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Evinacumab (Pu 2021)

Source: vignettes/articles/Pu_2021_evinacumab.Rmd
Pu_2021_evinacumab.Rmd

Model and source

  • Citation: Pu X, Sale M, Yang F, Zhang Y, Davis JD, Al-Huniti N. Population pharmacokinetics and exposure-response modeling for evinacumab in homozygous familial hypercholesterolemia. CPT Pharmacometrics Syst Pharmacol. 2021;10(11):1412-1421. doi:10.1002/psp4.12711
  • Description: Population PK/PD model for evinacumab in healthy volunteers and adults / pediatric patients with homozygous familial hypercholesterolemia (Pu 2021): two-compartment PK with first-order SC absorption (with lag time) and parallel linear plus Michaelis-Menten elimination from the central compartment, linked to a Type 1 indirect-response model for low-density lipoprotein cholesterol (LDL-C) where evinacumab inhibits LDL-C production.
  • Article: CPT Pharmacometrics Syst Pharmacol. 2021;10(11):1412-1421 (open access)

Population

Pu 2021 pooled six evinacumab clinical studies into the population PK analysis dataset (n = 278: 183 healthy volunteers and 95 patients with homozygous familial hypercholesterolemia). The exposure-response (PK/PD) analysis was restricted to the HoFH patients, pooling one phase II and two phase III studies (n = 95, 1194 LDL-C concentrations after outlier removal). Across the studies evinacumab was administered intravenously (5-20 mg/kg, single dose or repeated weekly, every 4 weeks, or every 12 weeks) or subcutaneously (75-450 mg, single dose or repeated weekly or every 2 weeks), either alone or in combination with other lipid-lowering therapies. The US-approved adult / adolescent (>= 12 years) HoFH dose is 15 mg/kg IV every 4 weeks. Median body weight in the PK analysis set was 74.1 kg; median weight in the PK/PD subset (HoFH only) was 71 kg, and median baseline LDL-C was 211 mg/dL (Pu 2021 Table 1 / Table 2 typical-patient definitions). Median baseline ANGPTL3 (the pharmacological target) was 0.08 mg/L and was comparable between the HV and HoFH cohorts. Race was retained as a White (reference) versus Other dichotomy on the maximum drug-induced LDL-C inhibitory effect.

The same information is available programmatically via readModelDb("Pu_2021_evinacumab")$population.

Source trace

Every structural parameter, covariate effect, IIV element, and residual-error term below is taken from Pu 2021 Table 1 (PK final model) and Table 2 (PK/PD final covariate model) and the supplementary control stream (191_supplementary_psp412711-sup-0001-supinfo.docx). PK reference covariates: WT = 74.1 kg, ANGPTL3 = 0.08 mg/L, DIS_HOFH = 0 (HV reference). PK/PD reference covariates: WT = 71 kg, baseline LDL-C = 211 mg/dL, RACE_WHITE = 1 (White reference).

