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Etrolizumab (Moein 2022)

Source: vignettes/articles/Moein_2022_etrolizumab.Rmd
Moein_2022_etrolizumab.Rmd
library(nlmixr2lib)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter
library(rxode2)
#> rxode2 5.1.8 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)

Model and source 

#> ℹ parameter labels from comments will be replaced by 'label()'

  • Citation: Moein A, Lu T, Jonsson S, Ribbing J, Kassir N, Zhang W, Sperinde G, Zhang R, Tang M, Oh YS, Bruno R, Zhu R. Population pharmacokinetic analysis of etrolizumab in patients with moderately-to-severely active ulcerative colitis. CPT Pharmacometrics Syst Pharmacol. 2022;11(9):1244-1255. doi:10.1002/psp4.12846.

  • Description: Two-compartment population PK model for etrolizumab with first-order SC absorption and time-decreasing clearance in adults with moderately-to-severely active ulcerative colitis (Moein 2022)

  • Article: https://doi.org/10.1002/psp4.12846

Population

The model was developed on 1263 subjects (non-missing covariates) pooled from five clinical studies of etrolizumab in adults with moderately-to-severely active ulcerative colitis: ABS4262g (phase I), EUCALYPTUS (phase II), HIBISCUS I/II (phase III), HICKORY (phase III), and LAUREL (phase III). GARDENIA (phase III) was held out for external validation. Baseline demographics (Moein 2022 Table 3): age range 18-79 years (median 38 years), weight range 38.0-216 kg (median 72.2 kg), 42% female, 45% with prior anti-TNF exposure, 23% ADA-positive. Disease extension: 53% left-sided colitis, 42% extensive/pancolitis, 2% other, 3% missing. Baseline medians: albumin 41 g/L, CRP 4.31 mg/L, fecal calprotectin 1500 ug/g. Dosing ranged from single doses of 0.3-10 mg/kg IV (phase I), 0.5-3 mg/kg Q4W SC (phase I), 315-420 mg loading SC (phase II), 4 mg/kg Q4W IV (phase I), to the phase III regimen of 105 mg Q4W SC.

The same information is available programmatically via readModelDb("Moein_2022_etrolizumab")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Moein_2022_etrolizumab.R. The table below collects them in one place.

Equation / parameter Value Source location (Moein 2022)
lka log(0.193) Table 4: ka = 0.193 /day
lcl log(0.260) Table 4: CL (at TSFD = 0) = 0.260 L/day
lvc log(2.61) Table 4: Vc = 2.61 L
lvp log(1.77) Table 4: Vp = 1.77 L
lq log(0.449) Table 4: Q = 0.449 L/day
logitfdepot logit(0.712) Table 4: F = 0.712
logitmaxred logit(0.263) Table 4: Maxred = 0.263
lonset log(4.81) Table 4: Onset = 4.81 weeks
e_wt_cl_q 0.872 Table 4 note a: WT exponent on CL and Q
e_wt_vc_vp 0.788 Table 4 note b: WT exponent on Vc and Vp
e_alb_cl -0.0314 Table 4: Albumin on CL
e_crp_cl 0.00458 Table 4: CRP on CL
e_adat_cl 0.0365 Table 4: ADAT on CL
e_priortnf_cl 0.0490 Table 4: Prior TNF on CL
e_extpan_cl 0.0816 Table 4: Extensive/pancolitis on CL
e_othext_cl 0.181 Table 4: Other disease extension on CL
IIV CL (etalcl) log(1+0.243^2) Table 4: IIV CL CV = 0.243
IIV Vc (etalvc) log(1+0.252^2) Table 4: IIV Vc CV = 0.252
IIV Vp (etalvp) log(1+0.262^2) Table 4: IIV Vp CV = 0.262
IIV F 0.733^2 Table 4: IIV F logit-SD = 0.733
IIV Maxred 0.597^2 Table 4: IIV Maxred logit-SD = 0.597
propSd 0.196 Table 4: Proportional residual CV = 0.196
addSd 0.427 Table 4: Additive residual SD = 0.427 ug/mL
CL time-decay Equation 1 Eq. 1: CL = CL0 * (1 - Maxred * (1 - exp(-log(2)/(Onset7) (TSFD - TAD))))
Covariate form exp(theta*(Cov - Cov_ref)) Table 4 note d (continuous)
Covariate form 1 + theta * indicator Table 4 note g (categorical)

Reference covariate values for the reference patient (Figure 1 caption): 72 kg WT, 41 g/L albumin, 4.23 mg/L CRP, phase III, no prior anti-TNF, left-sided colitis, ADA-negative.

