Suleiman_2019_risankizumab • nlmixr2lib

library(nlmixr2lib)
library(rxode2)
#> rxode2 5.0.2 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)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter

Risankizumab population PK in healthy volunteers and plaque psoriasis

Simulate risankizumab concentration-time profiles using the final population PK model of Suleiman et al. (2019) from the integrated phase I-III clinical-trial programme in healthy volunteers and patients with moderate-to-severe plaque psoriasis. The source paper pooled 13,123 plasma concentrations from 1899 subjects (67 healthy volunteers and 1832 psoriasis patients) across seven studies.

The model is a two-compartment structure with first-order subcutaneous absorption and linear elimination (NONMEM ADVAN4 TRANS4). Typical parameters for a 70 kg reference subject (median albumin, creatinine, and high-sensitivity C-reactive protein [hs-CRP], ADA titer < 128, phase III drug supply) are CL = 0.243 L/day, Vc = 4.86 L, Vp = 4.25 L, ka = 0.229 /day, Q = 0.656 L/day, and F = 0.890. The final covariate set is body weight on CL, Vc, and Vp; baseline serum albumin, serum creatinine, and hs-CRP on CL; and a time-varying ADA titer threshold effect on CL (+43% once titer ≥ 128).

Citation: Suleiman AA, Khatri A, Minocha M, Othman AA. Population Pharmacokinetics of Risankizumab in Healthy Volunteers and Subjects with Moderate to Severe Plaque Psoriasis: Integrated Analyses of Phase I-III Clinical Trials. Clin Pharmacokinet. 2019;58(10):1309-1321. doi:10.1007/s40262-019-00759-z
Article: https://doi.org/10.1007/s40262-019-00759-z

Source trace

Per-parameter origins are recorded as in-file comments in the model file; the table below collects them in one place.

Equation / parameter	Value	Source location
Two-compartment ODE structure (ka → central ↔︎ peripheral1, linear CL)	n/a	Sect. 3.2 and Eq. 6 (NONMEM ADVAN4 TRANS4)
CL (typical, 70 kg ref)	0.243 L/day	Table 3
Vc (typical, 70 kg ref)	4.86 L	Table 3
ka (typical)	0.229 /day	Table 3
Q (typical)	0.656 L/day	Table 3
Vp (typical, 70 kg ref)	4.25 L	Table 3
F, logit parameterisation, phase III drug supply	logit = 2.09 → F = 0.890	Table 3 footnote d; Eq. 2
F, phase I-II drug supply (not default)	logit = 0.896 → F = 0.710	Table 3 footnote c
WT on CL	(WT/70)^0.933	Table 3; Sect. 2.3 (70 kg reference explicitly stated)
WT on Vc	(WT/70)^1.17	Table 3
WT on Vp	(WT/70)^0.377	Table 3
ALB on CL	(ALB/44)^-0.715	Table 3; ref = all-subject median, Table 2
CREAT on CL	(CREAT/76)^-0.253	Table 3; ref = all-subject median, Table 2
CRP (hs-CRP) on CL	(CRP/2.8)^0.044	Table 3; ref = all-subject median, Table 2
ADA threshold effect on CL	1 + 0.428 × (ADA_TITER ≥ 128)	Eq. 8 and Sect. 3.2 (Titer_threshold = 128)
IIV CL	24% CV → ω² = log(1+0.24²) = 0.0560	Table 3 (footnote e conversion)
IIV Vc	34% CV → ω² = log(1+0.34²) = 0.1094	Table 3
IIV ka	63% CV → ω² = log(1+0.63²) = 0.3342	Table 3
IIV–IIV correlation CL:Vc	39% → cov = 0.03053	Table 3
IIV F (additive on logit)	variance 0.492	Table 3 footnote f
Residual error	proportional, 19% CV (σ² = 0.036)	Table 3
Dosing regimen (clinical)	150 mg SC weeks 0, 4, then q12w	Sect. 2.3.1 and Fig. 2 caption