Equation / parameter Value (paper / model file) Source location
lka (Ka) 0.181 /day Table 1, Ka row
lcl (CL at 74.1 kg) 0.0955 L/day Table 1, CL row
lvc (Vc / V2 at 74.1 kg) 2.56 L Table 1, V2 row
lq (Q = K23 * Vc) 0.109 * 2.56 = 0.279 L/day Table 1, K23 row
lvp (Vp = K23 * Vc / K32) 0.109 * 2.56 / 0.124 = 2.252 L Table 1, K23, K32 rows
lvmax (Vmax) 3.16 mg/day Table 1, Vmax row
lkm (Km) 1.02 mg/L Table 1, Km row
llag (Alag) 0.168 day Table 1, Alag row
lfdepot (F for SC) 0.714 Table 1, F row
e_wt_cl (FIXED) 0.75 Table 1, weight ~ linear clearance
e_wt_vc_vp 0.875 Table 1, weight ~ central V (estimated)
e_angptl3_vmax 0.405 Table 1, ANGPTL3 ~ Vmax
e_dis_hofh_vmax -0.289 Table 1, disease state ~ Vmax
var(etalcl) 0.355^2 = 0.126025 (CV ~ 36%) Table 1, sigma eta(CL)
var(etalvc) 0.213^2 = 0.045369 (CV ~ 21%) Table 1, sigma eta(V)
cov(etalcl, etalvc) 0.213 * 0.355 * 0.213 = 0.016108 Table 1, sigma eta(2,1) (correlation)
var(etalka) 0.686^2 = 0.470596 Table 1, sigma eta(Ka)
var(etallag) 1.19^2 = 1.4161 Table 1, sigma eta(Alag1)
addSd (Cc) 0.303 mg/L Table 1, sigma additive
propSd (Cc) 0.189 Table 1, sigma proportional CV%
lkin (Kin) 38.99 mg/dL/day Table 2, Kin row
limax (TVImax at White / 71 kg) log(0.7435) Table 2, Imax row (point estimate 0.74; supplement initial 0.7022)
lic50 (IC50 at LDLC = 211) 57.4 mg/L Table 2, IC50 row
e_wt_imax -0.27 Table 2, Imax ~ weight (power)
e_nonwhite_imax -0.191 Table 2 footnote (theta = -0.191248); model uses (1 - RACE_WHITE)
e_ldlc_ic50 -1.17 Table 2, IC50 ~ baseline LDL (power)
var(etalic50) 3.11 Table 2, sigma eta(IC50)
var(etalkin) 0.47 Table 2, sigma eta(Kin)
addSd_LDL 17.97 mg/dL Table 2, sigma additive
propSd_LDL 0.18 Table 2, sigma proportional
Structure (2-cmt PK + indirect-response LDL) n/a Figure 1 schematic and equations
Vmax = TVVmax * (ANGPTL3/0.08)^0.405 * exp(-0.289 * DIS_HOFH) n/a Table 1 covariate block
Imax = TVImax * (WT/71)^(-0.27) * exp(-0.191 * (1 - RACE_WHITE)) n/a Table 2 supplement; preserves White-reference TVImax = 0.7435
IC50 = TVIC50 * (LDLC / 211)^(-1.17) n/a Table 2 footnote
Kout = Kin / LDLC; LDL(0) = LDLC n/a Figure 1 caption (“baseline LDL-C = Kin / Kout”); supplement A_0(4) = LDLBL

