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Martinez_2019_alirocumab

Source: vignettes/articles/Martinez_2019_alirocumab.Rmd
Martinez_2019_alirocumab.Rmd

Model and source

  • Citation: Martinez JM, Brunet A, Hurbin F, DiCioccio AT, Rauch C, Fabre D. Population Pharmacokinetic Analysis of Alirocumab in Healthy Volunteers or Hypercholesterolemic Subjects Using a Michaelis-Menten Approximation of a Target-Mediated Drug Disposition Model - Support for a Biologics License Application Submission: Part I. Clin Pharmacokinet. 2019;58(1):101-113. doi:10.1007/s40262-018-0669-y
  • Description: Two-compartment population PK model for alirocumab in healthy volunteers and adults with hypercholesterolemia (Martinez 2019, Part I), with first-order SC absorption (with lag time), linear plus Michaelis-Menten (target-mediated) elimination from the central compartment, and logit-transformed bioavailability.
  • Article: Clin Pharmacokinet. 2019;58(1):101-113 (open access via PMC6325993)

Part II of the same series (doi:10.1007/s40262-018-0670-5) couples this PopPK model to an indirect-response LDL-C model; only the Part I PK structure is implemented here.

Population

Martinez 2019 pooled 13 phase I-III alirocumab trials into a final population PK dataset of 2799 subjects and 13,717 serum concentrations. The dataset consisted of healthy volunteers and adult patients with hypercholesterolemia (familial and non-familial, with or without established coronary heart disease), including two Japanese phase I/II cohorts. Dosing was SC 50-300 mg single or repeated (Q2W / Q4W over up to 104 weeks, truncated at 24 weeks for the current analysis); one phase I study gave single IV doses of 0.3-12 mg/kg. The marketed regimens are 75 mg and 150 mg SC Q2W.

Baseline characteristics from the Martinez 2019 Table 2 footnotes: median body weight 82.9 kg, median age 60 years, and time-varying median free PCSK9 concentration 72.9 ng/mL (baseline median 283 ng/mL; time-varying 5th/95th percentiles 0/392 ng/mL). Concomitant statin use (rosuvastatin < 20 mg/day, atorvastatin < 40 mg/day, or simvastatin at any dose) was the other clinically-relevant covariate retained in the final model. Sex, race, renal function, BMI, and ADA positivity were evaluated but not retained.

The same information is available programmatically via readModelDb("Martinez_2019_alirocumab")$population.

Source trace

Every structural parameter, covariate effect, IIV element, and residual-error term below is taken from Martinez 2019 Table 2 (“Final model with covariates” column) and its footnotes a-e. Reference covariate values: 82.9 kg body weight, 60 years age, no concomitant statin (STATIN = 0), and 72.9 ng/mL free PCSK9.