Covariate column naming

Source column	Canonical column used here
`WT` (kg)	`WT` (kg; per `covariate-columns.md`)
`ALB` (g/L)	`ALB` (g/L)
`CREAT` (umol/L)	`CREAT` (umol/L; canonical)
`hs-CRP` (mg/L)	`CRP` (mg/L; canonical general-scope; hs-CRP assay documented in `covariateData[[CRP]]`)
`ADA titer`	`ADA_TITER` (reciprocal-dilution; 0 = negative)

Virtual population

Phase III psoriasis trial-like covariate distributions. Suleiman 2019 does not publish individual-level data, so the distributions below approximate the “All subjects” demographics reported in Table 2 (median body weight 87 kg, median age 47 years, 29% female, median baseline albumin 44 g/L, median baseline serum creatinine 76 umol/L, median baseline hs-CRP 2.8 mg/L).

set.seed(2019)
n_subj <- 500

pop <- tibble(
  ID        = seq_len(n_subj),
  WT        = pmin(pmax(rlnorm(n_subj, log(87), 0.23), 42), 200),  # kg
  ALB       = pmin(pmax(rnorm(n_subj, 44, 3.0), 34), 58),          # g/L
  CREAT     = pmin(pmax(rnorm(n_subj, 76, 16), 35), 200),          # umol/L
  CRP       = rlnorm(n_subj, log(2.8), 1.0),                       # mg/L, hs-CRP; skewed right
  ADA_TITER = 0                                                     # ~98.5% of phase III subjects are < 128
)

Dosing dataset

Phase III clinical regimen: 150 mg SC at weeks 0 and 4, then every 12 weeks (q12w) thereafter. Simulate through week 52 to match the study-design window of UltIMMa-1 / UltIMMa-2 in Fig. 2 of the paper.

dose_weeks <- c(0, 4, 16, 28, 40)
dose_times <- dose_weeks * 7

obs_times <- sort(unique(c(
  seq(0,  28,  by = 0.5),
  seq(28, 52 * 7, by = 2)
)))

d_dose <- pop %>%
  crossing(TIME = dose_times) %>%
  mutate(
    AMT  = 150,       # mg SC
    EVID = 1,
    CMT  = 1,         # depot
    DV   = NA_real_
  )

d_obs <- pop %>%
  crossing(TIME = obs_times) %>%
  mutate(AMT = NA_real_, EVID = 0, CMT = 2, DV = NA_real_)

d_sim <- bind_rows(d_dose, d_obs) %>%
  arrange(ID, TIME, desc(EVID)) %>%
  as.data.frame()

Simulate

mod <- readModelDb("Suleiman_2019_risankizumab")
sim <- rxSolve(mod, d_sim, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'

Concentration-time profile (replicates Fig. 2, Suleiman 2019)

The median and 90% prediction interval of the simulated concentration-time profile for the 150 mg SC q12w regimen through week 52. Replicates the VPC layout of Fig. 2 (UltIMMa-1 and UltIMMa-2 combined, phase III clinical regimen).

sim_summary <- sim %>%
  filter(time > 0) %>%
  group_by(time) %>%
  summarise(
    median = median(Cc, na.rm = TRUE),
    lo     = quantile(Cc, 0.05, na.rm = TRUE),
    hi     = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summary, aes(x = time / 7)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.2, fill = "steelblue") +
  geom_line(aes(y = median), colour = "steelblue", linewidth = 1) +
  scale_y_log10() +
  labs(
    x        = "Time (weeks)",
    y        = "Risankizumab concentration (ug/mL)",
    title    = "Simulated risankizumab PK (150 mg SC weeks 0, 4, q12w)",
    subtitle = "Median and 90% prediction interval (N = 500 virtual psoriasis patients)",
    caption  = "Replicates Fig. 2 of Suleiman 2019 (UltIMMa-1 / UltIMMa-2 layout)."
  ) +
  theme_bw()

