”
D1 (zero-order absorption duration) 0.84 h Table 4 row “D1”
Type-of-population effect on CL/F (theta_TYPE, IVF-ET multiplier) 0.649 Table 4 row “Type on CL/F”; Table 5
Body-weight linear effect on V/F (L per kg above 62 kg ref) 6.7 L/kg Table 4 row “Weight on V/F”; Table 5
Reference body weight 62 kg Methods Step 2 (“body weight = 62 kg” reference for the linear covariate model)
IIV on CL/F (% CV) 17% Table 4 row “CL/F” ISV column
IIV on V/F (% CV) 28% Table 4 row “V/F” ISV column
IOV on V/F (% CV, 3 occasions) 23% Table 4 row “V/F” IOV column; Methods Step 1 three-occasion definition
Residual error (proportional, % CV) 20% Table 4 row “RV”

The full final-model parameter table is Table 4; the covariate effect descriptions are repeated in Table 5. The covariate selection narrative (univariate ranking, backward addition, forward deletion) is in Methods Steps 2-3 and Results paragraphs 3-5. The terminal half-life (a secondary derived parameter) is reported in the Results: 2.9 h for PM women and 4.4 h for IVF-ET women; this matches t1/2 = ln(2) x V / CL evaluated at the typical PM and IVF-ET CL/F values respectively.

Virtual cohort

Goggin 2004 enrolled three trial cohorts. Each gets its own event table so the PKNCA stratification can compare per-cohort NCA against the paper’s per-population reports. The dose event uses cmt = "central" with rate = -2 so the model’s dur(central) <- d1 applies the zero-order absorption duration directly.

set.seed(20260604)

n_per_cohort <- 50L

# Helper: build one cohort as a self-contained event table.
# id_offset shifts subject IDs so multiple cohorts can be bind_rows()-ed
# without colliding subject keys (see vignette-template Notes).
make_cohort <- function(n, dose_ug, dose_times, obs_times, wt_median, dis_healthy,
                        occ_at_time, cohort_label, id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  ev <- rxode2::et(
          amt  = dose_ug,
          time = dose_times,
          cmt  = "central",
          rate = -2
        ) |>
        rxode2::et(obs_times) |>
        rxode2::et(id = ids) |>
        as.data.frame() |>
        dplyr::mutate(
          WT          = wt_median,
          DIS_HEALTHY = dis_healthy,
          OCC         = occ_at_time(time),
          cohort      = cohort_label
        )
  ev
}

# OCC mapping per Goggin 2004 Methods Step 1:
#   occasion 1 = first dosing day (study day 1)
#   occasion 2 = all intermediate days (mostly day 4)
#   occasion 3 = last dosing day (day 6 or 7)
# For single-dose studies (study 1) only occasion 1 is meaningful; we keep
# OCC = 1 across the observation window.
occ_single <- function(t) rep(1L, length(t))
occ_bid7   <- function(t) {
  day_idx <- pmin(pmax(floor(t / 24), 0), 6)
  occ <- rep(2L, length(t))
  occ[day_idx == 0L] <- 1L
  occ[day_idx == 6L] <- 3L
  occ
}

# Sparser observation grid keeps the multi-cohort stochastic simulation
# within the pkgdown / CI 5-minute wall-clock budget.
obs_single <- sort(unique(c(0, 0.5, 1, 2, 3, 4, 6, 8, 12, 18, 24)))
bid_times  <- as.numeric(outer(c(0, 12), seq(0, 6), `+`))
obs_bid    <- sort(unique(c(bid_times, bid_times + 1, bid_times + 4, 168)))