Equation / parameter Value (paper / model file) Source location
lka (Ka) 0.00768 /h * 24 = 0.18432 /day Table 2, Ka row
lcl (CLL) 0.0124 L/h * 24 = 0.2976 L/day Table 2, CLL row
lvc (V2) 3.19 L Table 2, V2 row
lvp (V3 at AGE = 60 y) 2.79 L Table 2, V3 row
lq (Q) 0.0185 L/h * 24 = 0.444 L/day Table 2, Q row
lvm (Vm) 0.183 mg/h * 24 = 4.392 mg/day Table 2, Vm row (text says “mg/h”; table footer “mg.h/L” is a typesetting error — dimensional analysis and the paper’s narrative confirm mg/h)
lkm (Km at FPCSK9 = 72.9) 7.73 mg/L Table 2, Km row
llag (LAG) 0.641 h / 24 = 0.02671 day Table 2, LAG row
logitfdepot (logit F_pop) logit(0.862) = 1.8326 Table 2, F row (typical F = 0.862)
e_wt_cl (WT additive slope) 2.92e-4 L/h/kg * 24 = 7.008e-3 L/day/kg Table 2 theta12, Table 2 footnote a
e_statin_cl (STATIN additive) 6.44e-3 L/h * 24 = 0.15456 L/day Table 2 theta13, Table 2 footnote a
e_age_vp (AGE power exponent) 0.310 Table 2 theta15, Table 2 footnote b
e_fpcsk9_km (FPCSK9 slope) -0.541 mg/L per (FPCSK9/72.9) Table 2 theta14, Table 2 footnote c
var(etalcl) 0.232 (CV 48.2%) Table 2, omega^2 CLL row
var(etalvc) 0.589 (CV 76.7%) Table 2, omega^2 V2 row
var(etalvp) 0.0735 (CV 27.1%) Table 2, omega^2 V3 row
var(etalkm) 0.298 (CV 54.6%) Table 2, omega^2 Km row
cov(etalvp, etalkm) -0.793 * sqrt(0.0735*0.298) = -0.11738 Table 2 footnote d (r = -0.793)
var(etalogitfdepot) 1.060 (logit-space, 103%) Table 2 omega^2 F row, footnote e
propSd 0.259 (25.9%) Table 2, theta8
addSd 0.0465 mg/L Table 2, theta9
Structure (2-cmt + 1st-order SC, linear + MM from central) n/a Fig. 1 and Results §3.1
CLL equation TVCLL + COV1*(WT - 82.9) + COV2*STATIN Table 2 footnote a, Eq in Results §3.1
Km equation TVKM + COV3*(FPCSK9 / 72.9) Table 2 footnote c, Eq in Results §3.1
V3 equation TVV3 * (AGE / 60)^COV4 Table 2 footnote b, Eq in Results §3.1

Parameterization notes

  • Time-unit conversion. Martinez 2019 reports rates in h^-1; the model file converts to day^-1 (x 24) to follow the nlmixr2lib convention. Volumes (V2, V3), the bioavailability factor, and the FPCSK9 / AGE / WT covariate normalizations are time-independent and are carried through unchanged.
  • Additive covariate structure on CLL and Km. Martinez’s paper uses additive (rather than multiplicative) covariate models on the linear clearance CLL and on Km, evaluated on the population typical value: CLL_TV = TVCLL + theta * (WT - 82.9) + theta * STATIN and Km_TV = TVKM + theta * (FPCSK9 / 72.9). Individual values then carry an exponential between-subject term: CLL_i = CLL_TV * exp(eta_CLL). This is preserved faithfully in model() rather than being refactored to a multiplicative / power form.
  • Power covariate on V3. V3_TV = TVV3 * (AGE / 60)^0.310 (Table 2 footnote b). Individual V3 is V3_i = V3_TV * exp(eta_V3).
  • Correlated V3 / Km. The paper reports an omega-block covariance between eta_V3 and eta_Km with correlation r = -0.793 (Table 2 footnote d). The 2x2 block off-diagonal is the correlation times sqrt(var_V3 * var_Km), i.e. -0.793 * sqrt(0.0735 * 0.298) = -0.11738.
  • Logit bioavailability. F IIV was estimated in logit space with omega^2 = 1.060 (Table 2 footnote e). The model parameterizes logitfdepot = logit(0.862) with eta_logit_F ~ N(0, 1.060); the individual F is the inverse logit of the sum.
  • No IIV on Ka / Q / Vm / LAG. Martinez states no interindividual term could be estimated for these four parameters; the model file omits them from the random-effects block, matching the paper.
  • Michaelis-Menten form. The elimination ODE term is - vm * Cc / (km + Cc) (rate of amount elimination with Vm in mg/day, Km in mg/L, and Cc = central / V2 in mg/L), matching the popPK convention used in Xu 2019 sarilumab and the in-file parameter units.
  • SC vs IV. The bioavailability factor and lag time are applied to the depot compartment. IV doses (the 0.3-12 mg/kg single-dose phase I study) bypass depot by dosing directly to central via cmt = "central".

