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Rivipansel (Tammara 2017)

Source: vignettes/articles/Tammara_2017_rivipansel.Rmd
Tammara_2017_rivipansel.Rmd

Model and source

The integrated population PK model published by Tammara and Harnisch (2017) was used to inform the rivipansel phase III dose-selection exercise in pediatric patients with sickle cell disease (SCD). The model pools 109 subjects from three rivipansel phase I studies and the phase II study (NCT01119833) in adolescents and adults hospitalized for vaso-occlusive crisis (VOC). It is a three-compartment IV linear disposition model with creatinine clearance and body weight as the only structural covariates.

  • Citation: Tammara BK, Harnisch LO. Dose Selection Based on Modeling and Simulation for Rivipansel in Pediatric Patients Aged 6 to 11 Years With Sickle Cell Disease. CPT Pharmacometrics Syst Pharmacol. 2017;6(12):845-854.
  • Article: https://doi.org/10.1002/psp4.12263

Population

The integrated dataset pooled 109 subjects aged 12-51 years across four studies: rivipansel study 101 (single IV dose 2-40 mg/kg in healthy adults, n = 40), study 102 (multiple IV doses 2-20 mg/kg q8h plus a 40 mg/kg loading dose followed by 20 mg/kg q8h in healthy adults, n = 32), study 103 / NCT00911495 (two IV doses 20 mg/kg loading + 10 mg/kg in adults with SCD not in VOC, n = 15), and the phase II study NCT01119833 (Telen 2015) in patients with SCD aged 12-60 years hospitalized for VOC, n = 76 (56 adults and 20 children aged 12-17 years). Rivipansel is renally cleared with about 60% protein binding and a low volume of distribution; phase I half-life is approximately 7-8 hours.

The same population metadata is available programmatically:

readModelDb("Tammara_2017_rivipansel")$population

Source trace

Every ini() value carries a trailing comment in inst/modeldb/specificDrugs/Tammara_2017_rivipansel.R pointing to its source location. The table below collects them for review.

Equation / parameter Value Source location
Three-compartment IV linear disposition with central + peripheral1 + peripheral2 – Methods, “Study design and data sources”
Typical CL = 1.25 * (CRCL/150)^0.468 * (1 + 0.234 * STUD) – Table 1 footnote b
Typical V1 = 6.24 * (WT/70)^0.569 – Table 1 footnote c
Typical V2 = 4.02 * (WT/70)^0.569 – Table 1 footnote c
Typical V3 = 0.656 * (WT/70)^0.569 – Table 1 footnote c
lcl (CL, L/h) 1.25 Table 1, CL row
lvc (V1, L) 6.24 Table 1, V1 row
lq (Q_rapid, L/h) 2.62 Table 1, Q_rapid row
lvp (V2, L) 4.02 Table 1, V2 row
lq2 (Q_slow, L/h) 0.0316 Table 1, Q_slow row
lvp2 (V3, L) 0.656 Table 1, V3 row
e_study_riv201_cl (additive SCD shift, fraction) 0.234 Table 1, “Study effect on CL” row
e_crcl_cl (CRCL exponent on CL) 0.468 Table 1, “Exponent for CRCL on CL” row
e_wt_vc_vp_vp2 (shared WT exponent) 0.569 Table 1, “Exponent for WT on V1, V2, V3” row
IIV %CV on CL / V1 / Q_rapid / V2 / Q_slow / V3 18.8 / 24.1 / 19.8 / 15.5 / 15.5 / 15.3 Table 1, interindividual variability rows
Additive residual SD (phase I / study 201) 0.29 / 0.165 ug/mL Table 1, residual variability rows
Proportional residual %CV (phase I / study 201) 9.52 / 23.2 Table 1, residual variability rows

Virtual cohort

The original observed data are not publicly available. The cohort below approximates the phase II SCD population, with body weight and creatinine clearance distributions drawn from typical SCD-cohort ranges and STUDY_RIV201 set to 1 for every subject (the simulation target is the SCD population for which the dose-selection exercise applies).

set.seed(12263)  # DOI suffix
n_subj <- 100

# Body weight (kg). Phase II included adolescents and adults; weight
# distribution sampled to span a typical adolescent-adult SCD range
# (Tammara 2017 Figure 2; observed phase II weights ranged roughly
# 40-110 kg with median near 70 kg).
WT <- pmin(pmax(rnorm(n_subj, mean = 70, sd = 15), 45), 110)

# Creatinine clearance (mL/min, NOT BSA-normalized; raw Cockcroft-Gault
# scale per Tammara 2017). SCD hyperfiltration shifts the typical CRCL
# in adults upward of the 120 mL/min anchor; the simulated distribution
# centres on 130 mL/min and spans 60-200 mL/min, matching the observed
# range in Tammara 2017 Figure 4 (adult panel).
CRCL <- pmin(pmax(rnorm(n_subj, mean = 130, sd = 30), 60), 200)