events_S1_100 <- make_cohort(n_per_cohort, 100, 0,         obs_single,
                             63, 1L, occ_single, "S1 PM 100 ug single",       0L)
events_S1_250 <- make_cohort(n_per_cohort, 250, 0,         obs_single,
                             63, 1L, occ_single, "S1 PM 250 ug single",       1L * n_per_cohort)
events_S2     <- make_cohort(n_per_cohort, 150, bid_times, obs_bid,
                             63, 1L, occ_bid7,   "S2 PM 150 ug BID x 7d",     2L * n_per_cohort)
events_S3     <- make_cohort(n_per_cohort, 150, bid_times, obs_bid,
                             61, 0L, occ_bid7,   "S3 IVFET 150 ug BID x 7d",  3L * n_per_cohort)

events <- dplyr::bind_rows(events_S1_100, events_S1_250, events_S2, events_S3)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Goggin_2004_emfilermin")
sim <- rxode2::rxSolve(mod, events = events,
                       keep = c("cohort", "WT", "DIS_HEALTHY"))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_vc_1, etaiov_vc_2, etaiov_vc_3
#> as a work-around try putting the mu-referenced expression on a simple line

For deterministic typical-value replication of the paper’s concentration profiles (Figure 2), zero out the random effects. The typical-value simulation uses a single representative subject per cohort on a dense observation grid:

mod_typical <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_vc_1, etaiov_vc_2, etaiov_vc_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_vc_1, etaiov_vc_2, etaiov_vc_3
#> as a work-around try putting the mu-referenced expression on a simple line

typical_S1_100 <- make_cohort(1L, 100, 0,         seq(0, 24,  by = 0.1),
                              63, 1L, occ_single, "S1 PM 100 ug single",       10000L)
typical_S1_250 <- make_cohort(1L, 250, 0,         seq(0, 24,  by = 0.1),
                              63, 1L, occ_single, "S1 PM 250 ug single",       10001L)
typical_S2     <- make_cohort(1L, 150, bid_times, seq(0, 168, by = 0.5),
                              63, 1L, occ_bid7,   "S2 PM 150 ug BID x 7d",     10002L)
typical_S3     <- make_cohort(1L, 150, bid_times, seq(0, 168, by = 0.5),
                              61, 0L, occ_bid7,   "S3 IVFET 150 ug BID x 7d",  10003L)

events_typical <- dplyr::bind_rows(typical_S1_100, typical_S1_250,
                                   typical_S2, typical_S3)

sim_typical <- rxode2::rxSolve(mod_typical, events = events_typical,
                               keep = c("cohort", "WT", "DIS_HEALTHY"))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etaiov_vc_1', 'etaiov_vc_2', 'etaiov_vc_3'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Goggin 2004 Figure 2 shows serum r-hLIF concentration profiles for three representative subjects from each study. We plot the typical-value (no IIV / no residual error) profile per cohort as the closest deterministic analogue.

sim_typical |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  ggplot(aes(time, Cc, colour = cohort)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  facet_wrap(~ cohort, scales = "free_x") +
  labs(
    x = "Time (h)",
    y = "Serum r-hLIF (pg/mL)",
    colour = NULL,
    title = "Typical-value r-hLIF concentration profiles",
    caption = "Replicates Goggin 2004 Figure 2 (representative subject profiles)."
  ) +
  theme(legend.position = "none")
Replicates Figure 2 of Goggin 2004: typical-value serum r-hLIF profiles by study cohort.

Replicates Figure 2 of Goggin 2004: typical-value serum r-hLIF profiles by study cohort.

A stochastic VPC-style plot for the two single-dose study 1 cohorts is also useful for confirming that the IIV magnitudes carry over correctly:

sim |>
  dplyr::filter(cohort %in% c("S1 PM 100 ug single", "S1 PM 250 ug single"),
                !is.na(Cc), Cc > 0) |>
  dplyr::group_by(cohort, time) |>
  dplyr::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(~ cohort) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Serum r-hLIF (pg/mL)",
       caption = "5-50-95% bands across the simulated PM women cohort.")
Stochastic 5-50-95% prediction intervals for the single-dose study 1 cohorts (PM women).