Parameterization notes

  • Rate-constant to Q/Vp re-parameterization. Pu 2021 reports the inter-compartmental kinetics as the rate constants K23 (= 0.109 /day) and K32 (= 0.124 /day) with no IIV. The nlmixr2lib convention names the inter-compartmental clearance and peripheral volume q and vp; the mapping is Q = K23 * Vc and Vp = Q / K32. Because the source parameterizes K23 and K32 as weight-invariant constants, the implied Q and Vp inherit the (WT/74.1)^0.875 allometric exponent from Vc and the model file therefore declares a single shared exponent e_wt_vc_vp.
  • OMEGA in SD/correlation form. Pu 2021 Table 1 reports the lower triangle of OMEGA in SD/correlation form (NONMEM STD and COR print options): sigma(eta_CL) = 0.355, sigma(eta_V) = 0.213, with the off- diagonal sigma(eta_(2,1)) = 0.213 representing the correlation, not the covariance. Conversion to the variance/covariance form used inside ini() is therefore var(CL) = 0.355^2 = 0.126025, var(Vc) = 0.213^2 = 0.045369, and cov(CL, Vc) = 0.213 * 0.355 * 0.213 = 0.016108. The CV percentages predicted from the variances (sqrt(exp(sigma^2) - 1)) reproduce the paper’s prose claim of “36% for linear clearance and 21% for central volume of distribution.” For Ka and Alag1 the OMEGA is diagonal (no covariance), so var(Ka) = 0.686^2 = 0.470596 and var(Alag) = 1.19^2 = 1.4161.
  • PD OMEGA reported directly as variance. The supplement’s $OMEGA 0.602; ETAIC50 and $OMEGA 0.0643; ETAKIN initials, together with the Table 2 final estimates (3.11 for IC50 and 0.47 for Kin), are reported as variances on the internal NONMEM (log) scale, not as SDs. The model file uses these values directly for etalic50 and etalkin. Note that the IC50 random effect carries large between-subject variability (CV ~ 700%, but largely driven by the heavy-tail HoFH cohort distribution; the Pu 2021 bootstrap 95% CI on var(etalic50) is 1.78-5.44).
  • Race coding via the canonical RACE_WHITE column. The Pu 2021 source NM-TRAN dataset uses RAC1 = 1 for non-White and RAC1 = 0 for White. The nlmixr2lib canonical column is RACE_WHITE (1 = White, 0 = non-White). To preserve the paper’s reported White-reference TVImax = 0.7435 unchanged, the model uses (1 - RACE_WHITE) in the exp(e_nonwhite_imax * ...) factor, exactly mirroring the paper’s exp(-0.191 * RAC1) form. This is the same pattern Hu 2014 bapineuzumab uses with the same canonical column.
  • Indirect-response LDL state. The PD compartment carries LDL-C concentration directly (mg/dL). The supplement initialises A_0(4) = LDLBL, meaning the LDL state starts at the per-subject baseline value carried in the data column LDLBL (canonical LDLC). Kout is computed dynamically as Kin / LDLC so that Kin = Kout * LDL_baseline enforces steady state in the absence of drug, exactly matching the supplement’s KOUT = KIN/LDLBL line.
  • PK and PK/PD reference weights differ. PK uses the median pooled HV+HoFH weight (74.1 kg) while PK/PD uses the median HoFH-only weight (71 kg). The model file preserves both reference values verbatim so the published Table 1 and Table 2 parameter values reproduce the source.
  • SC vs IV. Bioavailability and absorption lag apply to the depot compartment. IV doses bypass the depot via cmt = "central" on the dose event. The supplement’s structural model initial estimates retain the bioavailability factor on the depot only; this is preserved here.

Virtual cohort

The simulations below use a virtual HoFH cohort whose covariate distributions approximate Pu 2021 study population medians and ranges. Subject-level data were not released with the paper.

set.seed(20260508)
n_subj <- 200

cohort <- tibble::tibble(
  id          = seq_len(n_subj),
  WT          = pmin(pmax(rnorm(n_subj, mean = 71, sd = 18),  42, 152)),
  ANGPTL3     = pmin(pmax(rlnorm(n_subj, meanlog = log(0.08), sdlog = 0.5),
                          0.0204, 0.287)),
  DIS_HOFH    = 1L,                             # PD analysis is HoFH-only
  LDLC        = pmin(pmax(rnorm(n_subj, mean = 211, sd = 90), 70, 600)),
  RACE_WHITE  = rbinom(n_subj, size = 1, prob = 0.85)
)

Three regimens are simulated in parallel: 15 mg/kg IV q4w (the US-approved adult / adolescent HoFH dose), 5 mg/kg IV q4w (the lower sensitivity-analysis dose in Pu 2021 Table 4), and 450 mg SC qw (the upper-end SC regimen tested in phase I). Dosing extends past the indirect-response time constant (1/Kout, on the order of weeks) to reach LDL-C steady state before any NCA window.

tau_q4w <- 28
n_doses_q4w <- 7                    # 7 q4w doses -> 168 days (~24 weeks; ELIPSE primary endpoint)
dose_days_q4w <- seq(0, tau_q4w * (n_doses_q4w - 1), by = tau_q4w)

tau_qw  <- 7
n_doses_qw <- 28                   # 28 weekly SC doses -> 189 days
dose_days_qw  <- seq(0, tau_qw * (n_doses_qw - 1), by = tau_qw)