# Phase II SCD study indicator: 1 for every subject in the target
# population (the simulation context is the SCD cohort).
STUDY_RIV201 <- rep(1L, n_subj)

cohort <- tibble(
  id           = seq_len(n_subj),
  WT           = WT,
  CRCL         = CRCL,
  STUDY_RIV201 = STUDY_RIV201
)

Simulation

Rivipansel is administered as a 20-minute IV infusion. The dose-selection regimen recommended by Tammara 2017 for phase III is a 40 mg/kg loading dose followed by 20 mg/kg every 12 hours; we simulate that regimen out to seven days so steady state is reached.

infusion_dur <- 20 / 60  # 20 minutes expressed in hours
tau          <- 12       # dosing interval (hours)
maint_doses  <- 13       # 13 maintenance doses after loading -> 14 doses, 7 days

# Per-subject dosing: loading dose at time 0, then maintenance doses
# at 12-hour intervals. amt is in mg (weight-based mg/kg dose times
# subject weight); rate is amt / 20-min infusion duration.
make_doses <- function(row) {
  load_amt  <- 40 * row$WT
  maint_amt <- 20 * row$WT
  dose_times <- c(0, tau * seq_len(maint_doses))
  amt        <- c(load_amt, rep(maint_amt, maint_doses))
  data.frame(
    id           = row$id,
    time         = dose_times,
    amt          = amt,
    rate         = amt / infusion_dur,
    evid         = 1L,
    cmt          = "central",
    WT           = row$WT,
    CRCL         = row$CRCL,
    STUDY_RIV201 = row$STUDY_RIV201
  )
}

doses <- cohort |>
  split(seq_len(nrow(cohort))) |>
  lapply(make_doses) |>
  bind_rows()

# Observation grid: every 0.5 h for the first 24 h to characterise the
# loading-dose phase, then every 2 h out to 168 h (7 days). The final
# dosing interval (156-168 h) is the steady-state window used for NCA.
obs_times <- sort(unique(c(
  seq(0, 24, by = 0.5),
  seq(24, 168, by = 2)
)))
obs <- expand_grid(
  id = cohort$id,
  time = obs_times
) |>
  mutate(amt = NA_real_, rate = NA_real_, evid = 0L, cmt = "central") |>
  left_join(cohort, by = "id")

events <- bind_rows(doses, obs) |>
  arrange(id, time, desc(evid))
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
mod <- readModelDb("Tammara_2017_rivipansel")
sim <- rxode2::rxSolve(mod, events = events,
                       keep = c("WT", "CRCL", "STUDY_RIV201")) |>
  as.data.frame() |>
  filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published figures 

# Approximate Tammara 2017 Figure 5 (adult panel column on the 40/20
# mg/kg regimen): predicted concentration-time trajectory in adult SCD
# subjects on the recommended regimen. Median and 5th/95th prediction
# intervals over 168 h.
sim |>
  group_by(time) |>
  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(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "steelblue") +
  geom_line(colour = "steelblue4") +
  geom_hline(yintercept = 10, linetype = "dashed", colour = "red") +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "Rivipansel concentration (ug/mL)",
    title = "Adult SCD prediction interval on 40/20 mg/kg q12h",
    caption = paste(
      "Replicates the adult panel of Tammara 2017 Figure 5 (rightmost",
      "row; 40/20 mg/kg regimen). Dashed line: 10 ug/mL preclinical",
      "efficacy threshold."
    )
  )
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.

# Approximate Tammara 2017 Figure 6 (high-dose panel for adults): the
# Cavg,ss distribution in adults on the 20 mg/kg q12h maintenance
# regimen. Computed analytically from each subject's individual CL
# rather than from the simulated concentration trace (per the paper:
# "Cavg,ss simulations did not contain residual error as they reflect
# a model-based summary measure across the whole dosing interval").
mod_typical <- mod  # individual CL from simulation already includes IIV
cavg_ss <- sim |>
  group_by(id) |>
  slice(1) |>
  ungroup() |>
  mutate(
    maint_amt = 20 * WT,
    cl_i      = exp(log(1.25)) * (CRCL / 150)^0.468 *
                  (1 + 0.234 * STUDY_RIV201),
    Cavg_ss   = (maint_amt / tau) / cl_i
  )

ggplot(cavg_ss, aes(x = "20 mg/kg q12h", y = Cavg_ss)) +
  geom_boxplot(fill = "darkseagreen", width = 0.4, outlier.alpha = 0.4) +
  geom_hline(yintercept = 10, linetype = "dashed", colour = "red") +
  labs(
    x = NULL,
    y = "Cavg,ss (ug/mL)",
    title = "Adult Cavg,ss on the recommended 40/20 mg/kg regimen",
    caption = paste(
      "Replicates the adult-panel portion of Tammara 2017 Figure 6",
      "(right panel, 40/20 mg/kg). Dashed line: 10 ug/mL preclinical",
      "efficacy threshold."
    )
  )