Per-dosing-interval exposures

Compute Cmax and Ctrough over the first three maintenance dosing intervals (weeks 4-16, 16-28, 28-40). The paper reports that steady-state plasma exposures are approached by week 16 of dosing (Abstract and Sect. 3.3), so intervals starting at week 16 onward reflect the steady-state.

intervals <- tribble(
  ~label,       ~start_wk, ~end_wk,
  "2 (4-16)",    4,  16,
  "3 (16-28)",  16,  28,
  "4 (28-40)",  28,  40
)

ivl_summary <- intervals %>%
  rowwise() %>%
  do({
    row <- .
    sub <- sim %>%
      filter(time >= row$start_wk * 7, time <= row$end_wk * 7, Cc > 0)
    per_id <- sub %>%
      group_by(id) %>%
      summarise(
        Cmax    = max(Cc, na.rm = TRUE),
        Ctrough = Cc[which.max(time)],
        AUCtau  = sum(diff(time) * (head(Cc, -1) + tail(Cc, -1)) / 2),
        .groups = "drop"
      )
    tibble(
      interval       = row$label,
      Cmax_median    = median(per_id$Cmax),
      Ctrough_median = median(per_id$Ctrough),
      AUCtau_median  = median(per_id$AUCtau)
    )
  }) %>%
  bind_rows()

knitr::kable(
  ivl_summary,
  digits  = 2,
  caption = "Simulated per-interval exposures (Cmax/Ctrough in ug/mL; AUCtau in ug*day/mL)."
)

Simulated per-interval exposures (Cmax/Ctrough in ug/mL; AUCtau in ug*day/mL).
interval	Cmax_median	Ctrough_median	AUCtau_median
2 (4-16)	15.14	2.19	589.49
3 (16-28)	12.20	1.73	463.43
4 (28-40)	11.87	1.67	448.77

PKNCA validation

Run PKNCA on the steady-state maintenance interval (weeks 16-28 of the phase III 150 mg SC q12w regimen). The expected terminal elimination half-life is ~28 days for a typical 90 kg psoriasis patient (Abstract).

nca_conc <- sim %>%
  filter(time >= 16 * 7, time <= 28 * 7, Cc > 0) %>%
  mutate(
    time_rel  = time - 16 * 7,
    treatment = "risankizumab_150mg_q12w"
  ) %>%
  rename(ID = id) %>%
  select(ID, time_rel, Cc, treatment)

nca_dose <- pop %>%
  mutate(
    time_rel  = 0,
    AMT       = 150,
    treatment = "risankizumab_150mg_q12w"
  ) %>%
  select(ID, time_rel, AMT, treatment)

conc_obj <- PKNCAconc(nca_conc, Cc ~ time_rel | treatment + ID)
dose_obj <- PKNCAdose(nca_dose, AMT ~ time_rel | treatment + ID)
data_obj <- PKNCAdata(
  conc_obj,
  dose_obj,
  intervals = data.frame(
    start     = 0,
    end       = 12 * 7,
    cmax      = TRUE,
    tmax      = TRUE,
    auclast   = TRUE,
    half.life = TRUE
  )
)
nca_results <- pk.nca(data_obj)
#>  ■■■                                6% |  ETA: 17s
#>  ■■■■■■■■                          22% |  ETA: 14s
#>  ■■■■■■■■■■■■■                     39% |  ETA: 11s
#>  ■■■■■■■■■■■■■■■■■■                55% |  ETA:  8s
#>  ■■■■■■■■■■■■■■■■■■■■■■■           72% |  ETA:  5s
#>  ■■■■■■■■■■■■■■■■■■■■■■■■■■■       88% |  ETA:  2s
nca_summary <- summary(nca_results)
knitr::kable(
  nca_summary,
  digits  = 2,
  caption = paste(
    "PKNCA summary for the steady-state maintenance interval (weeks 16-28).",
    "Expected terminal half-life ~28 days for a typical 90 kg psoriasis subject",
    "(Suleiman 2019, Abstract)."
  )
)