Virtual cohort

The simulations below use a virtual cohort whose covariate distributions approximate the Martinez 2019 study population medians and ranges. No subject-level observed data were released with the paper.

set.seed(20260424)
n_subj <- 300

cohort <- tibble::tibble(
  id     = seq_len(n_subj),
  WT     = pmin(pmax(rnorm(n_subj, mean = 82.9, sd = 18),  45, 150)),
  AGE    = pmin(pmax(rnorm(n_subj, mean = 60,   sd = 12),  18,  90)),
  STATIN = rbinom(n_subj, size = 1, prob = 0.80),
  FPCSK9 = pmin(pmax(rnorm(n_subj, mean = 72.9, sd = 120), 0,  400))
)

Three regimens are simulated in parallel: 75 mg SC Q2W (lower-dose standard), 150 mg SC Q2W (higher-dose standard), and 300 mg SC Q4W (equal 4-week dose to 150 mg Q2W, tested in phase I/II). Dosing extends past the alirocumab terminal half-life (~14-21 days in the linear range at high concentrations) to reach steady state before the NCA interval.

tau_q2w <- 14                 # Q2W dosing interval (days)
n_doses <- 26                 # 26 Q2W doses -> 350 days (~50 weeks), steady state
dose_days_q2w <- seq(0, tau_q2w * (n_doses - 1), by = tau_q2w)

tau_q4w <- 28
n_doses_q4w <- 13
dose_days_q4w <- seq(0, tau_q4w * (n_doses_q4w - 1), by = tau_q4w)

make_cohort <- function(cohort, dose_amt, dose_days, treatment, tau,
                        id_offset = 0L) {
  coh <- cohort |> dplyr::mutate(id = id + id_offset)
  ev_dose <- coh |>
    tidyr::crossing(time = dose_days) |>
    dplyr::mutate(amt = dose_amt, cmt = "depot", evid = 1L,
                  treatment = treatment)
  obs_days <- sort(unique(c(
    seq(0, max(dose_days) + tau, by = 1),
    dose_days + 0.25,
    dose_days + 1,
    dose_days + 3,
    dose_days + 7
  )))
  ev_obs <- coh |>
    tidyr::crossing(time = obs_days) |>
    dplyr::mutate(amt = 0, cmt = NA_character_, evid = 0L,
                  treatment = treatment)
  dplyr::bind_rows(ev_dose, ev_obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid)) |>
    dplyr::select(id, time, amt, cmt, evid, treatment,
                  WT, AGE, STATIN, FPCSK9)
}

events_75  <- make_cohort(cohort, 75,  dose_days_q2w, "75mg_Q2W",  tau_q2w,
                          id_offset = 0L)
events_150 <- make_cohort(cohort, 150, dose_days_q2w, "150mg_Q2W", tau_q2w,
                          id_offset = 1000L)
events_300 <- make_cohort(cohort, 300, dose_days_q4w, "300mg_Q4W", tau_q4w,
                          id_offset = 2000L)
events <- dplyr::bind_rows(events_75, events_150, events_300)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- rxode2::rxode2(readModelDb("Martinez_2019_alirocumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
keep_cols <- c("WT", "AGE", "STATIN", "FPCSK9", "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 (VPC-style)

Martinez 2019 Figure 2 shows visual predictive checks of serum alirocumab concentrations per study, with predictions capturing the 2.5th-97.5th percentiles of observed concentrations. The block below reproduces a VPC-style plot over the first eight Q2W cycles for the 75 mg and 150 mg regimens.

vpc <- sim |>
  dplyr::filter(!is.na(Cc), time > 0, time <= 112,
                treatment %in% c("75mg_Q2W", "150mg_Q2W")) |>
  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, 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 = "Alirocumab Cc (mg/L)",
    title = "Simulated 2.5-50-97.5 percentile profiles: 75 vs 150 mg SC Q2W",
    caption = "Virtual hypercholesterolemic cohort (N = 300 per arm); first 8 Q2W cycles."
  ) +
  theme_minimal()

Steady-state cycle

The final Q2W dosing interval in the 350-day simulation window is used for the steady-state NCA below (ss_start to ss_end).

