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TAK-079 anti-CD38 mAb in cynomolgus monkey (Roepcke 2018)

Source: vignettes/articles/Roepcke_2018_tak_079.Rmd
Roepcke_2018_tak_079.Rmd

Model and source

  • Citation: Roepcke S, Plock N, Yuan J, Fedyk ER, Lahu G, Zhao L, Smithson G. Pharmacokinetics and pharmacodynamics of the cytolytic anti-CD38 human monoclonal antibody TAK-079 in monkey - model assisted preparation for the first in human trial. Pharmacol Res Perspect. 2018;6(3):e00402. doi:10.1002/prp2.402. PMID 29864242.
  • Description: Preclinical (cynomolgus monkey) two-compartment QSS-TMDD population PK model of the cytolytic anti-CD38 human IgG1-kappa monoclonal antibody TAK-079, pooled from eight monkey studies over the dose range 0.03-100 mg/kg IV / SC. Three sequential PK-PD models add lymphocyte-depletion endpoints on the same PK backbone: an NK-cell turnover model with Emax on the elimination rate; a B-cell four-transit-compartment chain with Emax on the circulating depletion rate; and a T-cell direct-response model with Emax on the fractional depletion.
  • Article (open access): https://doi.org/10.1002/prp2.402.

Population

The model was fit to pooled data from eight preclinical studies in Macaca fascicularis (cynomolgus monkey) – 140 animals (58 males, 82 females) contributing 2199 measurable PK observations after ADA-affected samples were excluded (Roepcke 2018 Table 1 and Section 3.1).

  • Single-dose PK / PD: studies 2 (0.3, 3 mg/kg IV), 7 (0.1, 0.3, 1 mg/kg IV / SC), 8 (0.03, 0.1, 0.3 mg/kg IV / SC).
  • Repeat-dose toxicology: studies 1 (1, 2 mg/kg IV), 3 (1, 30, 100 mg/kg QW IV), 4 (3, 30, 80 mg/kg Q2W IV, 13 weeks), 5 (0.1, 0.3, 1 mg/kg QW IV, 13 weeks – with a documented 0.01 mg/kg dosing error in the lowest-dose group at the second dose), 6 (0.1 mg/kg QW IV, 13 weeks).
  • Body-weight range 2.1-4.7 kg; typical monkey body weight used for human-scaling of the model was 2.6 kg (Supplemental “Scaling of monkey PK parameters”). Sex did not enter the final model. Anti-drug antibodies (ADA) developed over time in the repeat-dose studies; 229 ADA-affected observations were flagged and excluded from model development (Supplemental “Data set preparation”).

The same information is available programmatically via readModelDb("Roepcke_2018_tak_079")()$population.

Source trace

Every parameter is annotated in inst/modeldb/specificDrugs/Roepcke_2018_tak_079.R with the source location. The tables below collect them for review.

PK layer (Roepcke 2018 Table 2)

Parameter (paper) Model name Value Source location
F (PAR) logitfdepot 0.227 Table 2 row 1 (%SE 121)
KA lka 0.399 Table 2 row 2 (%SE 20.5)
CL lcl 0.0187 Table 2 row 3 (%SE 5.17)
VC lvc 0.141 Table 2 row 4 (%SE 3.23)
Q lq 0.127 Table 2 row 5 (%SE 14.7)
VP lvp 0.127 Table 2 row 6 (%SE 6.45)
KINT (FIXED) lkint 0.1 Table 2 row 7 (FIXED)
KSS lkss 5.68 Table 2 row 8 (%SE 38.7)
KSYN (FIXED) lksyn 0.04 Table 2 row 9 (FIXED)
KDEG lkdeg 0.00452 Table 2 row 10 (%SE 30.1)
ROUT on VC e_route_iv_vc 0.697 Table 2 row 11 (%SE 6.51)
Var[Ka] etalka 42.1% CV Table 2 (%SE 53.8)
Var[CL] etalcl 42.9% CV Table 2 (%SE 20.1)
Var[Vc] etalvc 19.8% CV Table 2 (%SE 22.5)
Var[Vp] etalvp 39.4% CV Table 2 (%SE 20.8)
Var[KINT] etalkint 49.3% CV Table 2 (%SE 36.7)
Additive residual var addSd 3.17e-04 Table 2 (SD = 0.01780 ug/mL)
Proportional residual var propSd 0.0677 Table 2 (SD = 0.2602 fraction)
d/dt(central) etc. Figure 2, Berkeley Madonna Supplemental (d/dt(central), d/dt(rtot)) n/a Section 3.2 + Berkeley Madonna code

