Pegcetacoplan population PK and PK/PD (Crass 2024) • nlmixr2lib

Model and source

Crass 2024 reports three models built from the pegcetacoplan clinical development programme, and this package carries each one as a separate model file, matching the authors’ structure:

model_names <- c(
  "Crass_2024_pegcetacoplan",
  "Crass_2024_pegcetacoplan_hemoglobin",
  "Crass_2024_pegcetacoplan_ldh"
)
uis <- lapply(model_names, function(n) rxode2::rxode(readModelDb(n)))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ parameter labels from comments will be replaced by 'label()'
names(uis) <- model_names

tibble(
  Model = model_names,
  Role = c(
    "Population PK (284 participants, 11 studies)",
    "Hemoglobin PK/PD (165 patients, 5 studies)",
    "Lactate dehydrogenase PK/PD (165 patients, 5 studies)"
  )
) |>
  knitr::kable(caption = "The three models Crass 2024 reports.")

The three models Crass 2024 reports.
Model	Role
Crass_2024_pegcetacoplan	Population PK (284 participants, 11 studies)
Crass_2024_pegcetacoplan_hemoglobin	Hemoglobin PK/PD (165 patients, 5 studies)
Crass_2024_pegcetacoplan_ldh	Lactate dehydrogenase PK/PD (165 patients, 5 studies)

Citation: Crass RL, Smith B, Adriaens S, Chapel S, Langdon G. Population Pharmacokinetic and Pharmacokinetic/Pharmacodynamic Analyses of Pegcetacoplan in Patients with Paroxysmal Nocturnal Hemoglobinuria. Drugs R D. 2024;24(4):565-577. doi:10.1007/s40268-024-00500-7
Article: https://doi.org/10.1007/s40268-024-00500-7
Supplement (Electronic Supplementary Material, open access): https://doi.org/10.1007/s40268-024-00500-7

The Electronic Supplementary Material (ESM) is where the model actually lives. ESM Table 1 reproduces the three NONMEM control streams verbatim, and ESM Tables 3, 4, and 5 hold the final parameter estimates for the PK, hemoglobin, and lactate dehydrogenase (LDH) models respectively. The main article’s Table 2 reports only the back-transformed PK/PD structural parameters; every value in these model files is traced to the ESM tables (see the source-trace table below).

Population

The population PK analysis pooled 284 participants across 11 completed studies: 124 healthy adults (44%) from six phase 1 studies (including one renal-impairment study, AIRIS) and 160 adults with paroxysmal nocturnal hemoglobinuria (PNH, 56%) from five studies spanning phase 1 through phase 3 (PHAROAH, PADDOCK, PALOMINO, PEGASUS, PRINCE). Median age was 36 years (range 19-81), median body weight 70.0 kg (range 41-156 kg), and the cohort was 44% female. Slightly more than half of participants were White (54.2%), with 29.9% Asian, 2.5% Black, 7.7% other, and 5.6% missing; the PRINCE phase 3 cohort was predominantly Asian (32/45, 71%). Median baseline complement C3 was 1.00 g/L (range 0.47-1.64 g/L). 5195 PK samples were analysed, of which 4737 (91%) were quantifiable (Crass 2024 Sect. 3.1.1, Table 1, ESM Table 2).

The PK/PD analyses used the 165 patients with PNH from those five PNH studies, contributing 4498 hemoglobin samples and 3423 LDH samples. Median age was 45 years (range 19-81), 56% were female, 39% White and 38% Asian, and the cohort split 54% eculizumab-treated at baseline versus 46% complement C5 inhibitor naive (Crass 2024 Sect. 3.1.2). The PK/PD models were fitted sequentially, conditioned on individual empirical Bayes estimates of the PK parameters from the population PK model (Sect. 2.2), which is why the PK layer of both PK/PD model files is carried as fixed().

The same information is available programmatically:

str(uis[["Crass_2024_pegcetacoplan"]]$population)
#> List of 13
#>  $ species       : chr "human"
#>  $ n_subjects    : num 284
#>  $ n_studies     : num 11
#>  $ age_median    : chr "36 years"
#>  $ age_range     : chr "19-81 years"
#>  $ weight_median : chr "70.0 kg"
#>  $ weight_range  : chr "41-156 kg"
#>  $ sex_female_pct: num 44.4
#>  $ race_ethnicity: Named num [1:5] 54.2 2.5 29.9 7.7 5.6
#>   ..- attr(*, "names")= chr [1:5] "White" "Black" "Asian" "Other" ...
#>  $ disease_state : chr "44% healthy adults (including one renal-impairment study); 56% adults with paroxysmal nocturnal hemoglobinuria,"| __truncated__
#>  $ dose_range    : chr "Subcutaneous 25-2600 mg as single doses, once daily, twice weekly, or once weekly (including the approved 1080 "| __truncated__
#>  $ regions       : chr "Multinational; the PRINCE phase 3 cohort is predominantly Asian (32/45, 71%)"
#>  $ notes         : chr "Baseline demographics from Crass 2024 ESM Table 2 (categorical and continuous covariates by study) and Table 1 "| __truncated__

Model structure

The population PK model is a one-compartment disposition model with a single-transit-compartment subcutaneous absorption chain. ESM Table 1’s $DES block, with the source numbering DOSESC1 = 1, CENTRAL = 2, TRANSIT1 = 3, reads

DADT(1) = -KA*A(1)
DADT(2) =  KA*A(3) - (CL/V2)*A(2)
DADT(3) =  KA*A(1) - KA*A(3)

so the subcutaneous depot feeds one transit compartment, which feeds the central compartment, with the same rate constant ka governing both transfers. Intravenous doses (study 401) enter central directly and are not scaled by bioavailability. S2 = V2 with dose in mg gives concentration directly in mg/L = ug/mL, so no scaling factor is needed.

Both PK/PD models are direct (no-delay) sigmoidal Emax models on the concurrent pegcetacoplan concentration. Crass 2024 Sect. 3.2.2 gives

$\text{Biomarker} = \text{Baseline} \cdot \left(1 + \frac{E_{max} \cdot C^{Hill}}{EC_{50}^{Hill} + C^{Hill}}\right)$

with a positive Emax for hemoglobin (a 51% maximal increase) and a negative one for LDH (a 92% maximal decrease in eculizumab-naive patients), the latter implemented in the source control stream as EFF = BASELDH*(1-EDRUG) with a logit-transformed positive Emax. The paper is explicit (Sect. 4, limitations) that indirect PK/PD models incorporating a time delay could not be identified, so these direct models are best suited to steady-state dosing conditions.

lapply(uis, function(u) u$state)
#> $Crass_2024_pegcetacoplan
#> [1] "depot"    "transit1" "central" 
#> 
#> $Crass_2024_pegcetacoplan_hemoglobin
#> [1] "depot"    "transit1" "central" 
#> 
#> $Crass_2024_pegcetacoplan_ldh
#> [1] "depot"    "transit1" "central"

Source trace

Every ini() entry carries an in-file comment pointing at its source location. The table below collects them.