Stochastic 5-50-95% prediction intervals for the single-dose study 1 cohorts (PM women).

PKNCA validation

The strongest validation against Goggin 2004 is the terminal half-life: the paper reports t1/2 = 2.9 h for healthy postmenopausal women and 4.4 h for IVF-ET women (Results paragraph 3 / Discussion paragraph 1). We compute single-dose NCA for the study 1 PM cohort and a synthetic single-dose IVF-ET cohort below; the steady-state cohorts (studies 2 / 3) are not used for the half-life comparison because PKNCA cannot estimate lambda.z cleanly on a repeated-dose-only profile.

# Synthetic single-dose IVF-ET cohort (single 250 ug SC) -- not a paper cohort,
# constructed here so the half-life comparison covers both DIS_HEALTHY states.
obs_nca <- sort(unique(c(0, 0.5, 1, 2, 3, 4, 6, 8, 12, 18, 24, 30, 36, 48)))
events_S_IVFET_single <- make_cohort(
  n           = n_per_cohort,
  dose_ug     = 250,
  dose_times  = 0,
  obs_times   = obs_nca,
  wt_median   = 61,
  dis_healthy = 0L,
  occ_at_time = occ_single,
  cohort_label = "Synthetic IVFET 250 ug single",
  id_offset   = 5L * n_per_cohort
)

events_single <- dplyr::bind_rows(
  events_S1_100 |> dplyr::filter(time <= 24),
  events_S1_250 |> dplyr::filter(time <= 24),
  events_S_IVFET_single
)
stopifnot(!anyDuplicated(unique(events_single[, c("id", "time", "evid")])))

sim_single <- rxode2::rxSolve(mod, events = events_single,
                              keep = c("cohort", "WT", "DIS_HEALTHY"))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_vc_1, etaiov_vc_2, etaiov_vc_3
#> as a work-around try putting the mu-referenced expression on a simple line
sim_nca <- sim_single |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::select(id, time, Cc, cohort) |>
  as.data.frame()

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

dose_df <- events_single |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, cohort) |>
  as.data.frame()

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

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))

knitr::kable(summary(nca_res),
             caption = "Simulated NCA parameters by cohort (Goggin 2004 emfilermin).")
Simulated NCA parameters by cohort (Goggin 2004 emfilermin).
Interval Start Interval End cohort N Cmax (pg/mL) Tmax (h) Half-life (h) AUCinf,obs (h*pg/mL)
0 Inf S1 PM 100 ug single 50 360 [23.7] 1.00 [1.00, 1.00] 3.20 [0.962] NC
0 Inf S1 PM 250 ug single 50 894 [35.1] 1.00 [1.00, 1.00] 3.22 [1.45] NC
0 Inf Synthetic IVFET 250 ug single 50 943 [38.8] 1.00 [1.00, 1.00] 4.77 [1.95] NC

Comparison against published NCA

Goggin 2004 reports terminal half-life only as a secondary derived parameter (Results paragraph 3): 2.9 h for postmenopausal women and 4.4 h for IVF-ET women. The paper does not tabulate observed NCA Cmax / AUC; the “Methods” notes that NCA was performed but “data not shown” beyond the half-life mention. The simulated PKNCA half-lives should land near these values:

hl_published <- tibble::tibble(
  cohort = c("S1 PM 100 ug single",
             "S1 PM 250 ug single",
             "Synthetic IVFET 250 ug single"),
  half_life_pub_h = c(2.9, 2.9, 4.4)
)

hl_simulated <- as.data.frame(nca_res$result) |>
  dplyr::filter(PPTESTCD == "half.life") |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(
    median_h = median(PPORRES, na.rm = TRUE),
    q05_h    = quantile(PPORRES, 0.05, na.rm = TRUE),
    q95_h    = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups  = "drop"
  )

hl_compare <- dplyr::left_join(hl_published, hl_simulated, by = "cohort") |>
  dplyr::mutate(pct_diff = round(100 * (median_h - half_life_pub_h) / half_life_pub_h, 1))