NK-cell PD layer (Roepcke 2018 Table 3, NK Cells block; Section 3.4)

Parameter (paper) Model name Value Source location
KIN lkin_nk 13957 Table 3 (%SE 4.52)
C50 lec50_nk 27.5 Table 3 (%SE 20.8)
EMAX lemax_nk 414.6 Table 3 (%SE 10.4)
Baseline (median) lrbase_nk 685 Section 3.3 (cells/uL)
Var[KIN] etalkin_nk 111% CV Table 3 (%SE 21.0)
Var[C50] etalec50_nk 146% CV Table 3 (%SE 24.5)
Var[Baseline] etalrbase_nk 28.6% CV Table 3 (%SE 20.6)
Residual variance propSd_nkcell 0.2905 Table 3 (SD = 0.539)
d/dt(NK) equation Section 3.4 n/a KIN - KOUT*NK - NK*EFF; KOUT = KIN/BL; EFF = EMAX*c/(C50+c)

B-cell PD layer (Roepcke 2018 Table 3, B Cells block; Section 3.4)

Parameter (paper) Model name Value Source location
MTT lmtt_b 8.19 Table 3 day (%SE 15.3)
C50 lec50_b 19.8 Table 3 (%SE 8.95)
EMAX lemax_b 2.43 Table 3 (%SE 4.96)
Baseline (median) lrbase_b 1279 Section 3.3 (cells/uL)
Var[MTT] etalmtt_b 135% CV Table 3 (%SE 17.6)
Var[Baseline] etalrbase_b 24.03% CV Table 3 (%SE 10.7)
Residual variance propSd_bcell 0.136 Table 3 (SD = 0.369)
B-cell transit chain (5 equations) Section 3.4 n/a K_PROL = K_TR = K_CIRC = 4/MTT; drug effect on circulating pool only, no feedback

T-cell PD layer (Roepcke 2018 Table 3, T Cells block; Section 3.4)

Parameter (paper) Model name Value Source location
C50 lec50_t 11.86 Table 3 (%SE 7.267)
EMAX lemax_t 0.4656 Table 3 (%SE 6.578)
Baseline (median) lrbase_t 3732 Section 3.3 (cells/uL)
Var[EMAX] etalemax_t 69.46% CV Table 3 (%SE 29.50)
Var[Baseline] etalrbase_t 29.08% CV Table 3 (%SE 15.50)
Residual variance propSd_tcell 0.1343 Table 3 (SD = 0.367)
T-cell direct-response equation Section 3.4 n/a T(c) = BL * (1 - EMAX*c/(c+C50))

Units and dimensional analysis

Doses are in mg (per-animal absolute amount, dose(mg/kg) * pre-dose body weight (kg)). Concentrations are in ug/mL (= mg/L). Volumes (Vc, Vp) are in L; clearances (CL, Q) in L/day; rate constants in 1/day. Lymphocyte counts are cells/uL. The QSS binding constant KSS shares the same concentration units as Cc (ug/mL); the receptor synthesis rate KSYN (u/L / day) and degradation KDEG (1/day) give a receptor pool concentration Rtot(0) = KSYN/KDEG (~ 8.85 u/L) with the same drug-equivalent scaling as the QSS denominator (so the KINT * Rtot * central / (KSS + Cc) term in the central-drug ODE reduces to units of mg/day when integrated).