Per-parameter source trace. ‘ESM’ = the article’s open-access Electronic Supplementary Material.
Model	Equation / parameter	Value	Source location
PK	d/dt(depot), d/dt(transit1), d/dt(central)	n/a	ESM Table 1, PK control stream $DES
PK	lcl (CL, non-PNH, 70 kg)	0.0117 L/h	ESM Table 3, theta 1 TVCL (95% CI 0.0106-0.0128)
PK	lvc (Vc, 70 kg)	3.96 L	ESM Table 3, theta 2 TVV2 (95% CI 3.57-4.34)
PK	lka	0.0370 1/h	ESM Table 3, theta 3 TVKA (95% CI 0.0343-0.0397)
PK	lfdepot (SC bioavailability)	0.758	ESM Table 3, theta 4 F1 (95% CI 0.681-0.834)
PK	e_form_pegcet_lyophilized_fdepot	0.220	ESM Table 3, theta 8 ‘Lyophilized formulation on F1’
PK	e_dis_pnh_cl	0.257	ESM Table 3, theta 9 ‘PNH on CL’
PK	e_wt_cl	0.646	ESM Table 3, theta 10 ‘WT on CL’
PK	e_wt_vc	0.809	ESM Table 3, theta 11 ‘WT on V2’
PK	etalcl / etalvc block	0.042754 / 0.024984 / 0.044778	ESM Table 3 IIV: CL 20.9 CV%, rho 0.571, V2 21.4 CV%; omega^2 = log(CV^2 + 1)
PK	etalka	0.243436	ESM Table 3 IIV: KA 52.5 CV%
PK	expSd_healthy / _pnh_ph12 / _pnh_ph3	0.200 / 0.326 / 0.163	ESM Table 3 thetas 5, 6, 7 (residual variability rows)
Hb	hb = rbase * (1 + edrug)	n/a	ESM Table 1, Hb control stream $ERROR; Crass 2024 Sect. 3.2.2
Hb	lrbase (BaseHb)	8.74 g/dL	ESM Table 4, theta 1 (95% CI 8.55-8.93); Table 2
Hb	lemax	0.510	ESM Table 4, theta 2 (95% CI 0.431-0.589); Table 2 ‘51 (43-59)’
Hb	lec50	337 ug/mL	ESM Table 4, theta 3 (95% CI 302-372); Table 2
Hb	lhill	4.66	ESM Table 4, theta 4 (95% CI 3.81-5.52); Table 2
Hb	e_crcl_emax	0.641	ESM Table 4, theta 6 ‘CrCl on Emax’
Hb	e_sexf_emax	-0.337	ESM Table 4, theta 7 ‘Female sex on Emax’
Hb	e_conmed_eculizumab_bl_emax	fixed(0)	ESM Table 1, Hb $THETA line 8 ‘(0 FIX) ;8 BECU ON EMAX’
Hb	etalrbase / etalemax block; etalec50	0.0162 / -0.0437 / 0.351; 0.291	ESM Table 4 IIV rows (variances reported directly)
Hb	addSd	0.913 g/dL	ESM Table 4, theta 5 ‘RE Additive (g/dL)’
LDH	ldh = rbase * (1 - edrug)	n/a	ESM Table 1, LDH control stream $ERROR; Crass 2024 Sect. 3.2.2
LDH	lrbase / lrbase_ecu_bl	7.56 / 5.52 (log U/L)	ESM Table 5, thetas 1 and 2; transformed 1920 / 249 U/L
LDH	logitemax / logitemax_ecu_bl	2.40 / -1.39 (logit)	ESM Table 5, thetas 3 and 4; transformed 0.917 / 0.200
LDH	lec50	5.23 (log ug/mL)	ESM Table 5, theta 5; transformed 187 ug/mL
LDH	lhill	3.42	ESM Table 5, theta 6 (reported untransformed)
LDH	e_conmed_eculizumab_emax	0.783 (logit)	ESM Table 5, theta 8 ‘Eculizumab Co-treatment on Logit Emax’
LDH	etalrbase / etalogitemax / etalec50 block	0.182 / 0.265 / 0.745 / 0 / 0.167 / 0.121	ESM Table 5 IIV rows; omega3,1 not reported and entered as 0 in the ESM Table 1 $OMEGA BLOCK(3)
LDH	expSd	0.305	ESM Table 5, theta 7 ‘Log additive’; transformed 30.5%

Reproducing the published back-transforms

ESM Tables 4 and 5 report several parameters on their estimation scale together with the back-transformed values, and Crass 2024 Sect. 3.4.2 quotes several derived covariate-adjusted values in prose. Reproducing them is a cheap end-to-end check that the transform conventions in the model files are right.

th_hb  <- setNames(uis[["Crass_2024_pegcetacoplan_hemoglobin"]]$theta,
                   names(uis[["Crass_2024_pegcetacoplan_hemoglobin"]]$theta))
th_ldh <- setNames(uis[["Crass_2024_pegcetacoplan_ldh"]]$theta,
                   names(uis[["Crass_2024_pegcetacoplan_ldh"]]$theta))
ilogit <- function(x) exp(x) / (1 + exp(x))