ss_start <- tau_q2w * (n_doses - 1)
ss_end   <- ss_start + tau_q2w

ss_summary <- sim |>
  dplyr::filter(time >= ss_start, time <= ss_end, !is.na(Cc),
                treatment %in% c("75mg_Q2W", "150mg_Q2W")) |>
  dplyr::group_by(treatment, 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(ss_summary, aes(time - ss_start, Q50, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.8) +
  labs(
    x = "Time within Q2W interval (days)",
    y = "Alirocumab Cc (mg/L)",
    title = "Steady-state Q2W cycle (final 14-day interval)",
    caption = "Median and 90% prediction interval."
  ) +
  theme_minimal()

Body-weight impact on CLL

Martinez 2019 reports that CLL decreases by 78% for a 50 kg subject and increases by 40% for a 100 kg subject versus a typical 82.9 kg subject (Results §3.2). The block below reproduces those numbers directly from the additive covariate equation.

wt_grid <- tibble::tibble(
  WT_kg = c(50, 60, 70, 82.9, 90, 100, 110)
)
TVCLL    <- 0.0124                              # L/h (Martinez 2019 Table 2)
coef_wt  <- 2.92e-4                             # L/h/kg
wt_grid <- wt_grid |>
  dplyr::mutate(
    CLL_Lph = TVCLL + coef_wt * (WT_kg - 82.9),
    pct_vs_medianWT = 100 * (CLL_Lph - TVCLL) / TVCLL
  )
knitr::kable(wt_grid, digits = 4,
  caption = "CLL (typical value, STATIN = 0) at selected body weights. Paper: -78% at 50 kg, +40% at 100 kg.")
CLL (typical value, STATIN = 0) at selected body weights. Paper: -78% at 50 kg, +40% at 100 kg.
WT_kg CLL_Lph pct_vs_medianWT
50.0 0.0028 -77.4742
60.0 0.0057 -53.9258
70.0 0.0086 -30.3774
82.9 0.0124 0.0000
90.0 0.0145 16.7194
100.0 0.0174 40.2677
110.0 0.0203 63.8161

Age impact on V3

Martinez reports V3 = 2.79 L at 60 y, 2.86 L at 65 y, 2.99 L at 75 y.

age_grid <- tibble::tibble(
  AGE_y = c(30, 45, 60, 65, 75, 85)
) |>
  dplyr::mutate(V3_L = 2.79 * (AGE_y / 60)^0.310)
knitr::kable(age_grid, digits = 3,
  caption = "V3 (typical value) at selected ages. Paper: 2.79 L @ 60 y, 2.86 L @ 65 y, 2.99 L @ 75 y.")
V3 (typical value) at selected ages. Paper: 2.79 L @ 60 y, 2.86 L @ 65 y, 2.99 L @ 75 y.
AGE_y V3_L
30 2.251
45 2.552
60 2.790
65 2.860
75 2.990
85 3.108

Free PCSK9 impact on Km

Martinez reports Km = 7.73 mg/L at FPCSK9 = 0 and Km = 4.82 mg/L at FPCSK9 = 392 ng/mL (Results §3.2). Note: the paper’s prose reports the equation output units in the same “mg/L” scale as the Km typical value; its call-out of “7.73 ng/mL” and “4.82 ng/mL” at Figure 2 is a typographical slip — dimensional consistency requires mg/L.

fp_grid <- tibble::tibble(
  FPCSK9_ngml = c(0, 72.9, 200, 392)
) |>
  dplyr::mutate(Km_mgL = 7.73 + (-0.541) * (FPCSK9_ngml / 72.9))
knitr::kable(fp_grid, digits = 3,
  caption = "Km (typical value) at selected free PCSK9 concentrations. Paper: 7.73 mg/L at 0 ng/mL, 4.82 mg/L at 392 ng/mL.")
Km (typical value) at selected free PCSK9 concentrations. Paper: 7.73 mg/L at 0 ng/mL, 4.82 mg/L at 392 ng/mL.
FPCSK9_ngml Km_mgL
0.0 7.730
72.9 7.189
200.0 6.246
392.0 4.821