Virtual cohort

Original observed data are not publicly available. The simulations below use virtual populations whose covariate distributions approximate the published phase III demographics.

make_cohort <- function(n, n_doses = 6, dosing_interval_days = 28,
                        obs_days_per_dose = seq(0, 28, by = 2),
                        amt_mg = 105,
                        seed = 12846) {
  set.seed(seed)

  # Baseline covariates approximating the phase III population
  WT  <- pmax(35, pmin(200, rlnorm(n, log(72), 0.22)))
  ALB <- pmax(25, pmin(55, rnorm(n, 41, 4)))
  CRP <- pmax(0.1, exp(rnorm(n, log(4.31), 1.2)))
  PRIOR_TNF <- rbinom(n, 1, 0.45)
  disext <- sample(c("left", "extpan", "other"), n,
                   replace = TRUE, prob = c(0.55, 0.43, 0.02))
  DISEXT_EP    <- as.integer(disext == "extpan")
  DISEXT_OTHER <- as.integer(disext == "other")
  # Paper assumes ADA-negative until week 4; use a time-invariant titer of 0
  # for the primary cohort and a 97.5th-percentile value for a sensitivity arm
  ADA_TITER <- rep(0, n)

  dose_times <- seq(0, (n_doses - 1) * dosing_interval_days,
                    by = dosing_interval_days)

  pop <- data.frame(
    ID  = seq_len(n),
    WT, ALB, CRP, ADA_TITER, PRIOR_TNF, DISEXT_EP, DISEXT_OTHER
  )

  # Dose records (depot, SC injections Q4W)
  d_dose <- pop[rep(seq_len(n), each = length(dose_times)), ] |>
    mutate(
      TIME = rep(dose_times, times = n),
      AMT  = amt_mg,
      EVID = 1,
      CMT  = "depot",
      DV   = NA_real_
    )

  # Observation records: per-dose relative sample times, across all doses
  obs_grid <- as.vector(outer(obs_days_per_dose, dose_times, "+"))
  obs_grid <- sort(unique(obs_grid))

  d_obs <- pop[rep(seq_len(n), each = length(obs_grid)), ] |>
    mutate(
      TIME = rep(obs_grid, times = n),
      AMT  = 0,
      EVID = 0,
      CMT  = "central",
      DV   = NA_real_
    )

  bind_rows(d_dose, d_obs) |>
    arrange(ID, TIME, desc(EVID)) |>
    select(ID, TIME, AMT, EVID, CMT, DV,
           WT, ALB, CRP, ADA_TITER, PRIOR_TNF, DISEXT_EP, DISEXT_OTHER)
}
mod <- rxode2::rxode(readModelDb("Moein_2022_etrolizumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'

Simulation

Phase III dosing: 105 mg Q4W SC x 6 doses, with observations every 2 days over the 24-week treatment period.

events_vpc <- make_cohort(n = 300)
sim_vpc <- rxode2::rxSolve(mod, events = events_vpc) |> as.data.frame()

Replicate published figures

Figure 2 analogue: concentration-time VPC (phase III dose) 

d_vpc <- sim_vpc |>
  group_by(time) |>
  summarise(
    Q10 = quantile(Cc, 0.10, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q90 = quantile(Cc, 0.90, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(d_vpc, aes(x = time, y = Q50)) +
  geom_ribbon(aes(ymin = Q10, ymax = Q90), fill = "#4682b4", alpha = 0.25) +
  geom_line(colour = "#4682b4", linewidth = 0.8) +
  geom_line(aes(y = Q10), linetype = "dashed", linewidth = 0.4) +
  geom_line(aes(y = Q90), linetype = "dashed", linewidth = 0.4) +
  scale_x_continuous(breaks = seq(0, 168, by = 28),
                     labels = seq(0, 168, by = 28) / 7) +
  labs(
    x = "Time since first dose (weeks)",
    y = expression("Etrolizumab concentration (" * mu * "g/mL)"),
    title = "Figure 2 analogue - simulated concentration VPC",
    caption = paste0(
      "Simulated 10th/50th/90th percentiles, N = 300 virtual subjects, ",
      "105 mg Q4W SC x 6 doses.\n",
      "Replicates the shape of Figure 2 of Moein 2022 (phase III panels)."
    )
  ) +
  theme_bw()