make_cohort <- function(cohort, dose_amt_per_kg, dose_days, treatment, tau,
                        cmt_name = "central", id_offset = 0L,
                        sc_fixed_dose = NA_real_) {
  coh <- cohort |> dplyr::mutate(id = id + id_offset)
  ev_dose <- coh |>
    tidyr::crossing(time = dose_days) |>
    dplyr::mutate(amt = if (is.na(sc_fixed_dose)) dose_amt_per_kg * WT else sc_fixed_dose,
                  cmt = cmt_name, evid = 1L,
                  treatment = treatment)
  obs_days <- sort(unique(c(seq(0, max(dose_days) + tau, by = 1),
                            dose_days + 0.1,
                            dose_days + 1)))
  ev_obs_cc <- coh |>
    tidyr::crossing(time = obs_days) |>
    dplyr::mutate(amt = 0, cmt = "Cc",  evid = 0L, treatment = treatment)
  ev_obs_ldl <- coh |>
    tidyr::crossing(time = obs_days) |>
    dplyr::mutate(amt = 0, cmt = "LDL", evid = 0L, treatment = treatment)
  dplyr::bind_rows(ev_dose, ev_obs_cc, ev_obs_ldl) |>
    dplyr::arrange(id, time, dplyr::desc(evid)) |>
    dplyr::select(id, time, amt, cmt, evid, treatment,
                  WT, ANGPTL3, DIS_HOFH, LDLC, RACE_WHITE)
}

events_15 <- make_cohort(cohort, 15, dose_days_q4w, "15 mg/kg IV Q4W", tau_q4w,
                         cmt_name = "central", id_offset = 0L)
events_05 <- make_cohort(cohort,  5, dose_days_q4w,  "5 mg/kg IV Q4W", tau_q4w,
                         cmt_name = "central", id_offset = 1000L)
events_sc <- make_cohort(cohort,  0, dose_days_qw,  "450 mg SC QW",   tau_qw,
                         cmt_name = "depot",   id_offset = 2000L,
                         sc_fixed_dose = 450)
events <- dplyr::bind_rows(events_15, events_05, events_sc)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid", "cmt")])))

Simulation 

mod <- rxode2::rxode2(readModelDb("Pu_2021_evinacumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
keep_cols <- c("WT", "ANGPTL3", "DIS_HOFH", "LDLC", "RACE_WHITE", "treatment")

sim <- lapply(split(events, events$treatment), function(ev) {
  as.data.frame(rxode2::rxSolve(mod, events = ev, keep = keep_cols))
}) |> dplyr::bind_rows()

Replicate published figures

Concentration-time profile (Figure S1 / VPC-style, Figure S5)

Pu 2021 Figure S5 shows visual predictive checks of total evinacumab concentrations stratified by study, disease type, and route. The block below reproduces a VPC-style plot over the first six 4-week cycles for the two IV regimens.

vpc_pk <- sim |>
  dplyr::filter(!is.na(Cc), time > 0, time <= tau_q4w * 6,
                treatment %in% c("15 mg/kg IV Q4W", "5 mg/kg IV Q4W")) |>
  dplyr::group_by(treatment, time) |>
  dplyr::summarise(
    Q025 = quantile(Cc, 0.025, na.rm = TRUE),
    Q50  = quantile(Cc, 0.50,  na.rm = TRUE),
    Q975 = quantile(Cc, 0.975, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_pk, aes(time, Q50, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = Q025, ymax = Q975), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.8) +
  labs(
    x = "Time (days)",
    y = "Total evinacumab Cc (mg/L)",
    title = "Simulated 2.5 / 50 / 97.5 percentile profiles, IV q4w arms",
    caption = "Virtual HoFH cohort (N = 200 per arm); first 6 q4w cycles."
  ) +
  theme_minimal()

LDL-C trajectory (Figure S9 VPC)

Pu 2021 Figure S9 shows VPCs of LDL-C concentration after evinacumab 15 mg/kg IV q4w; the median LDL-C reaches its nadir around weeks 8-12 and remains near nadir through week 24.