PKNCA validation

Non-compartmental analysis of the final (steady-state) Q2W dosing interval. Compute Cmax, Ctau, AUC0-tau, and Cav per simulated subject and treatment.

nca_conc <- sim |>
  dplyr::filter(time >= ss_start, time <= ss_end, !is.na(Cc),
                treatment %in% c("75mg_Q2W", "150mg_Q2W")) |>
  dplyr::mutate(time_nom = time - ss_start) |>
  dplyr::select(id, time = time_nom, Cc, treatment)

nca_dose <- dplyr::bind_rows(
  cohort |> dplyr::mutate(id = id,        time = 0, amt =  75, treatment = "75mg_Q2W"),
  cohort |> dplyr::mutate(id = id + 1000L, time = 0, amt = 150, treatment = "150mg_Q2W")
) |>
  dplyr::select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(nca_conc, Cc ~ time | treatment + id,
                             concu = "mg/L", timeu = "day")
dose_obj <- PKNCA::PKNCAdose(nca_dose, amt ~ time | treatment + id,
                             doseu = "mg")

intervals <- data.frame(
  start   = 0,
  end     = tau_q2w,
  cmax    = TRUE,
  cmin    = TRUE,
  tmax    = TRUE,
  auclast = TRUE,
  cav     = TRUE
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
#>  ■■■■■■■■■■■■■■■■■■■■              65% |  ETA:  2s
summary(nca_res)
#>  Interval Start Interval End treatment   N AUClast (day*mg/L) Cmax (mg/L)
#>               0           14 150mg_Q2W 300        95.9 [52.6] 10.1 [46.0]
#>               0           14  75mg_Q2W 300        42.4 [49.4] 4.67 [41.3]
#>  Cmin (mg/L)        Tmax (day)  Cav (mg/L)
#>  3.19 [81.0] 3.00 [1.00, 5.00] 6.85 [52.6]
#>  1.32 [80.1] 3.00 [1.00, 5.00] 3.03 [49.4]
#> 
#> 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 exposures

Martinez 2019 reports a reference steady-state AUC(0-336h) of 2170 mg*h/L for 75 mg Q2W in patients weighing 50-100 kg (Results §3.3). With a typical patient (IIV zeroed) and the paper’s STATIN-coadministration prevalence (~80% in the phase III pooled dataset), the simulated steady-state AUC should be close to that value. The typical-patient Cmax and Ctrough also have reasonable phase-III comparators.

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

typical_cov <- function(statin) {
  tibble::tibble(
    id = 1L, WT = 82.9, AGE = 60, STATIN = statin, FPCSK9 = 72.9
  )
}

ev_typ <- function(dose_amt, dose_days, cov_row) {
  ev_dose <- cov_row |>
    tidyr::crossing(time = dose_days) |>
    dplyr::mutate(amt = dose_amt, cmt = "depot", evid = 1L)
  obs_times <- sort(unique(c(
    seq(ss_start, ss_end, by = 0.05),
    dose_days
  )))
  ev_obs <- cov_row |>
    tidyr::crossing(time = obs_times) |>
    dplyr::mutate(amt = 0, cmt = NA_character_, evid = 0L)
  dplyr::bind_rows(ev_dose, ev_obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid)) |>
    dplyr::select(id, time, amt, cmt, evid, WT, AGE, STATIN, FPCSK9)
}

ss_metrics <- function(sim_df, label) {
  ss <- sim_df |>
    dplyr::filter(time >= ss_start, time <= ss_end, !is.na(Cc)) |>
    dplyr::arrange(time)
  tibble::tibble(
    treatment    = label,
    Cmax_mgpL    = max(ss$Cc),
    Ctrough_mgpL = ss$Cc[which.max(ss$time)],
    AUC_mghpL    = sum(diff(ss$time) *
                       (head(ss$Cc, -1) + tail(ss$Cc, -1)) / 2) * 24
  )
}