Figure S3 analogue: typical CL vs. time since first dose

Time-dependent CL per Equation 1 reaches its asymptote over the first 4-8 weeks, stepping down after each dose.

# Population-typical CL trajectory for the reference patient (72 kg, 41 g/L
# ALB, 4.23 mg/L CRP, no prior TNF, left-sided colitis, ADA-negative).
# zeroRe() removes IIV to get typical values.
mod_typical <- mod |> rxode2::zeroRe()
events_typ <- make_cohort(n = 1) |>
  mutate(WT = 72, ALB = 41, CRP = 4.23,
         ADA_TITER = 0, PRIOR_TNF = 0, DISEXT_EP = 0, DISEXT_OTHER = 0)
sim_typ <- rxode2::rxSolve(mod_typical, events = events_typ,
                           keep = c("WT", "ALB", "CRP")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalogitfdepot', 'etalogitmaxred'

ggplot(sim_typ, aes(x = time, y = cl)) +
  geom_line(linewidth = 0.8, colour = "#4682b4") +
  scale_x_continuous(breaks = seq(0, 168, by = 28),
                     labels = seq(0, 168, by = 28) / 7) +
  labs(
    x = "Time since first dose (weeks)",
    y = "Typical CL (L/day)",
    title = "Figure S3 analogue - typical CL vs time since first dose",
    caption = paste0(
      "Reference patient (72 kg, 41 g/L ALB, 4.23 mg/L CRP, no prior TNF, ",
      "left-sided colitis, ADA-).\n",
      "Maxred = 26% asymptotic reduction; Onset = 4.8 weeks half-life."
    )
  ) +
  theme_bw()

PKNCA validation

Compute NCA on the simulated typical-value profile for the reference patient:

  1. Single-dose phase using the first dosing interval (0-28 days) as the analog for the phase I single-dose pK profile.
  2. Steady-state phase using the final dosing interval (days 140-168) where the time-dependent CL has reached its asymptote.

The paper reports typical terminal half-lives derived from the population PK parameters:

  • After a single dose: 13.0 days (95% CI 12.2-13.9).
  • At steady state: 17.1 days (95% CI 16.1-18.3).

For a clean terminal-phase characterization we simulate a single 105 mg dose with dense post-peak sampling, and a 6-dose steady-state regimen with one dense post-final-dose sampling interval.

Single-dose NCA 

# Single 105 mg SC dose, dense sampling out to 84 days (3 half-lives past
# the expected 13-day t1/2).
events_single <- make_cohort(
  n = 1, n_doses = 1,
  obs_days_per_dose = c(0, 0.25, 0.5, 1, 2, 3, 5, 7, 10, 14, 21,
                        28, 35, 42, 49, 56, 63, 70, 77, 84)
) |>
  mutate(WT = 72, ALB = 41, CRP = 4.23,
         ADA_TITER = 0, PRIOR_TNF = 0, DISEXT_EP = 0, DISEXT_OTHER = 0)

sim_single <- rxode2::rxSolve(mod_typical, events = events_single) |>
  as.data.frame() |>
  mutate(id = 1L, treatment = "single_105mg")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalogitfdepot', 'etalogitmaxred'

sim_nca_single <- sim_single |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, treatment)

dose_single <- events_single |>
  filter(EVID == 1) |>
  transmute(id = ID, time = TIME, amt = AMT, treatment = "single_105mg")

conc_single <- PKNCA::PKNCAconc(sim_nca_single, Cc ~ time | treatment + id)
dose_single_obj <- PKNCA::PKNCAdose(dose_single, amt ~ time | treatment + id)