vpc_ldl <- sim |>
  dplyr::filter(!is.na(LDL), time >= 0, time <= 168,
                treatment %in% c("15 mg/kg IV Q4W", "5 mg/kg IV Q4W")) |>
  dplyr::group_by(treatment, time) |>
  dplyr::summarise(
    Q025 = quantile(LDL, 0.025, na.rm = TRUE),
    Q50  = quantile(LDL, 0.50,  na.rm = TRUE),
    Q975 = quantile(LDL, 0.975, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_ldl, aes(time, Q50, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = Q025, ymax = Q975), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.8) +
  labs(
    x = "Time (days)",
    y = "LDL-C (mg/dL)",
    title = "Simulated LDL-C trajectory by IV q4w dose",
    caption = "Virtual HoFH cohort (N = 200 per arm); LDL-C target 100 mg/dL shown for reference."
  ) +
  geom_hline(yintercept = 100, linetype = "dashed", colour = "grey40") +
  theme_minimal()

Body-weight impact on linear CL (Figure 2 tornado)

Pu 2021 Figure 2 panel a shows the steady-state AUC ratio for evinacumab spanning the observed weight range (42.4-152 kg) at fixed median ANGPTL3 and HoFH disease status. The CL allometric power is fixed at 0.75 (theoretical), so a 50 kg subject has CL = 0.0955 * (50 / 74.1)^0.75 = 0.0735 L/day (-23%) and a 110 kg subject has CL = 0.0955 * (110 / 74.1)^0.75 = 0.130 L/day (+36%).

wt_grid <- tibble::tibble(WT_kg = c(42.4, 50, 60, 74.1, 90, 110, 130, 152))
TVCL  <- 0.0955
e_wt_cl <- 0.75
wt_grid <- wt_grid |>
  dplyr::mutate(
    CL_Lpd = TVCL * (WT_kg / 74.1)^e_wt_cl,
    pct_vs_medianWT = 100 * (CL_Lpd - TVCL) / TVCL
  )
knitr::kable(wt_grid, digits = 4,
  caption = "Linear CL (typical value) at selected body weights. Reference 74.1 kg = 0.0955 L/day.")
Linear CL (typical value) at selected body weights. Reference 74.1 kg = 0.0955 L/day.
WT_kg CL_Lpd pct_vs_medianWT
42.4 0.0628 -34.2099
50.0 0.0711 -25.5501
60.0 0.0815 -14.6409
74.1 0.0955 0.0000
90.0 0.1105 15.6960
110.0 0.1284 34.4872
130.0 0.1456 52.4382
152.0 0.1637 71.4032

ANGPTL3 impact on Vmax (Figure 2 tornado)

Increasing baseline ANGPTL3 predicts a faster target-mediated Vmax. Pu 2021 Figure 2 spans 0.0204-0.287 mg/L (Min-Max). The reference is the median 0.08 mg/L.

ang_grid <- tibble::tibble(ANGPTL3_mgpL = c(0.0204, 0.05, 0.08, 0.10, 0.15, 0.20, 0.287))
TVVMAX <- 3.16
e_angptl3_vmax <- 0.405
ang_grid <- ang_grid |>
  dplyr::mutate(
    Vmax_HV   = TVVMAX * (ANGPTL3_mgpL / 0.08)^e_angptl3_vmax,
    Vmax_HoFH = TVVMAX * (ANGPTL3_mgpL / 0.08)^e_angptl3_vmax * exp(-0.289),
    ratio_HoFH_vs_HV = exp(-0.289)
  )
knitr::kable(ang_grid, digits = 3,
  caption = "Vmax (typical value) at selected baseline ANGPTL3 concentrations, by disease state. Reference HV at 0.08 mg/L = 3.16 mg/day; HoFH multiplier 0.749 (i.e. -25%).")
Vmax (typical value) at selected baseline ANGPTL3 concentrations, by disease state. Reference HV at 0.08 mg/L = 3.16 mg/day; HoFH multiplier 0.749 (i.e. -25%).
ANGPTL3_mgpL Vmax_HV Vmax_HoFH ratio_HoFH_vs_HV
0.020 1.817 1.361 0.749
0.050 2.612 1.957 0.749
0.080 3.160 2.367 0.749
0.100 3.459 2.591 0.749
0.150 4.076 3.053 0.749
0.200 4.580 3.430 0.749
0.287 5.301 3.971 0.749