Simulation setup

The paper’s Figure 4 groups animals by dose level (0.03, 0.1, 0.3, 3, 30, 80, 100 mg/kg) and route (IV vs SC). Below we build a compact virtual cohort spanning the low-to-mid IV dose range that best characterises the PD models (0.03, 0.1, 0.3, 1, 3 mg/kg IV in a 2.6-kg reference monkey) and a parallel SC arm (0.03, 0.1, 0.3, 1 mg/kg SC) to reproduce the SC vs IV contrast highlighted in Figure 4C, F, I.

set.seed(20260709)

# Reference-monkey body weight used to convert mg/kg dose levels into absolute
# mg. Roepcke 2018 Supplemental "Scaling of monkey PK parameters" uses 2.6 kg.
bw_ref <- 2.6

sample_grid <- c(
  seq(0, 1, by = 0.1),      # dense early phase for Cc peak
  seq(1.5, 14, by = 0.5),   # PD depletion window
  seq(15, 30, by = 1)       # recovery phase
)

# Multi-cohort event table: IV and SC dose groups. Disjoint id ranges across
# cohorts are mandatory when bind_rows()-ing so rxSolve doesn't merge them.
make_cohort <- function(dose_mgkg, route, id_offset, n = 1) {
  ROUTE_IV <- if (route == "IV") 1L else 0L
  dose_amt <- dose_mgkg * bw_ref
  target_cmt <- if (route == "IV") "central" else "depot"
  dose_ev <- data.frame(
    id       = id_offset + seq_len(n),
    time     = 0,
    amt      = dose_amt,
    cmt      = target_cmt,
    evid     = 1L,
    ROUTE_IV = ROUTE_IV,
    treatment = paste0(dose_mgkg, " mg/kg ", route)
  )
  obs_ev <- expand.grid(
    id   = id_offset + seq_len(n),
    time = sample_grid,
    cmt  = c("Cc", "nkcell", "bcell", "tcell"),
    stringsAsFactors = FALSE
  )
  obs_ev$amt      <- NA_real_
  obs_ev$evid     <- 0L
  obs_ev$ROUTE_IV <- ROUTE_IV
  obs_ev$treatment <- paste0(dose_mgkg, " mg/kg ", route)
  dplyr::bind_rows(dose_ev, obs_ev)
}

iv_doses <- c(0.03, 0.1, 0.3, 1, 3)
sc_doses <- c(0.03, 0.1, 0.3, 1)

events_iv <- purrr::imap_dfr(
  iv_doses,
  ~ make_cohort(.x, "IV", id_offset = (.y - 1) * 5L, n = 1)
)
events_sc <- purrr::imap_dfr(
  sc_doses,
  ~ make_cohort(.x, "SC", id_offset = 100L + (.y - 1) * 5L, n = 1)
)
events <- dplyr::bind_rows(events_iv, events_sc)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid", "cmt")])))

Typical-value simulation

The paper’s Figure 4 overlays median and range of observed data with model-based population predictions (typical-value curves). We reproduce the typical curves by zeroing between-subject variability with rxode2::zeroRe().

mod <- readModelDb("Roepcke_2018_tak_079")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