tibble::tribble(
  ~Quantity, ~Computed, ~Published, ~`Source`,
  "LDH baseline, eculizumab-naive (U/L)",  exp(th_ldh[["lrbase"]]),            1920,  "ESM Table 5 transformed estimate",
  "LDH baseline, eculizumab-treated (U/L)", exp(th_ldh[["lrbase_ecu_bl"]]),     249,  "ESM Table 5 transformed estimate",
  "LDH Emax, eculizumab-naive (fraction)",  ilogit(th_ldh[["logitemax"]]),      0.917, "ESM Table 5 transformed estimate",
  "LDH Emax, eculizumab-treated (fraction)", ilogit(th_ldh[["logitemax_ecu_bl"]]), 0.200, "ESM Table 5 transformed estimate",
  "LDH Emax during eculizumab co-treatment (fraction)",
      ilogit(th_ldh[["logitemax_ecu_bl"]] + th_ldh[["e_conmed_eculizumab_emax"]]), 0.350, "Sect. 3.4.2 '35.0% decrease from baseline'",
  "LDH EC50 (ug/mL)", exp(th_ldh[["lec50"]]), 187, "ESM Table 5 transformed estimate",
  "Hb Emax, male at CrCl 120 mL/min (fraction)",
      exp(th_hb[["lemax"]]), 0.510, "ESM Table 4 theta 2 / Table 2",
  "Hb Emax, female at CrCl 120 mL/min (fraction)",
      exp(th_hb[["lemax"]]) * (1 + th_hb[["e_sexf_emax"]]), 0.338, "Sect. 3.4.2 '33.8% increase'",
  "Hb Emax, male at CrCl 40 mL/min (fraction)",
      exp(th_hb[["lemax"]]) * (40 / 120)^th_hb[["e_crcl_emax"]], 0.252, "Sect. 3.4.2 '25.2% maximal increase'"
) |>
  mutate(Computed = signif(Computed, 4),
         `Difference (%)` = round(100 * (Computed - Published) / Published, 1)) |>
  knitr::kable(caption = "Model back-transforms versus the values Crass 2024 reports.")

Model back-transforms versus the values Crass 2024 reports.
Quantity	Computed	Published	Source	Difference (%)
LDH baseline, eculizumab-naive (U/L)	1920.0000	1920.000	ESM Table 5 transformed estimate	0.0
LDH baseline, eculizumab-treated (U/L)	249.6000	249.000	ESM Table 5 transformed estimate	0.2
LDH Emax, eculizumab-naive (fraction)	0.9168	0.917	ESM Table 5 transformed estimate	0.0
LDH Emax, eculizumab-treated (fraction)	0.1994	0.200	ESM Table 5 transformed estimate	-0.3
LDH Emax during eculizumab co-treatment (fraction)	0.3527	0.350	Sect. 3.4.2 ‘35.0% decrease from baseline’	0.8
LDH EC50 (ug/mL)	186.8000	187.000	ESM Table 5 transformed estimate	-0.1
Hb Emax, male at CrCl 120 mL/min (fraction)	0.5100	0.510	ESM Table 4 theta 2 / Table 2	0.0
Hb Emax, female at CrCl 120 mL/min (fraction)	0.3381	0.338	Sect. 3.4.2 ‘33.8% increase’	0.0
Hb Emax, male at CrCl 40 mL/min (fraction)	0.2522	0.252	Sect. 3.4.2 ‘25.2% maximal increase’	0.1

Every quantity reproduces the published value to the precision the paper prints.

Virtual cohort

Original observed data are not publicly available (Crass 2024 “Availability of data and material”). The simulations below use virtual populations whose covariate distributions approximate the published trial demographics.

Two PK arms are simulated, each with 150 participants: healthy adults and patients with PNH. Both receive the approved regimen of subcutaneous pegcetacoplan 1080 mg twice weekly, modelled as a fixed 84-hour interval so that exactly two doses fall in each 168-hour week.

set.seed(20241129)

N_PER_ARM <- 150L
TAU <- 84      # h, twice weekly
WEEK <- 168    # h
N_WEEKS <- 26L
T_LAST_DOSE <- TAU * (2 * N_WEEKS - 1)
T_END_SS <- TAU * 2 * N_WEEKS            # end of the last steady-state week
T_END <- T_END_SS + 60 * 24              # 60-day washout for terminal-phase NCA

# Body weight: log-normal centred on the analysis-set median of 70.0 kg,
# truncated to the observed 41-156 kg range (ESM Table 2, Total column).
draw_wt <- function(n) pmin(pmax(exp(rnorm(n, log(70), 0.22)), 41), 156)

make_pk_arm <- function(n, arm, pnh, phase3, id_offset = 0L) {
  subj <- tibble(
    id = id_offset + seq_len(n),
    arm = arm,
    WT = draw_wt(n),
    DIS_PNH = pnh,
    STUDY_PEGCET_PHASE3 = phase3,
    # Phase 3 used a ready-to-use solution formulation; the reference level.
    FORM_PEGCET_LYOPHILIZED = 0
  )
  dose <- subj |>
    crossing(time = seq(0, T_LAST_DOSE, by = TAU)) |>
    mutate(evid = 1L, amt = 1080, cmt = "depot")
  # Observation grid: fine over week 1 (needed for the accumulation ratio) and
  # over the final steady-state week, coarse elsewhere.
  obs_times <- sort(unique(c(
    seq(0, WEEK, by = 6),
    seq(0, T_END_SS, by = 24),
    seq(T_END_SS - WEEK, T_END_SS, by = 6),
    seq(T_END_SS, T_END, by = 24)
  )))
  obs <- subj |>
    crossing(time = obs_times) |>
    mutate(evid = 0L, amt = NA_real_, cmt = "central")
  bind_rows(dose, obs) |> arrange(id, time, desc(evid))
}

pk_events <- bind_rows(
  make_pk_arm(N_PER_ARM, "Healthy adults", pnh = 0, phase3 = 0, id_offset = 0L),
  make_pk_arm(N_PER_ARM, "Adults with PNH", pnh = 1, phase3 = 1, id_offset = 1000L)
) |>
  as.data.frame()

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

Simulation

pk_sim <- rxode2::rxSolve(
  readModelDb("Crass_2024_pegcetacoplan"),
  events = pk_events,
  keep = c("arm", "WT")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

nrow(pk_sim)
#> [1] 85500

Replicate published figures

Figure 1 – predicted exposure in adults with PNH at 1080 mg twice weekly

Crass 2024 Figure 1 shows the predicted pegcetacoplan concentration-time profile in adults with PNH under the approved regimen, with the EC90 thresholds for the hemoglobin and LDH responses overlaid. EC90 is derived from the fitted sigmoidal Emax parameters as $EC_{90} = EC_{50}\cdot 9^{1/Hill}$ .