LDL-C impact on IC50 (Figure 3 tornado)

Higher baseline LDL-C predicts a smaller IC50, which means greater sensitivity to evinacumab. Pu 2021 Figure 3 spans 39-907 mg/dL (Min-Max randomised) and 70-907 mg/dL (Min-Max ITT, baseline LDL-C > 70 mg/dL). Reference LDL-C is 211 mg/dL.

ldl_grid <- tibble::tibble(LDLC_mgpdL = c(70, 100, 150, 211, 300, 500, 700, 907))
TVIC50 <- 57.4
e_ldlc_ic50 <- -1.17
ldl_grid <- ldl_grid |>
  dplyr::mutate(
    IC50_mgpL = TVIC50 * (LDLC_mgpdL / 211)^e_ldlc_ic50,
    pct_vs_211 = 100 * (IC50_mgpL - TVIC50) / TVIC50
  )
knitr::kable(ldl_grid, digits = 2,
  caption = "IC50 (typical value) at selected baseline LDL-C concentrations. Reference 211 mg/dL = 57.4 mg/L.")
IC50 (typical value) at selected baseline LDL-C concentrations. Reference 211 mg/dL = 57.4 mg/L.
LDLC_mgpdL IC50_mgpL pct_vs_211
70 208.72 263.62
100 137.51 139.56
150 85.56 49.07
211 57.40 0.00
300 38.03 -33.75
500 20.92 -63.56
700 14.11 -75.42
907 10.42 -81.84

PKNCA validation

Non-compartmental analysis of the final (steady-state) q4w dosing interval of the 15 mg/kg IV q4w arm. Compute Cmax, Ctau, AUC0-tau, and Cav per simulated subject.

ss_start_15 <- tau_q4w * (n_doses_q4w - 1)
ss_end_15   <- ss_start_15 + tau_q4w

nca_conc <- sim |>
  dplyr::filter(time >= ss_start_15, time <= ss_end_15, !is.na(Cc),
                treatment == "15 mg/kg IV Q4W") |>
  dplyr::mutate(time_nom = time - ss_start_15) |>
  dplyr::select(id, time = time_nom, Cc, treatment) |>
  # The simulation emits one row per output compartment (Cc and LDL); collapse
  # to one row per (id, time) for PKNCA's uniqueness check.
  dplyr::distinct(id, time, treatment, .keep_all = TRUE)

nca_dose <- cohort |>
  dplyr::mutate(amt = 15 * WT, time = 0, treatment = "15 mg/kg IV Q4W") |>
  dplyr::select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(nca_conc, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(nca_dose, amt ~ time | treatment + id)

intervals <- data.frame(
  start   = 0,
  end     = tau_q4w,
  cmax    = TRUE,
  cmin    = TRUE,
  tmax    = TRUE,
  auclast = TRUE,
  cav     = TRUE
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
nca_summary <- summary(nca_res)
nca_summary
#>  start end       treatment   N      auclast       cmax       cmin
#>      0  28 15 mg/kg IV Q4W 200 13000 [30.0] 804 [20.1] 328 [42.7]
#>                  tmax        cav
#>  0.000 [0.000, 0.000] 465 [30.0]
#> 
#> Caption: auclast, cmax, cmin, cav: geometric mean and geometric coefficient of variation; tmax: median and range; N: number of subjects

Comparison against published steady-state troughs

Pu 2021 Results Section3.1 reports mean (SD) evinacumab trough concentrations at steady state of 171.8 (40.1) mg/L, 245.6 (102.7) mg/L, and 275.8 (91.9) mg/L for HoFH patients with body weights of <= 60 kg, 60-80 kg, and > 80 kg, respectively, on the 15 mg/kg IV q4w regimen. The block below stratifies the simulated steady-state troughs by the same weight bins.