PKNCA summary for the steady-state maintenance interval (weeks 16-28). Expected terminal half-life ~28 days for a typical 90 kg psoriasis subject (Suleiman 2019, Abstract).
start	end	treatment	N	auclast	cmax	tmax	half.life
0	84	risankizumab_150mg_q12w	500	466 [35.7]	12.2 [35.6]	6.00 [2.00, 20.0]	29.2 [7.46]

Typical-subject comparison against the published abstract

The abstract states CL ≈ 0.31 L/day, Vss ≈ 11.2 L, and terminal half-life ≈ 28 days for a typical 90 kg psoriatic subject with median covariates. Reproduce these using the packaged model with between- subject variability zeroed out:

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

typ_pop <- tibble(
  ID        = 1L,
  WT        = 90,
  ALB       = 44,
  CREAT     = 76,
  CRP       = 2.8,
  ADA_TITER = 0
)

typ_dose <- typ_pop %>%
  crossing(TIME = dose_times) %>%
  mutate(AMT = 150, EVID = 1, CMT = 1, DV = NA_real_)

typ_obs <- typ_pop %>%
  crossing(TIME = obs_times) %>%
  mutate(AMT = NA_real_, EVID = 0, CMT = 2, DV = NA_real_)

typ_events <- bind_rows(typ_dose, typ_obs) %>%
  arrange(TIME, desc(EVID)) %>%
  as.data.frame()

sim_typ <- rxSolve(mod_typ, typ_events, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka', 'etalogitfdepot'

# Typical-subject parameter values
cl_typ <- 0.243 * (90/70)^0.933
vc_typ <- 4.86  * (90/70)^1.17
vp_typ <- 4.25  * (90/70)^0.377
q_typ  <- 0.656
kel_typ <- cl_typ / vc_typ
vss_typ <- vc_typ + vp_typ

# True terminal-phase half-life from the 2-cpt rate-constant eigenvalues
k12 <- q_typ / vc_typ
k21 <- q_typ / vp_typ
sum_k <- kel_typ + k12 + k21
lambda_z <- (sum_k - sqrt(sum_k^2 - 4 * kel_typ * k21)) / 2
t_half_terminal <- log(2) / lambda_z

cat(sprintf(
  paste0(
    "Typical 90 kg psoriasis subject (vs paper abstract):\n",
    "  CL  = %.3f L/day (paper: 0.31)\n",
    "  Vc  = %.2f L    (paper: 6.52)\n",
    "  Vp  = %.2f L    (paper: 4.67)\n",
    "  Vss = %.2f L    (paper: 11.2)\n",
    "  t1/2 terminal = %.1f days (paper: 28)\n",
    "  F (phase III) = %.3f    (paper: 0.890)\n"
  ),
  cl_typ, vc_typ, vp_typ, vss_typ, t_half_terminal,
  exp(2.09) / (1 + exp(2.09))
))
#> Typical 90 kg psoriasis subject (vs paper abstract):
#>   CL  = 0.307 L/day (paper: 0.31)
#>   Vc  = 6.52 L    (paper: 6.52)
#>   Vp  = 4.67 L    (paper: 4.67)
#>   Vss = 11.19 L    (paper: 11.2)
#>   t1/2 terminal = 27.6 days (paper: 28)
#>   F (phase III) = 0.890    (paper: 0.890)

ggplot(sim_typ %>% filter(time > 0), aes(time / 7, Cc)) +
  geom_line(colour = "darkred", linewidth = 1) +
  scale_y_log10() +
  labs(
    x        = "Time (weeks)",
    y        = "Risankizumab concentration (ug/mL)",
    title    = "Typical 90 kg psoriasis patient (zeroed random effects)",
    caption  = "Reproduces the 'approaches steady-state by week 16' behaviour from Abstract."
  ) +
  theme_bw()

ADA-positive subgroup

The paper reports that patients with ADA titer ≥ 128 (~1.5% of phase III ADA-evaluable subjects) have ~43% increased CL and ~30% decreased AUC on the 150 mg SC q12w regimen (Sect. 3.3). Simulate a typical ADA-positive subject and compare AUC at steady state.