ec90 <- function(ui, ec50_name, hill_name, log_ec50 = TRUE) {
  th <- ui$theta
  ec50 <- if (log_ec50) exp(th[[ec50_name]]) else th[[ec50_name]]
  ec50 * 9^(1 / exp(th[[hill_name]]))
}
ec90_hb <- ec90(uis[["Crass_2024_pegcetacoplan_hemoglobin"]], "lec50", "lhill")
ec90_ldh <- ec90(uis[["Crass_2024_pegcetacoplan_ldh"]], "lec50", "lhill")
c(EC90_Hb = ec90_hb, EC90_LDH = ec90_ldh)
#>  EC90_Hb EC90_LDH 
#> 540.0115 355.1227

pk_sim |>
  filter(arm == "Adults with PNH", time <= T_END_SS, time %% 24 == 0) |>
  group_by(time) |>
  summarise(
    Q25 = quantile(Cc, 0.25), Q50 = median(Cc), Q75 = quantile(Cc, 0.75),
    .groups = "drop"
  ) |>
  ggplot(aes(time / 24, Q50)) +
  geom_ribbon(aes(ymin = Q25, ymax = Q75), alpha = 0.25, fill = "steelblue") +
  geom_line(linewidth = 0.8, colour = "steelblue") +
  geom_hline(yintercept = ec90_hb, linetype = "dashed", colour = "goldenrod3") +
  geom_hline(yintercept = ec90_ldh, linetype = "dashed", colour = "darkred") +
  annotate("text", x = 5, y = ec90_hb * 1.07, hjust = 0, size = 3,
           colour = "goldenrod3", label = "EC90 hemoglobin") +
  annotate("text", x = 5, y = ec90_ldh * 1.07, hjust = 0, size = 3,
           colour = "darkred", label = "EC90 LDH") +
  labs(x = "Time (days)", y = "Pegcetacoplan concentration (ug/mL)",
       title = "Predicted exposure, SC 1080 mg twice weekly (PNH)",
       subtitle = "Median with interquartile range",
       caption = "Replicates Figure 1 of Crass 2024.")

Replicates Figure 1 of Crass 2024: predicted exposure among adults with PNH receiving subcutaneous pegcetacoplan 1080 mg twice weekly, with the hemoglobin and LDH EC90 thresholds overlaid.

The paper states that steady-state concentrations exceed the EC90 for both biomarkers in approximately 75% of patients with PNH, and that median steady-state concentration exceeds those thresholds by week 4:

ss_pnh <- pk_sim |>
  filter(arm == "Adults with PNH", time >= T_END_SS - WEEK, time <= T_END_SS) |>
  group_by(id) |>
  summarise(cavg = mean(Cc), .groups = "drop")

week4 <- pk_sim |>
  filter(arm == "Adults with PNH", time >= 4 * WEEK - WEEK, time <= 4 * WEEK) |>
  group_by(id) |>
  summarise(cavg = mean(Cc), .groups = "drop")

tibble::tribble(
  ~Statement, ~Simulated, ~Published,
  "Steady-state Cavg above BOTH EC90 thresholds (i.e. above the hemoglobin EC90, which is the higher of the two)",
      sprintf("%.0f%% of patients", 100 * mean(ss_pnh$cavg > ec90_hb)),
      "approximately 75% (Sect. 3.3)",
  "Steady-state Cavg above the LDH EC90 alone (not the binding threshold)",
      sprintf("%.0f%% of patients", 100 * mean(ss_pnh$cavg > ec90_ldh)),
      "not reported separately",
  "Median Cavg over week 4 already above both EC90 thresholds",
      sprintf("median %.0f ug/mL", median(week4$cavg)),
      sprintf("yes; the two EC90 are %.0f and %.0f ug/mL", ec90_hb, ec90_ldh)
) |>
  knitr::kable(caption = "EC90 coverage checks against Crass 2024 Sect. 3.3. Because the hemoglobin EC90 is the higher of the two, exceeding it implies exceeding both.")

EC90 coverage checks against Crass 2024 Sect. 3.3. Because the hemoglobin EC90 is the higher of the two, exceeding it implies exceeding both.
Statement	Simulated	Published
Steady-state Cavg above BOTH EC90 thresholds (i.e. above the hemoglobin EC90, which is the higher of the two)	78% of patients	approximately 75% (Sect. 3.3)
Steady-state Cavg above the LDH EC90 alone (not the binding threshold)	99% of patients	not reported separately
Median Cavg over week 4 already above both EC90 thresholds	median 569 ug/mL	yes; the two EC90 are 540 and 355 ug/mL

Figure 3A – effect of body weight on steady-state exposure

Crass 2024 Figure 3A shows average steady-state concentration over 1-week intervals across the observed body-weight range, with the biomarker EC90 thresholds overlaid. Body weight enters both clearance (exponent 0.646) and central volume (exponent 0.809), so exposure falls with increasing weight.

ss_pnh_wt <- pk_sim |>
  filter(arm == "Adults with PNH", time >= T_END_SS - WEEK, time <= T_END_SS) |>
  group_by(id, WT) |>
  summarise(cavg = mean(Cc), .groups = "drop") |>
  mutate(wt_band = cut(WT, breaks = c(40, 55, 70, 85, 100, 160),
                       labels = c("40-55", "55-70", "70-85", "85-100", ">100"),
                       right = FALSE))

ss_pnh_wt |>
  ggplot(aes(wt_band, cavg)) +
  geom_boxplot(fill = "grey85", outlier.size = 0.8) +
  geom_hline(yintercept = ec90_hb, linetype = "dashed", colour = "goldenrod3") +
  geom_hline(yintercept = ec90_ldh, linetype = "dashed", colour = "darkred") +
  labs(x = "Body weight (kg)", y = "Cavg,ss over 1 week (ug/mL)",
       title = "Steady-state exposure by body weight (PNH, 1080 mg twice weekly)",
       caption = "Replicates Figure 3A of Crass 2024. Dashed lines: hemoglobin (upper) and LDH (lower) EC90.")

Replicates Figure 3A of Crass 2024: average steady-state pegcetacoplan concentration over 1-week intervals by body-weight band in adults with PNH.