trough_sim <- sim |>
  dplyr::filter(treatment == "15 mg/kg IV Q4W",
                time == ss_end_15, !is.na(Cc)) |>
  dplyr::mutate(WT_bin = dplyr::case_when(
    WT <= 60        ~ "<= 60 kg",
    WT > 60 & WT <= 80 ~ "60-80 kg",
    TRUE            ~ "> 80 kg"
  )) |>
  dplyr::group_by(WT_bin) |>
  dplyr::summarise(
    n      = dplyr::n(),
    mean_Cc = mean(Cc),
    sd_Cc   = stats::sd(Cc),
    .groups = "drop"
  )

published <- tibble::tibble(
  WT_bin = c("<= 60 kg", "60-80 kg", "> 80 kg"),
  mean_Cc_paper = c(171.8, 245.6, 275.8),
  sd_Cc_paper   = c(40.1, 102.7, 91.9)
)

trough_compare <- dplyr::full_join(trough_sim, published, by = "WT_bin") |>
  dplyr::mutate(pct_diff_mean = 100 * (mean_Cc - mean_Cc_paper) / mean_Cc_paper)

knitr::kable(trough_compare, digits = 1,
  caption = "Simulated vs Pu 2021 Results Section3.1 steady-state evinacumab trough concentrations (mg/L) by body-weight bin, 15 mg/kg IV q4w (HoFH cohort). Differences > 20% would warrant investigation.")
Simulated vs Pu 2021 Results Section3.1 steady-state evinacumab trough concentrations (mg/L) by body-weight bin, 15 mg/kg IV q4w (HoFH cohort). Differences > 20% would warrant investigation.
WT_bin n mean_Cc sd_Cc mean_Cc_paper sd_Cc_paper pct_diff_mean
> 80 kg 400 354.3 132.1 275.8 91.9 28.5
<= 60 kg NA NA NA 171.8 40.1 NA
60-80 kg NA NA NA 245.6 102.7 NA

Comparison against published LDL-C reduction targets

Pu 2021 Table 3 reports the predicted percentage of HoFH patients achieving prespecified LDL-C reduction targets at week 24 with 15 mg/kg IV q4w (post-hoc PK/PD prediction): >= 30% reduction in 86.3%, >= 50% in 56.8%, >= 70% in 8.4%, and LDL-C < 100 mg/dL in 52.6%. The block below stratifies the simulated cohort at week 24 (the ELIPSE primary endpoint).

week24 <- sim |>
  dplyr::filter(treatment == "15 mg/kg IV Q4W",
                time == 168, !is.na(LDL)) |>
  dplyr::mutate(pct_change = 100 * (LDL - LDLC) / LDLC)

target_summary <- tibble::tibble(
  target = c(">= 30% reduction", ">= 50% reduction",
             ">= 70% reduction", "LDL-C < 100 mg/dL"),
  pct_paper = c(86.3, 56.8, 8.4, 52.6),
  pct_sim   = c(
    100 * mean(week24$pct_change <= -30),
    100 * mean(week24$pct_change <= -50),
    100 * mean(week24$pct_change <= -70),
    100 * mean(week24$LDL          <  100)
  )
) |>
  dplyr::mutate(abs_diff_pp = pct_sim - pct_paper)

knitr::kable(target_summary, digits = 1,
  caption = "Simulated vs Pu 2021 Table 3 percentage of HoFH patients achieving LDL-C goals at week 24 with 15 mg/kg IV q4w. Absolute differences are in percentage points.")
Simulated vs Pu 2021 Table 3 percentage of HoFH patients achieving LDL-C goals at week 24 with 15 mg/kg IV q4w. Absolute differences are in percentage points.
target pct_paper pct_sim abs_diff_pp
>= 30% reduction 86.3 93.5 7.2
>= 50% reduction 56.8 67.5 10.7
>= 70% reduction 8.4 0.0 -8.4
LDL-C < 100 mg/dL 52.6 0.0 -52.6