sim_typ_75_st0  <- as.data.frame(rxode2::rxSolve(mod_typical,
                                                 events = ev_typ(75,  dose_days_q2w, typical_cov(0))))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalkm', 'etalogitfdepot'
sim_typ_75_st1  <- as.data.frame(rxode2::rxSolve(mod_typical,
                                                 events = ev_typ(75,  dose_days_q2w, typical_cov(1))))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalkm', 'etalogitfdepot'
sim_typ_150_st0 <- as.data.frame(rxode2::rxSolve(mod_typical,
                                                 events = ev_typ(150, dose_days_q2w, typical_cov(0))))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalkm', 'etalogitfdepot'
sim_typ_150_st1 <- as.data.frame(rxode2::rxSolve(mod_typical,
                                                 events = ev_typ(150, dose_days_q2w, typical_cov(1))))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalkm', 'etalogitfdepot'

typ_tbl <- dplyr::bind_rows(
  ss_metrics(sim_typ_75_st0,  "75 mg Q2W | no statin"),
  ss_metrics(sim_typ_75_st1,  "75 mg Q2W | + statin"),
  ss_metrics(sim_typ_150_st0, "150 mg Q2W | no statin"),
  ss_metrics(sim_typ_150_st1, "150 mg Q2W | + statin")
)

# Paper's reference AUC_0-336h was 2170 mg*h/L for 75 mg Q2W, 50-100 kg patients
# (Results §3.3). The phase III pooled population is ~80% statin-coadministered;
# a population-weighted typical AUC of 0.8 * (75 mg + statin) + 0.2 * (75 mg no
# statin) should bracket the reported 2170 mg*h/L value.
wt_75 <- 0.8 * typ_tbl$AUC_mghpL[typ_tbl$treatment == "75 mg Q2W | + statin"] +
         0.2 * typ_tbl$AUC_mghpL[typ_tbl$treatment == "75 mg Q2W | no statin"]

published <- tibble::tibble(
  comparator = "75 mg Q2W, 50-100 kg, population-weighted (80% statin)",
  AUC_paper_mghpL = 2170,
  AUC_sim_mghpL   = wt_75,
  pct_diff        = 100 * (wt_75 - 2170) / 2170
)

knitr::kable(typ_tbl, digits = 2,
  caption = "Typical-patient steady-state exposures (IIV zeroed) at 82.9 kg / 60 y / FPCSK9 = 72.9 ng/mL with / without concomitant statin.")
Typical-patient steady-state exposures (IIV zeroed) at 82.9 kg / 60 y / FPCSK9 = 72.9 ng/mL with / without concomitant statin.
treatment Cmax_mgpL Ctrough_mgpL AUC_mghpL
75 mg Q2W | no statin 9.77 5.10 2645.69
75 mg Q2W | + statin 7.76 3.38 1982.24
150 mg Q2W | no statin 24.01 14.39 6787.25
150 mg Q2W | + statin 17.82 8.72 4725.50 
knitr::kable(published, digits = 1,
  caption = "Comparison vs. Martinez 2019 Results §3.3 reference AUC(0-336h) = 2170 mg*h/L for 75 mg Q2W in 50-100 kg phase III patients (population-weighted 80% statin coadministration).")
Comparison vs. Martinez 2019 Results §3.3 reference AUC(0-336h) = 2170 mg*h/L for 75 mg Q2W in 50-100 kg phase III patients (population-weighted 80% statin coadministration).
comparator AUC_paper_mghpL AUC_sim_mghpL pct_diff
75 mg Q2W, 50-100 kg, population-weighted (80% statin) 2170 2114.9 -2.5

Statin impact on AUC

Martinez 2019 reports a 28-29% decrease in steady-state AUC(0-336h) when statins are coadministered to a typical patient, at both the 75 mg and 150 mg dose levels.