Figure 6 – maximal effect on hemoglobin and LDH

Crass 2024 Figure 6 plots the fitted exposure-response curves for both biomarkers against pegcetacoplan concentration. Rather than re-typing the Emax equation here, the curves below are read out of the packaged models by driving a range of steady-state doses through the model and recording the resulting (Cc, hb) and (Cc, ldh) pairs for a typical subject.

dose_levels <- round(exp(seq(log(20), log(6000), length.out = 30)))

make_typ_arm <- function(cov_row, doses, id_offset = 0L) {
  subj <- cov_row[rep(1, length(doses)), , drop = FALSE]
  subj$id <- id_offset + seq_along(doses)
  subj$dose_mg <- doses
  d <- subj |> crossing(time = seq(0, TAU * 39, by = TAU)) |>
    mutate(evid = 1L, amt = dose_mg, cmt = "depot")
  o <- subj |> crossing(time = seq(TAU * 38, TAU * 40, by = 12)) |>
    mutate(evid = 0L, amt = NA_real_, cmt = "central")
  bind_rows(d, o) |> arrange(id, time, desc(evid))
}

hb_cov <- tibble(WT = 70, DIS_PNH = 1, FORM_PEGCET_LYOPHILIZED = 0,
                 CRCL = 120, SEXF = 0, CONMED_ECULIZUMAB_BL = 0)
ldh_cov_naive <- tibble(WT = 70, DIS_PNH = 1, FORM_PEGCET_LYOPHILIZED = 0,
                        CONMED_ECULIZUMAB_BL = 0, CONMED_ECULIZUMAB = 0)
ldh_cov_treated <- ldh_cov_naive |> mutate(CONMED_ECULIZUMAB_BL = 1)

solve_typical <- function(nm, ev) {
  rxode2::rxSolve(rxode2::zeroRe(readModelDb(nm)), as.data.frame(ev), omega = NA,
                  keep = c("dose_mg")) |>
    as.data.frame()
}

hb_curve <- solve_typical("Crass_2024_pegcetacoplan_hemoglobin",
                          make_typ_arm(hb_cov, dose_levels)) |>
  group_by(dose_mg) |>
  summarise(Cc = mean(Cc), value = mean(hb), .groups = "drop") |>
  mutate(Biomarker = "Hemoglobin (g/dL)")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: multi-subject simulation without without 'omega'

ldh_curve <- bind_rows(
  solve_typical("Crass_2024_pegcetacoplan_ldh",
                make_typ_arm(ldh_cov_naive, dose_levels)) |>
    mutate(Biomarker = "LDH, eculizumab-naive (U/L)"),
  solve_typical("Crass_2024_pegcetacoplan_ldh",
                make_typ_arm(ldh_cov_treated, dose_levels, id_offset = 100L)) |>
    mutate(Biomarker = "LDH, eculizumab-treated (U/L)")
) |>
  group_by(Biomarker, dose_mg) |>
  summarise(Cc = mean(Cc), value = mean(ldh), .groups = "drop")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: multi-subject simulation without without 'omega'

med_css <- median(ss_pnh$cavg)

bind_rows(hb_curve, ldh_curve) |>
  ggplot(aes(Cc, value)) +
  geom_line(linewidth = 0.8, colour = "steelblue") +
  geom_vline(aes(xintercept = xi), linetype = "dashed", colour = "grey40",
             data = tibble(
               Biomarker = c("Hemoglobin (g/dL)", "LDH, eculizumab-naive (U/L)",
                             "LDH, eculizumab-treated (U/L)"),
               xi = c(exp(th_hb[["lec50"]]), exp(th_ldh[["lec50"]]),
                      exp(th_ldh[["lec50"]]))
             )) +
  geom_vline(xintercept = med_css, colour = "darkred") +
  facet_wrap(~Biomarker, scales = "free_y", ncol = 1) +
  scale_x_log10() +
  labs(x = "Pegcetacoplan concentration (ug/mL, log scale)", y = "Biomarker",
       caption = "Replicates Figure 6 of Crass 2024.")

Replicates Figure 6 of Crass 2024: exposure-response for hemoglobin and LDH. Dashed vertical lines mark each endpoint’s EC50; the solid vertical line marks the median steady-state concentration at SC 1080 mg twice weekly.

Biomarker response at steady state

Crass 2024 Sect. 3.4.3 reports the predicted steady-state biomarker distributions under the approved regimen. These are reproduced with stochastic cohorts drawn to match the PK/PD analysis-set demographics.

make_pd_arm <- function(n, extra, id_offset = 0L) {
  subj <- tibble(
    id = id_offset + seq_len(n),
    WT = draw_wt(n),
    DIS_PNH = 1,
    FORM_PEGCET_LYOPHILIZED = 0
  ) |>
    bind_cols(extra(n))
  d <- subj |> crossing(time = seq(0, TAU * 39, by = TAU)) |>
    mutate(evid = 1L, amt = 1080, cmt = "depot")
  o <- subj |> crossing(time = seq(TAU * 38, TAU * 40, by = 6)) |>
    mutate(evid = 0L, amt = NA_real_, cmt = "central")
  bind_rows(d, o) |> arrange(id, time, desc(evid)) |> as.data.frame()
}

# Hemoglobin cohort: 56% female, CrCl centred on the reference 120 mL/min with
# 5th/95th percentiles near the 40 / 191 mL/min the paper quotes.
hb_events <- make_pd_arm(N_PER_ARM, function(n) tibble(
  SEXF = rbinom(n, 1, 0.56),
  CRCL = pmin(pmax(exp(rnorm(n, log(112), 0.42)), 20), 300),
  CONMED_ECULIZUMAB_BL = rbinom(n, 1, 0.54)
))

hb_sim <- rxode2::rxSolve(readModelDb("Crass_2024_pegcetacoplan_hemoglobin"),
                          hb_events, keep = c("WT")) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

hb_ss <- hb_sim |>
  filter(time >= TAU * 38) |>
  group_by(id) |>
  summarise(hb = mean(hb), .groups = "drop")

# LDH cohorts: one eculizumab-naive, one eculizumab-treated at baseline, both
# on pegcetacoplan monotherapy at steady state (CONMED_ECULIZUMAB = 0).
ldh_events <- bind_rows(
  make_pd_arm(N_PER_ARM, function(n) tibble(
    CONMED_ECULIZUMAB_BL = 0L, CONMED_ECULIZUMAB = 0L)),
  make_pd_arm(N_PER_ARM, function(n) tibble(
    CONMED_ECULIZUMAB_BL = 1L, CONMED_ECULIZUMAB = 0L), id_offset = 1000L)
)

ldh_sim <- rxode2::rxSolve(readModelDb("Crass_2024_pegcetacoplan_ldh"),
                           ldh_events, keep = c("CONMED_ECULIZUMAB_BL")) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

ldh_ss <- ldh_sim |>
  filter(time >= TAU * 38) |>
  group_by(id, CONMED_ECULIZUMAB_BL) |>
  summarise(ldh = mean(ldh), .groups = "drop")

fmt_iqr <- function(x, digits = 0) {
  sprintf("%s (%s-%s)", round(median(x), digits),
          round(quantile(x, 0.25), digits), round(quantile(x, 0.75), digits))
}

tibble::tribble(
  ~Endpoint, ~Simulated, ~Published,
  "Hemoglobin at steady state, all patients (g/dL)",
      fmt_iqr(hb_ss$hb, 1), "11.7 (10.5-13.3)",
  "LDH at steady state, eculizumab-naive (U/L)",
      fmt_iqr(ldh_ss$ldh[ldh_ss$CONMED_ECULIZUMAB_BL == 0]), "217 (170-292)",
  "LDH at steady state, eculizumab-treated (U/L)",
      fmt_iqr(ldh_ss$ldh[ldh_ss$CONMED_ECULIZUMAB_BL == 1]), "192 (152-239)"
) |>
  knitr::kable(caption = "Median (IQR) steady-state biomarker predictions versus Crass 2024 Sect. 3.4.3.")