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

nca_single <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_single, dose_single_obj, intervals = intervals_single)
)
knitr::kable(as.data.frame(nca_single$result),
             caption = "Single-dose NCA on the typical-patient profile.")
Single-dose NCA on the typical-patient profile.
treatment id start end PPTESTCD PPORRES exclude
single_105mg 1 0 Inf cmax 10.1850524 NA
single_105mg 1 0 Inf tmax 7.0000000 NA
single_105mg 1 0 Inf tlast 84.0000000 NA
single_105mg 1 0 Inf clast.obs 0.2042195 NA
single_105mg 1 0 Inf lambda.z 0.0534240 NA
single_105mg 1 0 Inf r.squared 0.9999765 NA
single_105mg 1 0 Inf adj.r.squared 0.9999736 NA
single_105mg 1 0 Inf lambda.z.time.first 21.0000000 NA
single_105mg 1 0 Inf lambda.z.time.last 84.0000000 NA
single_105mg 1 0 Inf lambda.z.n.points 10.0000000 NA
single_105mg 1 0 Inf clast.pred 0.2051397 NA
single_105mg 1 0 Inf half.life 12.9744575 NA
single_105mg 1 0 Inf span.ratio 4.8556943 NA
single_105mg 1 0 Inf aucinf.obs 279.3925233 NA

Steady-state NCA 

# Six 105 mg SC doses Q4W, with dense post-peak sampling in the final
# interval for terminal-phase characterization.
events_ss <- make_cohort(
  n = 1, n_doses = 6,
  obs_days_per_dose = c(0, 0.25, 0.5, 1, 2, 3, 5, 7, 10, 14, 21, 28)
) |>
  mutate(WT = 72, ALB = 41, CRP = 4.23,
         ADA_TITER = 0, PRIOR_TNF = 0, DISEXT_EP = 0, DISEXT_OTHER = 0)

# Add dense post-final-dose terminal-phase samples out to day 252 (84 days
# past the final dose, for t1/2 estimation at steady state)
final_dose_day <- 5 * 28
extra_obs <- data.frame(
  ID = 1L, TIME = final_dose_day + c(35, 42, 49, 56, 63, 70, 77, 84),
  AMT = 0, EVID = 0, CMT = "central", DV = NA_real_,
  WT = 72, ALB = 41, CRP = 4.23,
  ADA_TITER = 0, PRIOR_TNF = 0, DISEXT_EP = 0, DISEXT_OTHER = 0
)

events_ss <- bind_rows(events_ss, extra_obs) |>
  arrange(ID, TIME, desc(EVID))

sim_ss <- rxode2::rxSolve(mod_typical, events = events_ss) |>
  as.data.frame() |>
  mutate(id = 1L, treatment = "ss_105mg_Q4W")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalogitfdepot', 'etalogitmaxred'

sim_nca_ss <- sim_ss |>
  filter(!is.na(Cc), time >= final_dose_day) |>
  mutate(time = time - final_dose_day) |>
  select(id, time, Cc, treatment)

dose_ss <- data.frame(
  id = 1L, time = 0, amt = 105, treatment = "ss_105mg_Q4W"
)

conc_ss <- PKNCA::PKNCAconc(sim_nca_ss, Cc ~ time | treatment + id)
dose_ss_obj <- PKNCA::PKNCAdose(dose_ss, amt ~ time | treatment + id)

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

nca_ss <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_ss, dose_ss_obj, intervals = intervals_ss)
)
knitr::kable(as.data.frame(nca_ss$result),
             caption = "Steady-state NCA on the final dosing interval.")
Steady-state NCA on the final dosing interval.
treatment id start end PPTESTCD PPORRES exclude
ss_105mg_Q4W 1 0 Inf cmax 17.0457440 NA
ss_105mg_Q4W 1 0 Inf tmax 5.0000000 NA
ss_105mg_Q4W 1 0 Inf tlast 84.0000000 NA
ss_105mg_Q4W 1 0 Inf lambda.z 0.0411157 NA
ss_105mg_Q4W 1 0 Inf r.squared 0.9999132 NA
ss_105mg_Q4W 1 0 Inf adj.r.squared 0.9999035 NA
ss_105mg_Q4W 1 0 Inf lambda.z.time.first 14.0000000 NA
ss_105mg_Q4W 1 0 Inf lambda.z.time.last 84.0000000 NA
ss_105mg_Q4W 1 0 Inf lambda.z.n.points 11.0000000 NA
ss_105mg_Q4W 1 0 Inf clast.pred 0.8055760 NA
ss_105mg_Q4W 1 0 Inf half.life 16.8584402 NA
ss_105mg_Q4W 1 0 Inf span.ratio 4.1522228 NA