typ_pop_ada <- typ_pop %>% mutate(ADA_TITER = 256)  # above threshold 128

typ_events_ada <- bind_rows(
  typ_pop_ada %>% crossing(TIME = dose_times) %>%
    mutate(AMT = 150, EVID = 1, CMT = 1, DV = NA_real_),
  typ_pop_ada %>% crossing(TIME = obs_times) %>%
    mutate(AMT = NA_real_, EVID = 0, CMT = 2, DV = NA_real_)
) %>%
  arrange(TIME, desc(EVID)) %>%
  as.data.frame()

sim_typ_ada <- rxSolve(mod_typ, typ_events_ada, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka', 'etalogitfdepot'

# AUC over interval 3 (weeks 16-28) for both typical profiles
auc_window <- function(df) {
  d <- df %>% filter(time >= 16 * 7, time <= 28 * 7, Cc > 0) %>% arrange(time)
  sum(diff(d$time) * (head(d$Cc, -1) + tail(d$Cc, -1)) / 2)
}
auc_ref <- auc_window(sim_typ)
auc_ada <- auc_window(sim_typ_ada)
cat(sprintf(
  paste0(
    "Typical-subject AUCtau (weeks 16-28):\n",
    "  ADA-negative:       %.1f ug*day/mL\n",
    "  ADA titer >= 128:   %.1f ug*day/mL  (%.1f%% change vs negative; paper: -30%%)\n"
  ),
  auc_ref, auc_ada, 100 * (auc_ada - auc_ref) / auc_ref
))
#> Typical-subject AUCtau (weeks 16-28):
#>   ADA-negative:       449.8 ug*day/mL
#>   ADA titer >= 128:   307.9 ug*day/mL  (-31.5% change vs negative; paper: -30%)

Assumptions and deviations

Suleiman 2019 does not publish individual-level PK or per-subject covariate values, so the virtual population above approximates the all-subject demographics in Table 2 rather than reproducing them:

Weight: sampled log-normal around an 87 kg median (Table 2 all- subject median) with SD 0.23 on the log scale, clipped to 42-200 kg.
Serum albumin: normal around 44 g/L (all-subject median), SD 3, clipped to 34-58 g/L (observed range).
Serum creatinine: normal around 76 umol/L (all-subject median), SD 16, clipped to 35-200 umol/L (observed range).
hs-CRP: log-normal around a 2.8 mg/L median (all-subject median), SD 1.0 on the log scale. hs-CRP is highly right-skewed.
ADA titer: set to 0 (negative) for the main virtual cohort because ~98.5% of phase III ADA-evaluable subjects had titers < 128. A separate typical-subject simulation with ADA titer = 256 demonstrates the above-threshold effect.
No correlation between continuous covariates is imposed; the paper does not report joint distributions.
Sex, age, race, country, baseline PASI, bilirubin, AST, ALT, NAb status were evaluated in the paper but not retained in the final model and are not part of the packaged model.
Phase I-II drug supply (F = 0.710). The packaged model’s default F uses the phase III drug-supply logit (2.09 → F = 0.890), because the approved clinical regimen uses the phase III drug supply. Users wishing to simulate the early-phase formulation can override logitfdepot to 0.896 when constructing the model object.
Terminal half-life of 28 days. The abstract’s ~28-day terminal half-life derives from the full bi-exponential eigenvalue of the 2-compartment system; a rough Vss / CL back-of-envelope under- estimates it by a few days.

Reference

Suleiman AA, Khatri A, Minocha M, Othman AA. Population Pharmacokinetics of Risankizumab in Healthy Volunteers and Subjects with Moderate to Severe Plaque Psoriasis: Integrated Analyses of Phase I-III Clinical Trials. Clin Pharmacokinet. 2019;58(10):1309-1321. doi:10.1007/s40262-019-00759-z