Median (IQR) steady-state biomarker predictions versus Crass 2024 Sect. 3.4.3.
Endpoint	Simulated	Published
Hemoglobin at steady state, all patients (g/dL)	11.7 (10.6-13.2)	11.7 (10.5-13.3)
LDH at steady state, eculizumab-naive (U/L)	220 (168-329)	217 (170-292)
LDH at steady state, eculizumab-treated (U/L)	183 (148-224)	192 (152-239)

All three medians and interquartile ranges reproduce the published values.

Crass 2024 also states that the median steady-state concentration achieves at least 95% of the maximal effect for both biomarkers:

frac_max <- function(cc, ec50, hill) cc^hill / (ec50^hill + cc^hill)
tibble(
  Endpoint = c("Hemoglobin", "LDH"),
  `Fraction of maximal effect at the median Cavg,ss` = c(
    frac_max(med_css, exp(th_hb[["lec50"]]), exp(th_hb[["lhill"]])),
    frac_max(med_css, exp(th_ldh[["lec50"]]), exp(th_ldh[["lhill"]]))
  )
) |>
  mutate(`Fraction of maximal effect at the median Cavg,ss` =
           sprintf("%.1f%%", 100 * `Fraction of maximal effect at the median Cavg,ss`)) |>
  knitr::kable(caption = "Crass 2024 Sect. 3.4.3 states >= 95% of the maximal effect is achieved for both endpoints at the median steady-state concentration.")

Crass 2024 Sect. 3.4.3 states >= 95% of the maximal effect is achieved for both endpoints at the median steady-state concentration.
Endpoint	Fraction of maximal effect at the median Cavg,ss
Hemoglobin	95.8%
LDH	98.7%

Effective half-life from the accumulation ratio

Crass 2024 Sect. 2.3.1 states that “effective half-life was calculated from the accumulation ratio for simulated exposure measures from week 1 to steady state”, where the exposure measures derived over 1-week intervals were maximum concentration and average concentration. Two readings are therefore possible: the accumulation ratio of Cmax, or the accumulation ratio of Cavg. They give materially different answers here, because the transit-compartment absorption chain is still filling during week 1 and so deflates the week-1 AUC far more than it deflates the week-1 peak. Both are computed below; the Cmax-based reading is the one that reproduces the published values, and it is also the classical definition of the effective half-life.

rac_metrics <- pk_sim |>
  mutate(win = case_when(
    time <= WEEK ~ "week1",
    time >= T_END_SS - WEEK & time <= T_END_SS ~ "ss",
    TRUE ~ NA_character_
  )) |>
  filter(!is.na(win)) |>
  group_by(arm, id, win) |>
  summarise(cmax = max(Cc), cavg = mean(Cc), .groups = "drop") |>
  pivot_wider(names_from = win, values_from = c(cmax, cavg)) |>
  mutate(
    rac_cmax = cmax_ss / cmax_week1,
    rac_cavg = cavg_ss / cavg_week1,
    # t(1/2),eff = -tau * ln(2) / ln(1 - 1/Rac) with tau = the 1-week interval
    # over which the exposure metrics were derived.
    thalf_cmax = -WEEK * log(2) / log(1 - 1 / rac_cmax) / 24,
    thalf_cavg = -WEEK * log(2) / log(1 - 1 / rac_cavg) / 24
  )

rac_metrics |>
  group_by(arm) |>
  summarise(
    `t1/2,eff from Rac(Cmax), days` = fmt_iqr(thalf_cmax, 1),
    `t1/2,eff from Rac(Cavg), days` = fmt_iqr(thalf_cavg, 1),
    .groups = "drop"
  ) |>
  left_join(
    tibble(arm = c("Healthy adults", "Adults with PNH"),
           `Published (Table 3), days` = c("11.0 (8.70-14.2)", "8.60 (6.90-11.0)")),
    by = "arm"
  ) |>
  arrange(match(arm, c("Healthy adults", "Adults with PNH"))) |>
  rename("Arm" = arm) |>
  knitr::kable(caption = "Effective half-life, median (IQR), versus Crass 2024 Table 3.")

Effective half-life, median (IQR), versus Crass 2024 Table 3.
Arm	t1/2,eff from Rac(Cmax), days	t1/2,eff from Rac(Cavg), days	Published (Table 3), days
Healthy adults	12 (10.5-14.5)	24 (19.8-31.4)	11.0 (8.70-14.2)
Adults with PNH	9.4 (8.1-11)	18.5 (14.7-24.4)	8.60 (6.90-11.0)

The Cmax-based accumulation ratio reproduces both published medians closely, while the Cavg-based ratio overstates the effective half-life roughly two-fold. Note that the effective half-life is not the same quantity as the terminal half-life: for this model the terminal half-life of a typical 70 kg subject is 9.8 days (healthy) and 7.8 days (PNH), about 11% shorter than the published effective half-lives, because the slow subcutaneous absorption chain adds to the apparent accumulation.