Assumptions and deviations

  • Compartment naming. The PD compartment is named LDL (paper-named) rather than the canonical effect, mirroring Pu 2021 Figure 1 which labels the indirect-response state “LDL”. This is a paper-name deviation acknowledged in checkModelConventions() output and is the same pattern used by Aguiar 2021 ustekinumab (fc for fecal calprotectin). The canonical convention does not yet register a cardiometabolic biomarker compartment.
  • Race coding via (1 - RACE_WHITE). The Pu 2021 source-data column encodes 1 = non-White and 0 = White; the canonical nlmixr2lib column RACE_WHITE flips this convention. The model therefore writes exp(e_nonwhite_imax * (1 - RACE_WHITE)) so the published White-reference TVImax = 0.7435 reproduces unchanged. This matches the Hu 2014 bapineuzumab pattern documented in inst/references/covariate-columns.md for the same canonical column.
  • Per-subject baseline LDL-C is held time-fixed. The data column LDLC carries the per-subject baseline value (constant across rows for a given subject) and is used both to initialise the LDL state (LDL(0) <- LDLC) and to drive the IC50 covariate effect. This is the paper’s parameterization (supplement M_LDLBL = 211; A_0(4) = LDLBL). Users who supply time-varying observed LDL-C in the same column will trigger spurious time-dependent IC50 dynamics – the column is meant for the baseline value only.
  • PK and PK/PD reference weights differ. PK reference is 74.1 kg (median pooled HV+HoFH); PK/PD reference is 71 kg (median HoFH-only). Both are preserved verbatim so the published Table 1 and Table 2 parameter values reproduce the source. A typical-value HoFH simulation would use WT close to 71 kg; mixed PK/PD comparisons against the pooled-population CL/V at 74.1 kg would require WT close to 74.1 kg.
  • PK/PD layer fits HoFH only; HV PK/PD parameters are not extrapolated. The PK/PD fit uses 95 HoFH patients (no HV PD observations). Simulating LDL-C trajectories for HV (DIS_HOFH = 0) with this model is therefore an extrapolation outside the fitted domain. The PK component remains valid for HV via the DIS_HOFH = 0 Vmax modulation.
  • DIS_HOFH appears at the PK level only. The disease-state effect on Vmax (-0.289) was fit on the pooled HV+HoFH PK dataset. The PK/PD model has no DIS_HOFH covariate (since the PD analysis set is HoFH-only). The model file therefore does not declare a DIS_HOFH-on-PD parameter – covariate coverage matches the source.
  • Virtual-cohort covariate distributions. Body weight is drawn from N(71, 18) kg truncated to [42.4, 152]; baseline ANGPTL3 from lognormal(meanlog = log(0.08), sdlog = 0.5) truncated to [0.0204, 0.287]; baseline LDL-C from N(211, 90) truncated to [70, 600]; RACE_WHITE = Bernoulli(0.85) (Pu 2021 does not publish per-subject race fractions; 85% reflects the typical White predominance in HoFH trials and is documented as an approximation). These distributions are illustrative and approximate the published covariate ranges but do not exactly reproduce the per-subject distributions.
  • Imax bounded only implicitly by typical covariate ranges. The model parameterizes imax = exp(limax) * (WT/71)^e_wt_imax * exp(...) with no logit transform. For the published covariate ranges Imax stays below 1; pathological combinations (very low weight + White) could push the typical-value Imax above 1 and produce non-physical negative LDL-C production rates. The supplement bounds TVIMAX between 0.5 and 1 in $THETA; users running uncertainty-propagation simulations should clamp imax accordingly.
  • No unit conversion on concentrations. Dose units are mg, central volume units are L, so central / vc yields mg/L (= ug/mL) directly for evinacumab Cc. LDL-C is in mg/dL throughout the PD layer. PKNCA uses mg/L for evinacumab and day for time, matching units in the model file.