sim <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("treatment", "ROUTE_IV")
) |> as.data.frame()
#> Warning in file.exists(obj): expanded path length 4096 would be too long for
#>     params(logitfdepot, lka, lcl, lvc, lq, lvp, lkint, lkss, 
#>         lksyn, lkdeg, e_route_iv_vc, addSd, propSd, lkin_nk, 
#>         lec50_nk, lemax_nk, lrbase_nk, propSd_nkcell, lmtt_b, 
#>         lec50_b, lemax_b, lrbase_b, propSd_bcell, lec50_t, lemax_t, 
#>         lrbase_t, propSd_tcell, etalka, etalcl, etalvc, etalvp, 
#>         etalkint, etalkin_nk, etalec50_nk, etalrbase_nk, etalmtt_b, 
#>         etalrbase_b, etalemax_t, etalrbase_t, ROUTE_IV)
#>     fdepot <- exp(logitfdepot)/(1 + exp(logitfdepot))
#>     ka <- exp(lka + etalka)
#>     cl <- exp(lcl + etalcl)
#>     vc <- exp(lvc + etalvc) * (1 - e_route_iv_vc * (1 - ROUTE_IV))
#>     q <- exp(lq)
#>     vp <- exp(lvp + etalvp)
#>     kint <- exp(lkint + etalkint)
#>     kss <- exp(lkss)
#>     ksyn <- exp(lksyn)
#>     kdeg <- exp(lkdeg)
#>     kel <- cl/vc
#>     k12 <- q/vc
#>     k21 <- q/vp
#>     conc <- central/vc
#>     d/dt(depot) <- -ka * depot
#>     d/dt(central) <- ka * depot - k12 * central + k21 * peripheral1 - 
#>         k [... truncated]
#> Warning in file.exists(model): expanded path length 4096 would be too long for
#>     params(logitfdepot, lka, lcl, lvc, lq, lvp, lkint, lkss, 
#>         lksyn, lkdeg, e_route_iv_vc, addSd, propSd, lkin_nk, 
#>         lec50_nk, lemax_nk, lrbase_nk, propSd_nkcell, lmtt_b, 
#>         lec50_b, lemax_b, lrbase_b, propSd_bcell, lec50_t, lemax_t, 
#>         lrbase_t, propSd_tcell, etalka, etalcl, etalvc, etalvp, 
#>         etalkint, etalkin_nk, etalec50_nk, etalrbase_nk, etalmtt_b, 
#>         etalrbase_b, etalemax_t, etalrbase_t, ROUTE_IV)
#>     fdepot <- exp(logitfdepot)/(1 + exp(logitfdepot))
#>     ka <- exp(lka + etalka)
#>     cl <- exp(lcl + etalcl)
#>     vc <- exp(lvc + etalvc) * (1 - e_route_iv_vc * (1 - ROUTE_IV))
#>     q <- exp(lq)
#>     vp <- exp(lvp + etalvp)
#>     kint <- exp(lkint + etalkint)
#>     kss <- exp(lkss)
#>     ksyn <- exp(lksyn)
#>     kdeg <- exp(lkdeg)
#>     kel <- cl/vc
#>     k12 <- q/vc
#>     k21 <- q/vp
#>     conc <- central/vc
#>     d/dt(depot) <- -ka * depot
#>     d/dt(central) <- ka * depot - k12 * central + k21 * peripheral1 - 
#>         k [... truncated]
#> Warning in file.exists(model): expanded path length 4096 would be too long for
#>     params(logitfdepot, lka, lcl, lvc, lq, lvp, lkint, lkss, 
#>         lksyn, lkdeg, e_route_iv_vc, addSd, propSd, lkin_nk, 
#>         lec50_nk, lemax_nk, lrbase_nk, propSd_nkcell, lmtt_b, 
#>         lec50_b, lemax_b, lrbase_b, propSd_bcell, lec50_t, lemax_t, 
#>         lrbase_t, propSd_tcell, etalka, etalcl, etalvc, etalvp, 
#>         etalkint, etalkin_nk, etalec50_nk, etalrbase_nk, etalmtt_b, 
#>         etalrbase_b, etalemax_t, etalrbase_t, ROUTE_IV)
#>     fdepot <- exp(logitfdepot)/(1 + exp(logitfdepot))
#>     ka <- exp(lka + etalka)
#>     cl <- exp(lcl + etalcl)
#>     vc <- exp(lvc + etalvc) * (1 - e_route_iv_vc * (1 - ROUTE_IV))
#>     q <- exp(lq)
#>     vp <- exp(lvp + etalvp)
#>     kint <- exp(lkint + etalkint)
#>     kss <- exp(lkss)
#>     ksyn <- exp(lksyn)
#>     kdeg <- exp(lkdeg)
#>     kel <- cl/vc
#>     k12 <- q/vc
#>     k21 <- q/vp
#>     conc <- central/vc
#>     d/dt(depot) <- -ka * depot
#>     d/dt(central) <- ka * depot - k12 * central + k21 * peripheral1 - 
#>         k [... truncated]
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etalvc', 'etalvp', 'etalkint', 'etalkin_nk', 'etalec50_nk', 'etalrbase_nk', 'etalmtt_b', 'etalrbase_b', 'etalemax_t', 'etalrbase_t'
#> Warning: multi-subject simulation without without 'omega'

# Compute % of baseline for each cell type using typical baselines
bl_nk <- 685; bl_b <- 1279; bl_t <- 3732
sim <- sim |>
  dplyr::mutate(
    nk_pct = 100 * nkcell / bl_nk,
    b_pct  = 100 * bcell  / bl_b,
    t_pct  = 100 * tcell  / bl_t
  )

Replicate Figure 1 – PK profiles by dose (typical values)

Figure 1A of Roepcke 2018 shows individual PK profiles for the first 7 days after the first dose across all eight studies; here we plot the typical PK trajectory for each of five IV dose levels. All curves converge on the same log-linear terminal slope at the same Vc (0.141 L for IV), scaled by dose.