knitr::kable(hl_compare,
             caption = "Goggin 2004 reported t1/2 vs simulated single-dose t1/2 (median, 5-95%).")
Goggin 2004 reported t1/2 vs simulated single-dose t1/2 (median, 5-95%).
cohort half_life_pub_h median_h q05_h q95_h pct_diff
S1 PM 100 ug single 2.9 2.992702 1.808051 4.911349 3.2
S1 PM 250 ug single 2.9 2.902665 1.692402 6.094209 0.1
Synthetic IVFET 250 ug single 4.4 4.554220 2.087160 8.448966 3.5

The simulated medians should be within ~5% of the paper’s secondary-parameter values: a closed-form check gives t1/2 = ln(2) x V / CL = 0.693 x 235 / 57 = 2.86 h for PM women and 0.693 x 235 / 37 = 4.40 h for IVF-ET women at the cohort-median WT of 62 kg. Larger WT or extreme percentiles will shift these.

Assumptions and deviations

  • Reference categories. The paper’s effect of “type of population” is encoded with TYPE = 1 for IVF-ET patients and a 0.649 multiplier on CL/F, with healthy postmenopausal women as the implicit reference (Methods Step 2; Table 4). The canonical DIS_HEALTHY register (inst/references/covariate-columns.md) uses 0 = patient as the reference, so the model file shifts lcl to the IVF-ET (patient) typical 37 L/h and the e_dis_healthy_cl coefficient -log(0.649) = +0.4325 restores the PM-typical 57 L/h at DIS_HEALTHY = 1. The mapping is mathematically identical to the paper’s encoding.
  • Covariate form on V/F is linear-additive on the natural scale. Goggin 2004 fits TVP_V = Ppop + theta_WT x (WT - 62) with theta_WT = 6.7 L/kg (Methods Step 2 and Table 4). This is NOT a log-multiplicative effect; the model file applies it on the natural scale before the log-normal IIV. The studied weight range is 48-83 kg; below ~27 kg the typical V/F becomes negative, so the model is extrapolation-unsafe outside the studied range. The description field flags this.
  • IOV is shared across three occasions. The paper estimates a single 23% CV IOV variance (Methods Step 1) on V/F across three occasions defined as first / intermediate / last dosing day. nlmixr2 has no NONMEM $OMEGA BLOCK(1) SAME shortcut, so the model file uses three per-occasion etas with occasions 2 and 3 fix()’d to the occasion-1 variance (matching the Jonsson 2011 ethambutol idiom for IOV in nlmixr2).
  • D1 has no IIV. Goggin 2004 Methods Step 1 (“Results” paragraph 1) reports that the estimated intersubject variability on D1 was 10^-9 and was therefore omitted from the base model. The packaged model has no etald1 parameter.
  • No covariates on absorption. ALT, AST, creatinine, and bilirubin were screened as univariate covariates but not retained (Methods Step 3, Table 3). The packaged model exposes only WT, DIS_HEALTHY, and OCC.
  • DOI. The DOI in the reference field (10.1111/j.1365-2125.2003.02064.x) was supplied by the dispatcher’s task metadata. The DOI string is not visible inside the on-disk PDF trimmed-markdown excerpt (the PMC-XML / PDF preprocessor strips the copyright header where Wiley typically prints DOI). It is presented here unverified against the publisher’s landing page; users who need a citable identifier should cross-check against the journal’s table of contents for Br J Clin Pharmacol 57(4) (April 2004).
  • Validation scope. The paper does not publish observed Cmax / AUC NCA values, so the validation here is restricted to the secondary terminal half-life parameter (the only NCA-style value reported in the paper). VPC reproduction is qualitative: the paper’s Figure 2 shows three representative subjects per study, and the vignette plots the typical-value profile per cohort as the closest deterministic analogue.