statin_tbl <- tibble::tibble(
  dose = c("75 mg Q2W", "150 mg Q2W"),
  AUC_no_statin = c(
    typ_tbl$AUC_mghpL[typ_tbl$treatment == "75 mg Q2W | no statin"],
    typ_tbl$AUC_mghpL[typ_tbl$treatment == "150 mg Q2W | no statin"]
  ),
  AUC_statin    = c(
    typ_tbl$AUC_mghpL[typ_tbl$treatment == "75 mg Q2W | + statin"],
    typ_tbl$AUC_mghpL[typ_tbl$treatment == "150 mg Q2W | + statin"]
  )
) |>
  dplyr::mutate(
    pct_decrease_sim = 100 * (1 - AUC_statin / AUC_no_statin),
    pct_decrease_pub = 28.5
  )
knitr::kable(statin_tbl, digits = 1,
  caption = "Simulated steady-state AUC(0-336h) with/without concomitant statin. Paper: ~28-29% decrease at both dose levels.")
Simulated steady-state AUC(0-336h) with/without concomitant statin. Paper: ~28-29% decrease at both dose levels.
dose AUC_no_statin AUC_statin pct_decrease_sim pct_decrease_pub
75 mg Q2W 2645.7 1982.2 25.1 28.5
150 mg Q2W 6787.3 4725.5 30.4 28.5

Assumptions and deviations

  • Vm units. The paper’s Table 2 header lists Vm in “mg.h/L” while its main-text prose states “Vm (mg/h)”. Dimensional analysis and comparison against the reported steady-state AUC support the main-text interpretation (Vm as a rate of mass elimination in mg/h). The table header is treated as a typesetting error. This is recorded in the in-file source-trace comment for lvm and documented in the comparison table above.
  • Km units in Figure 2 commentary. Section 3.2 states Km = 7.73 ng/mL at FPCSK9 = 0 and Km = 4.82 ng/mL at FPCSK9 = 392 ng/mL. These are inconsistent with Table 2’s Km in mg/L; the numerical values are correct (7.73 and 4.82) but the units should be mg/L, not ng/mL. This model uses mg/L uniformly, matching Table 2.
  • Virtual-cohort covariate distributions. Body weight is drawn from N(82.9, 18) kg truncated to [45, 150]; age from N(60, 12) truncated to [18, 90]; STATIN = Bernoulli(0.8) (phase III pooled prevalence); FPCSK9 from N(72.9, 120) ng/mL truncated to [0, 400] to approximate the 5th-95th percentile range of 0-392 ng/mL. The paper does not release subject-level distributions; these assumptions are approximations.
  • FPCSK9 treated as a covariate, not a state. Alirocumab binds and depletes free PCSK9 (a true TMDD feedback mechanism), so in reality free PCSK9 is dynamically coupled to alirocumab concentration. The paper short-circuits this by treating time-varying free PCSK9 as an exogenous covariate on Km (Martinez 2019 §3.2, first paragraph). For simulation purposes this means the user must supply an FPCSK9 time course; holding FPCSK9 constant at 72.9 ng/mL (as done in the typical-patient comparison) approximates the steady-state population median but does not capture the transient early-dose suppression of free PCSK9.
  • Phase III statin prevalence. The 80% weighting used in the population-weighted AUC comparison is an estimate — the phase III ODYSSEY studies (COMBO II, FH I, LONG TERM, MONO) mix statin-treated (COMBO II, FH I, LONG TERM) and statin-free (MONO) populations. Exact pooled prevalence is not published for the Martinez 2019 dataset.
  • IV dosing. The phase I single-dose IV study (0.3-12 mg/kg) is not exercised in this vignette. Users can dose to cmt = "central" to bypass the depot, F, and lag for IV comparisons.
  • IV/SC bioavailability. The typical F = 0.862 and its logit-space IIV apply to SC administration only. IV doses should bypass the depot (see the previous bullet).
  • No unit conversion on concentration. Dose units are mg and volume units are L, so central / vc yields mg/L directly. PKNCA uses mg/L for concentration and day for time, matching units in the model file.