sim |>
  dplyr::filter(ROUTE_IV == 1L, time <= 30) |>
  ggplot(aes(time, Cc, colour = treatment)) +
  geom_line(linewidth = 0.9) +
  scale_y_log10() +
  labs(x = "Time (day)", y = "TAK-079 serum concentration (ug/mL)",
       title = "Figure 1 -- typical PK profiles after IV dosing",
       caption = "Replicates Figure 1 of Roepcke 2018 (log-scale conc-time; typical-value simulation).") +
  theme_bw() +
  theme(legend.position = "right", legend.title = element_blank())

Replicate Figure 1C – IV vs SC (0.3 mg/kg)

The paper’s Figure 1C compares smoothed IV and SC profiles at low doses. Here we show 0.3 mg/kg IV vs SC in the packaged model – the SC curve has a slower rise (Ka = 0.399/day) and a substantially smaller Cmax reflecting the ~70% smaller Vc estimate for SC (e_route_iv_vc = 0.697).

sim |>
  dplyr::filter(treatment %in% c("0.3 mg/kg IV", "0.3 mg/kg SC")) |>
  ggplot(aes(time, Cc, colour = treatment, linetype = treatment)) +
  geom_line(linewidth = 0.9) +
  scale_y_log10() +
  labs(x = "Time (day)", y = "TAK-079 serum concentration (ug/mL)",
       title = "Figure 1C -- 0.3 mg/kg IV vs SC (typical values)",
       caption = "Replicates Figure 1C of Roepcke 2018.") +
  theme_bw() +
  theme(legend.title = element_blank())
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

Replicate Figure 4 – lymphocyte depletion profiles

Figure 4 shows the three cell-type depletion profiles (as % of baseline) after IV dosing at 0.1, 0.3, 1 mg/kg. Below we render the typical-value predictions for NK, B, and T cells across the same IV dose levels.

pd_long <- sim |>
  dplyr::filter(ROUTE_IV == 1L, time <= 20) |>
  dplyr::select(treatment, time, nk_pct, b_pct, t_pct) |>
  tidyr::pivot_longer(
    cols       = c(nk_pct, b_pct, t_pct),
    names_to   = "cell",
    values_to  = "pct_baseline"
  ) |>
  dplyr::mutate(
    cell = dplyr::recode(cell,
                         nk_pct = "NK cells",
                         b_pct  = "B cells",
                         t_pct  = "T cells")
  )

ggplot(pd_long, aes(time, pct_baseline, colour = treatment)) +
  geom_line(linewidth = 0.9) +
  geom_hline(yintercept = 50, linetype = "dashed", colour = "grey60") +
  facet_wrap(~ cell) +
  labs(x = "Time (day)", y = "Cell count (% of baseline)",
       title = "Figure 4 -- typical lymphocyte-depletion profiles (IV)",
       caption = "Replicates Figure 4 of Roepcke 2018. 50% dashed line marks a common qualitative cut-off.") +
  theme_bw() +
  theme(legend.title = element_blank())

The T-cell curve rises immediately at t = 0 because the T-cell PD model is a direct response to plasma concentration – with EMAX = 0.4656, the maximum fractional depletion is roughly 47%, so tcell / BL never falls below ~53% at any concentration (Roepcke 2018 Section 3.4: “in this case only about half of the T cells can be depleted by TAK-079”).

PKNCA validation (Cc after single-dose IV / SC)

Compute non-compartmental parameters on the typical-value PK curves for each dose level (single-dose treatments in Roepcke 2018 studies 7 and 8 span the 0.03, 0.1, 0.3, 1 mg/kg IV / SC groups). The paper reports terminal-phase volume of distribution Vz between 64 and 116 mL/kg and clearance between 6.04 and 14.7 mL/kg per day; we compare our simulated central-compartment NCA against those ranges.