PKNCA validation

Non-compartmental analysis is run over the final steady-state dosing interval for the peak / trough / interval-average metrics, and over the post-treatment washout for the terminal half-life. Times are converted to days so PKNCA reports half-life in days, matching the paper.

sim_nca <- pk_sim |>
  filter(!is.na(Cc)) |>
  transmute(id, arm, time_d = time / 24, Cc)

# Guarantee a time-zero record per subject; pre-dose Cc is 0 for an
# extravascular route.
sim_nca <- bind_rows(
  sim_nca,
  sim_nca |> distinct(id, arm) |> mutate(time_d = 0, Cc = 0)
) |>
  distinct(id, arm, time_d, .keep_all = TRUE) |>
  arrange(id, arm, time_d)

conc_obj <- PKNCA::PKNCAconc(as.data.frame(sim_nca), Cc ~ time_d | arm + id)

dose_df <- pk_events |>
  filter(evid == 1) |>
  transmute(id, arm, time_d = time / 24, amt)

dose_obj <- PKNCA::PKNCAdose(as.data.frame(dose_df), amt ~ time_d | arm + id)

intervals <- data.frame(
  start = c(T_LAST_DOSE / 24, T_END_SS / 24),
  end   = c(T_END_SS / 24,    T_END / 24),
  cmax      = c(TRUE,  FALSE),
  tmax      = c(TRUE,  FALSE),
  cav       = c(TRUE,  FALSE),
  auclast   = c(TRUE,  FALSE),
  half.life = c(FALSE, TRUE)
)

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

as.data.frame(nca_res) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "cav", "auclast", "half.life")) |>
  group_by(arm, PPTESTCD) |>
  summarise(Median = median(PPORRES, na.rm = TRUE),
            `P05` = quantile(PPORRES, 0.05, na.rm = TRUE),
            `P95` = quantile(PPORRES, 0.95, na.rm = TRUE),
            .groups = "drop") |>
  mutate(across(c(Median, P05, P95), \(x) signif(x, 3))) |>
  rename("Arm" = arm, "NCA parameter" = PPTESTCD) |>
  knitr::kable(caption = "PKNCA results. cmax / tmax / cav / auclast over the final steady-state dosing interval (84 h); half.life over the 60-day post-treatment washout. Concentrations in ug/mL, times in days.")

PKNCA results. cmax / tmax / cav / auclast over the final steady-state dosing interval (84 h); half.life over the 60-day post-treatment washout. Concentrations in ug/mL, times in days.
Arm	NCA parameter	Median	P05	P95
Adults with PNH	auclast	2310.00	1560.00	3310.0
Adults with PNH	cav	659.00	446.00	946.0
Adults with PNH	cmax	668.00	458.00	969.0
Adults with PNH	half.life	7.81	5.67	10.9
Adults with PNH	tmax	0.50	0.00	2.5
Healthy adults	auclast	2970.00	2130.00	4740.0
Healthy adults	cav	848.00	608.00	1360.0
Healthy adults	cmax	856.00	624.00	1380.0
Healthy adults	half.life	10.30	7.09	13.5
Healthy adults	tmax	0.50	0.00	2.5

Comparison against published NCA

Crass 2024 reports the median (IQR) steady-state average concentration for patients with PNH under the approved regimen (Sect. 3.3) and the median effective half-life for both cohorts (Table 3). The effective half-life is the accumulation-derived quantity discussed above; PKNCA’s half.life is the terminal half-life, so the two are compared here as the closest available counterparts, with the more faithful accumulation-ratio comparison given in the previous section.

# Long form (PPTESTCD / PPORRES) so the healthy arm can carry a half-life
# reference without also needing a Cavg,ss reference the paper never reports.
published <- tibble::tribble(
  ~arm,               ~PPTESTCD,   ~PPORRES,
  "Adults with PNH",  "cav",       667,
  "Adults with PNH",  "half.life", 8.60,
  "Healthy adults",   "half.life", 11.0
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by = "arm",
  params = c("cav", "half.life"),
  units = c(cav = "ug/mL", half.life = "day"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated versus published exposure metrics. * marks a difference above 20%.",
  align = c("l", "l", "r", "r", "r")
)

Simulated versus published exposure metrics. * marks a difference above 20%.
NCA parameter	arm	Reference	Simulated	% diff
t½ (day)	Adults with PNH	8.6	7.81	-9.2%
t½ (day)	Healthy adults	11	10.3	-6.2%
Cavg (ug/mL)	Adults with PNH	667	659	-1.2%