Comparison against published values 

get_param <- function(res, ppname) {
  tbl <- as.data.frame(res$result)
  val <- tbl$PPORRES[tbl$PPTESTCD == ppname]
  if (length(val) == 0) return(NA_real_)
  val[1]
}

hl_single_sim <- get_param(nca_single, "half.life")
hl_ss_sim     <- get_param(nca_ss,     "half.life")

comparison <- data.frame(
  Quantity     = c("Terminal half-life after single dose (days)",
                   "Terminal half-life at steady state (days)"),
  Published    = c("13.0 (95% CI 12.2-13.9)",
                   "17.1 (95% CI 16.1-18.3)"),
  Simulated    = c(round(hl_single_sim, 2), round(hl_ss_sim, 2))
)
knitr::kable(comparison,
             caption = "Simulated vs. published terminal half-lives.")
Simulated vs. published terminal half-lives.
Quantity Published Simulated
Terminal half-life after single dose (days) 13.0 (95% CI 12.2-13.9) 12.97
Terminal half-life at steady state (days) 17.1 (95% CI 16.1-18.3) 16.86

The simulated terminal half-lives should fall within about 20% of the published central estimates. The single-dose value is shorter than the steady-state value because CL is at its maximum (0.260 L/day) after the first dose and drops to approximately 0.260 * (1 - 0.263) = 0.192 L/day at steady state, lengthening t1/2 proportionally.

Assumptions and deviations

  • PHASE12 covariate on residual error not implemented. Moein 2022 Table 4 reports a -19.2% relative change in the combined residual error for phase I/II studies vs. phase III. nlmixr2’s add() / prop() residual-error terms do not accept per-observation expressions, so the packaged model uses the phase III residual-error magnitude (propSd = 0.196, addSd = 0.427 ug/mL) unconditionally. For typical phase III simulations (the primary usage pattern) this is exact; for phase I/II simulations the residual error will be slightly over-stated. If a future release of nlmixr2 supports per-observation error magnitudes, this covariate can be added.
  • Time-varying ADA titer simplified. Moein 2022 treats ADA titer as a time-varying covariate. The reference patient used in the source figures (Figure 1) is ADA-negative at least until week 4, so ADA_TITER = 0 is the appropriate reference for reproducing the published figures. Users simulating ADA-positive patients should supply a time-series of titer values per subject.
  • Reference CRP. The model centers CRP at 4.23 mg/L (the reference- patient value reported in the Figure 1 caption). The population baseline median CRP is 4.31 mg/L (Table 3); both values produce effectively identical exposures.
  • Virtual covariate distributions. Exact baseline distributions are not published. The demo cohort uses log-normal WT (median 72 kg, CV 22%), normal ALB (41 +/- 4 g/L), log-normal CRP (median 4.31 mg/L, log-SD 1.2), binary prior anti-TNF (45% probability), and a three- level disease extension (55% left / 43% extpan / 2% other) to approximate Table 3 of Moein 2022.
  • SC-only dosing. The packaged model uses SC dosing into depot. Moein 2022 also pooled phase I IV dose-levels; for IV simulations the event table should dose into central directly and bioavailability f(depot) = 1 is irrelevant. The time-dependent CL remains correct because time - tad(depot) still resolves to the time of the most recent dose; when dosing IV into central, use tad(central) or pre-compute the TSFD/TAD difference in the event table.

Reference

  • Moein A, Lu T, Jonsson S, Ribbing J, Kassir N, Zhang W, Sperinde G, Zhang R, Tang M, Oh YS, Bruno R, Zhu R. Population pharmacokinetic analysis of etrolizumab in patients with moderately-to-severely active ulcerative colitis. CPT Pharmacometrics Syst Pharmacol. 2022;11(9):1244-1255. doi:10.1002/psp4.12846.