# Deduplicate Cc rows -- the event table observes at each time under several
# `cmt` values (Cc / nkcell / bcell / tcell) to trigger every output, so the
# simulation returns four rows per (id, time) that share identical Cc
# values; PKNCA rejects duplicate (id, treatment, time) rows.
sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment) |>
  dplyr::group_by(id, treatment, time) |>
  dplyr::slice(1) |>
  dplyr::ungroup()

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, treatment)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)

intervals <- data.frame(
  start      = 0,
  end        = Inf,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE
)

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

nca_wide <- as.data.frame(nca_res$result) |>
  dplyr::select(treatment, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

# Derived summary: CL_obs (L/day) = dose / AUCinf,  Vz_obs (mL/kg) = CL / (log(2) / t1/2) / bw_ref * 1000
nca_summary <- nca_wide |>
  dplyr::mutate(
    dose_mg      = as.numeric(sub(" mg/kg .*", "", treatment)) * bw_ref,
    cl_L_per_day = dose_mg / aucinf.obs,
    kel_1perday  = log(2) / half.life,
    vz_L         = cl_L_per_day / kel_1perday,
    cl_mL_per_kg_day = 1000 * cl_L_per_day / bw_ref,
    vz_mL_per_kg     = 1000 * vz_L         / bw_ref
  )

nca_summary |>
  dplyr::select(treatment, cmax, tmax, aucinf.obs, half.life, cl_mL_per_kg_day, vz_mL_per_kg) |>
  dplyr::mutate(dplyr::across(where(is.numeric), ~ round(., 3))) |>
  dplyr::rename(
    "Dose"                    = treatment,
    "Cmax (ug/mL)"            = cmax,
    "Tmax (day)"              = tmax,
    "AUCinf,obs (ug*day/mL)"  = aucinf.obs,
    "t1/2 (day)"              = half.life,
    "CL (mL/kg/day)"          = cl_mL_per_kg_day,
    "Vz (mL/kg)"              = vz_mL_per_kg
  ) |>
  knitr::kable(
    caption = "NCA of typical-value simulated Cc profiles by treatment (dose x route). Compare CL and Vz against Roepcke 2018 Section 3.1: CL 6.04-14.7 mL/kg/day; Vz 64-116 mL/kg (SC data are apparent, not directly comparable)."
  )
NCA of typical-value simulated Cc profiles by treatment (dose x route). Compare CL and Vz against Roepcke 2018 Section 3.1: CL 6.04-14.7 mL/kg/day; Vz 64-116 mL/kg (SC data are apparent, not directly comparable).
Dose Cmax (ug/mL) Tmax (day) AUCinf,obs (ug*day/mL) t1/2 (day) CL (mL/kg/day) Vz (mL/kg)
0.03 mg/kg IV 0.553 0.0 1.964 4.987 15.271 109.877
0.03 mg/kg SC 0.138 3.0 1.724 5.289 17.397 132.738
0.1 mg/kg IV 1.844 0.0 6.877 5.172 14.541 108.499
0.1 mg/kg SC 0.461 3.0 5.845 5.364 17.109 132.406
0.3 mg/kg IV 5.532 0.0 23.069 5.676 13.005 106.492
0.3 mg/kg SC 1.401 3.0 18.248 5.553 16.440 131.705
1 mg/kg IV 18.440 0.0 96.020 7.063 10.415 106.114
1 mg/kg SC 4.791 3.5 66.126 5.976 15.123 130.382
3 mg/kg IV 55.319 0.0 352.844 8.717 8.502 106.927

Comparison against reported NCA ranges

Roepcke 2018 Section 3.1 (NCA on the single-dose studies) reports:

  • Vz (terminal volume of distribution): 64-116 mL/kg
  • CL (clearance): 6.04-14.7 mL/kg/day
  • Terminal half-life: 4.75-11.2 days

For IV dosing, our typical-value predictions should sit inside these ranges (they reflect the same physiology, aggregated to typical values). SC dosing typically yields lower calculated CL (dose divided by AUCinf, which is dose x F / CL_true) and higher apparent Vz because the SC formulation has ~30% of the IV Vc; the SC apparent-Vz value is not directly comparable to the IV Vz reported in the paper.