Assumptions and deviations

The model lives in the supplement, not the article. All structural equations and every parameter value come from the open-access Electronic Supplementary Material: ESM Table 1 (the three NONMEM control streams) and ESM Tables 3, 4, and 5 (final parameter estimates). The main article’s Table 2 reports only the back-transformed PK/PD structural parameters and no PK parameters at all. Nothing in these model files is derived from a figure or from correspondence.
Inter-individual variability was back-transformed from reported CV%. ESM Table 3 reports the PK IIV as CV% rather than as variances, so the model file uses $\omega^2 = \log(CV^2 + 1)$ (CL 20.9% $\to$ 0.042754, Vc 21.4% $\to$ 0.044778, ka 52.5% $\to$ 0.243436) and recovers the CL-Vc covariance from the reported correlation as $\rho\sqrt{\omega^2_{CL}\omega^2_{Vc}} = 0.024984$ . ESM Tables 4 and 5 report the PK/PD IIV as variances directly and those are used as printed; the CV% and correlation values printed alongside them reproduce exactly from the variances, which confirms the reading.
One LDH IIV block element is not reported. The LDH $OMEGA BLOCK(3) covers (baseline, logit Emax, EC50), which has six unique elements, but ESM Table 5 lists only five: $\omega_{3,1}$ (EC50 : baseline LDH) is absent. The ESM Table 1 control stream initialises that element at 0, so it is encoded as 0 here. The resulting matrix is positive definite (eigenvalues 0.882, 0.144, 0.022), so no numerical nudge was needed.
The PK layer of both PK/PD models is carried as fixed(). Crass 2024 Sect. 2.2 states the PK/PD models were fitted sequentially, conditioned on individual empirical Bayes estimates of the PK parameters, and the ESM Table 1 PK/PD control streams read the individual PK parameters straight from $INPUT columns ICL / IV2 / IKA / IF1. There is therefore no re-estimated PK layer to report. The population PK typical values and their IIV are carried into both PK/PD files, wrapped in fixed(), so that each file is self-contained and simulatable; without the IIV the PK/PD files could not generate the concentration variability that drives the published steady-state biomarker distributions. The population PK residual error is not carried, because the PK/PD runs exclude pegcetacoplan concentration records (IGNORE=(TYPE.EQ.2)) and fit only the biomarker; Cc is exposed as an output column in both PK/PD models but is not a fitted endpoint.
DIS_PNH and FORM_PEGCET_LYOPHILIZED are inert in the PK/PD cohorts. Every subject in the PK/PD analysis set is a patient with PNH, and the phase 3 studies used a ready-to-use solution formulation. Both covariates are retained in the PK/PD model files anyway so their PK layer is structurally identical to the parent Crass_2024_pegcetacoplan, following the precedent set by Zhang_2023_brazikumab_il22.R / Zhang_2023_brazikumab_crp.R.
Three residual-error strata are switched by covariate. The PK $ERROR block selects one of three log-scale residual standard deviations by the source PNH / PNH2 / PNH3 study-group flags. Because PNH2 and PNH3 partition the PNH cohort exactly, the model re-expresses the switch as DIS_PNH x STUDY_PEGCET_PHASE3 and selects among expSd_healthy (0.200), expSd_pnh_ph3 (0.163), and expSd_pnh_ph12 (0.326). This follows the covariate-switched residual-error pattern already used by deAlwis_1998_ondansetron.R, Li_2017_CC292.R, and Marathe_2023_belzutifan.R.
Log-transformed-both-sides residual error is encoded as lnorm(). Both the PK and the LDH $ERROR blocks set IPRED = LOG(F) with $SIGMA 1 FIXED, so each W is a standard deviation on the natural-log scale and maps to nlmixr2’s log-normal error model rather than to a linear-space proportional error. The hemoglobin $ERROR block sets IPRED = EFF on the natural scale, so its residual is additive in g/dL.
The baseline-eculizumab effect on hemoglobin Emax is fixed at zero. ESM Table 1 enters that $THETA as (0 FIX) and ESM Table 4 omits it, which is why Crass 2024 Table 2 reports the same 51% Emax for eculizumab-naive and eculizumab-treated patients. It is retained as fixed(0) so the structural form and the fixed status remain visible rather than silently dropped.
The simulated formulation is inferred, not stated. Neither the article nor the ESM says which of the four FORM levels each study used; only the control stream reveals that the levels are sorbitol, dextrose, mannitol, and lyophilized powder. The simulations here set FORM_PEGCET_LYOPHILIZED = 0 (a ready-to-use solution), which is what reproduces the published exposure: at the reference bioavailability of 0.758 a typical 70 kg patient with PNH reaches a steady-state Cavg of 663 ug/mL against the published median of 667 ug/mL, whereas the lyophilized level (F = 0.758 x 1.220 = 0.925) would give about 809 ug/mL, roughly 20% above the published value and outside its published 5th-95th percentile centre. The inference is therefore well supported but is an inference; a user who knows a given study used the powder should set the covariate to 1.
Twice-weekly dosing is simulated as a fixed 84-hour interval. The paper does not state the calendar days used for the twice-weekly regimen; an 84-hour interval places exactly two doses in each 168-hour week, which is what the paper’s 1-week exposure metrics require. A real Day 1 / Day 4 schedule alternates 72-hour and 96-hour intervals; given a terminal half-life of roughly 8-10 days, the difference in the 1-week exposure metrics is negligible (the simulated peak-to-trough ratio at steady state is under 1.1).
Covariate distributions are assumed, not published per subject. Body weight is drawn log-normally, centred on the analysis-set median of 70.0 kg and truncated to the observed 41-156 kg range; creatinine clearance is drawn to place its 5th and 95th percentiles near the 40 and 191 mL/min the paper quotes; sex and baseline eculizumab status are drawn as Bernoulli variables at the published 56% female and 54% eculizumab-treated marginals. Correlation between covariates is not modelled because the paper reports only marginals.
CRCL here is raw Cockcroft-Gault clearance in mL/min, not BSA-normalized. ESM Table 4’s footnote defines it as “creatinine clearance calculated using the Cockcroft-Gault equation”, which returns mL/min. The canonical CRCL column accommodates both raw and BSA-normalized forms; the per-model covariateData entry records which applies, following the same convention as Delattre_2010_amikacin.R, Chen_2023_nemonoxacin.R, and Wada_2023_sparsentan.R.
New canonical names registered with this extraction. Four covariate columns – CONMED_ECULIZUMAB (time-varying co-treatment), CONMED_ECULIZUMAB_BL (time-fixed baseline status), FORM_PEGCET_LYOPHILIZED, and STUDY_PEGCET_PHASE3 – and one PD-output compartment, ldh, are added to the package registers in the same change. The ldh output-state canonical is the counterpart of the pre-existing LDH covariate canonical, following the pairing convention the register already documents for Hba1c / HBA1C; the sibling hemoglobin endpoint uses the pre-existing hb canonical.

Errata and points of divergence

The paper’s “probability of reaching LDH < 1.5 x ULN” cannot be a steady-state probability. Crass 2024 Sect. 3.4.3 reports that probability as 84% for eculizumab-naive and 97% for eculizumab-treated patients, against a threshold of 226 U/L. But the same sentence’s steady-state LDH distributions are 217 (IQR 170-292) and 192 (IQR 152-239) U/L: in both cases the 75th percentile already exceeds 226 U/L, so no more than about 75% of patients can be below the threshold at steady state. The two statements are only compatible if the 84% / 97% figures describe the probability of reaching that level at some point during treatment rather than the fraction below it at steady state. The simulation reproduces the published medians and IQRs (see the table above) but gives correspondingly lower steady-state fractions below 226 U/L, which is the arithmetic consequence of the published IQRs rather than a model discrepancy.

ldh_ss |>
  group_by(CONMED_ECULIZUMAB_BL) |>
  summarise(
    `Median LDH (U/L)` = round(median(ldh)),
    `75th percentile (U/L)` = round(quantile(ldh, 0.75)),
    `Fraction below 226 U/L` = sprintf("%.0f%%", 100 * mean(ldh < 226)),
    .groups = "drop"
  ) |>
  mutate(Cohort = ifelse(CONMED_ECULIZUMAB_BL == 0, "Eculizumab-naive",
                         "Eculizumab-treated")) |>
  select(Cohort, everything(), -CONMED_ECULIZUMAB_BL) |>
  knitr::kable(caption = "Steady-state LDH versus the 1.5 x ULN threshold of 226 U/L.")

Steady-state LDH versus the 1.5 x ULN threshold of 226 U/L.
Cohort	Median LDH (U/L)	75th percentile (U/L)	Fraction below 226 U/L
Eculizumab-naive	220	329	51%
Eculizumab-treated	183	224	75%

No erratum or corrigendum was located for Crass 2024 at the time of extraction. The article is open access under CC BY-NC 4.0 and its PubMed Central record (PMC11652457) carries no correction notice.
Method-sentence ambiguity on the effective half-life. As shown above, Sect. 2.3.1 names two candidate exposure measures for the accumulation ratio and only the Cmax-based reading reproduces Table 3. This is recorded here so a future reader does not mistake the Cavg-based value for a model error.