Assumptions and deviations

  • Baseline lymphocyte counts. The paper’s models used individual baselines carried in the dataset (column BL). We use the paper-reported median baselines from Section 3.3 (NK 685 cells/uL, B 1279 cells/uL, T 3732 cells/uL) as the typical values for lrbase_nk, lrbase_b, lrbase_t, with BSV etas at the CVs reported in Table 3.
  • B-cell transit compartment structure. Section 3.4 reports “five equations” with four transit compartments TR1..TR4 followed by circulating B cells B and the rate constants K_PROL = K_TR = K_CIRC = 4/MTT, but the five equations themselves are not decoded in the trimmed PDF text (Figure text only). We encode the standard Friberg-style constant-source chain d/dt(precursor1) = K_TR * (BL - precursor1), d/dt(precursor_{n+1}) = K_TR * (precursor_n - precursor_{n+1}), d/dt(bcell) = K_TR * precursor4 - K_TR * bcell - bcell * EFF with all rate constants equal to 4/MTT and all initial conditions at rbase_b. This is the parameterisation that (i) reproduces the paper’s steady state at BL when drug is absent, (ii) implements “the drug effect on the depletion rate of circulating B cells” with no feedback on progenitors, and (iii) yields the correct total delay MTT through the chain. Under this encoding TR1 receives a constant source flux K_PROL * rbase_b, so K_PROL is the paper-reported rate constant with an implicit “reservoir” baseline term equal to the individual baseline; there is no separate Prol state.
  • Route-of-administration encoding. The paper models Vc_SC = Vc * (1 - 0.697) where SC = 1 for SC animals. We use the canonical ROUTE_IV covariate (1 = IV, 0 = SC) and rewrite as vc = exp(lvc + etalvc) * (1 - e_route_iv_vc * (1 - ROUTE_IV)). IV animals have Vc = 0.141 L; SC animals have Vc = 0.043 L, matching the paper.
  • KINT typical value vs BSV. Table 2 reports KINT typical = 0.1/day as FIXED but the BSV on KINT is 49.3% CV (%SE 36.7). We encode this as lkint <- fixed(log(0.1)) with etalkint ~ 0.21785 estimated – typical value fixed, IIV estimated.
  • Residual variance vs SD. Both Table 2 and Table 3 report the “Magnitude” column for residual variability as variances; we take the square root (sqrt(...) inside ini()) because nlmixr2’s ~ prop() and ~ add() families expect SDs.
  • BSV %CV to variance conversion. The paper reports BSV as %CV; we use the exact log-normal reverse-transform omega^2 = log(1 + (CV/100)^2) (so the on-run reported %CV back-reconstructs to Table 2 / Table 3 to within roundoff). This differs from the shorthand omega^2 = (CV/100)^2 by <5% up to CV = 50% and matters at CV = 100%+.
  • ADA data excluded during model development. ADA-affected observations (ADAF = 1, 229 samples) were excluded during the paper’s original fit; this exclusion is not encoded in the packaged model (no ADA covariate). For simulation purposes ADA is not required. Set ROUTE_IV = 1 for IV cohorts, ROUTE_IV = 0 for SC cohorts; no ADA column is used.
  • Typical-value simulation vs observed median. Simulating with zeroRe() returns the population typical-value prediction, which for the strongly non-linear PD models (especially NK cells, where BSV on both KIN and C50 exceeds 100% CV) is systematically shallower than the observed median across animals reported in Section 3.3. This is expected behaviour for log-normal IIV with high CV, not a model-file bug.
  • T-cell direct-response caveat. Section 3.4 explicitly notes that the direct-response T-cell model under-predicts the initial depletion at the first high dose (e.g., 3 mg/kg group) even though it captures the low-dose and later-time-point behaviour well. We inherit this limitation verbatim; users comparing to Figure 4G-I at high single doses should expect model curves shallower than observed.
  • Human scaling projection is not a fit. The paper’s Figure 5 simulates human PK / PD by scaling the monkey PK parameters (CL_human = CL_monkey * (70 / 2.6)^0.85, etc.) using a straightforward allometric approach for monoclonal antibodies. The packaged model is the monkey fit; users who need the human projection should apply the Supplemental “Scaling of monkey PK parameters” formulas to the loaded model rather than rely on refitted human parameters.
  • Errata. No published erratum was located for this paper via the trimmed source; if one exists, please open an issue at https://github.com/nlmixr2/nlmixr2lib.

References

  • Roepcke S, Plock N, Yuan J, Fedyk ER, Lahu G, Zhao L, Smithson G. Pharmacokinetics and pharmacodynamics of the cytolytic anti-CD38 human monoclonal antibody TAK-079 in monkey - model assisted preparation for the first in human trial. Pharmacol Res Perspect. 2018;6(3):e00402. doi:10.1002/prp2.402.