PKNCA validation

Validation against the published Cavg,ss summary (Figure 6) and the phase I terminal half-life (Methods narrative: mean phase I half-life 7-8 hours). The steady-state NCA window is the final dosing interval (156-168 h) at the 20 mg/kg q12h maintenance dose; results are grouped by the single treatment label.

sim_nca <- sim |>
  mutate(treatment = "40/20 mg/kg q12h") |>
  select(id, time, Cc, treatment)

dose_df <- events |>
  filter(evid == 1) |>
  mutate(treatment = "40/20 mg/kg q12h") |>
  select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ time | treatment + id,
  concu = "ug/mL", timeu = "hour"
)
dose_obj <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | treatment + id,
  doseu = "mg"
)

start_ss <- max(dose_df$time)
end_ss   <- start_ss + tau

intervals <- data.frame(
  start    = c(0,        start_ss),
  end      = c(tau,      end_ss),
  cmax     = c(TRUE,     TRUE),
  tmax     = c(TRUE,     TRUE),
  cmin     = c(FALSE,    TRUE),
  auclast  = c(TRUE,     TRUE),
  cav      = c(FALSE,    TRUE),
  ctrough  = c(FALSE,    TRUE)
)

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

nca_tbl <- as.data.frame(nca_res$result)
nca_summary <- nca_tbl |>
  group_by(PPTESTCD, start, end) |>
  summarise(
    median = median(PPORRES, na.rm = TRUE),
    q05    = quantile(PPORRES, 0.05, na.rm = TRUE),
    q95    = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  arrange(start, PPTESTCD)

knitr::kable(
  nca_summary,
  digits = 3,
  caption = paste(
    "Simulated NCA parameters for the 40/20 mg/kg q12h regimen.",
    "Start = 0 covers the loading-dose interval; start =", start_ss,
    "covers the steady-state interval (last maintenance dose +",
    tau, "h)."
  )
)
Simulated NCA parameters for the 40/20 mg/kg q12h regimen. Start = 0 covers the loading-dose interval; start = 156 covers the steady-state interval (last maintenance dose + 12 h).
PPTESTCD start end median q05 q95
auclast 0 12 1516.846 1028.825 2061.162
cmax 0 12 366.380 256.237 503.384
tmax 0 12 0.500 0.500 0.500
auclast 156 168 807.992 461.565 1500.439
cav 156 168 67.333 38.464 125.037
cmax 156 168 127.121 83.967 185.605
cmin 156 168 31.320 11.254 78.076
ctrough 156 168 NA NA NA
tmax 156 168 2.000 2.000 2.000

Terminal half-life from a single-dose simulation

The paper reports a mean phase I terminal half-life of 7-8 hours. To verify the model reproduces that value, simulate a single 40 mg/kg dose in a typical 70-kg phase I subject (STUDY_RIV201 = 0, CRCL = 100) and compute the terminal half-life via PKNCA.

typ <- tibble(
  id           = 1L,
  WT           = 70,
  CRCL         = 100,
  STUDY_RIV201 = 0L
)

typ_events <- bind_rows(
  data.frame(
    id   = 1L, time = 0, amt = 40 * 70,
    rate = (40 * 70) / infusion_dur, evid = 1L, cmt = "central",
    WT = 70, CRCL = 100, STUDY_RIV201 = 0L
  ),
  data.frame(
    id   = 1L, time = seq(0, 72, by = 0.25),
    amt = NA_real_, rate = NA_real_, evid = 0L, cmt = "central",
    WT = 70, CRCL = 100, STUDY_RIV201 = 0L
  )
) |>
  arrange(time, desc(evid))

mod_zero <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: No sigma parameters in the model
typ_sim <- rxode2::rxSolve(mod_zero, events = typ_events,
                           keep = c("WT", "CRCL", "STUDY_RIV201")) |>
  as.data.frame() |>
  filter(!is.na(Cc), time > 0) |>
  mutate(id = 1L, treatment = "single 40 mg/kg")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp', 'etalq2', 'etalvp2'

conc_obj_typ <- PKNCA::PKNCAconc(
  typ_sim |> select(id, time, Cc, treatment),
  Cc ~ time | treatment + id,
  concu = "ug/mL", timeu = "hour"
)
dose_obj_typ <- PKNCA::PKNCAdose(
  data.frame(id = 1L, time = 0, amt = 40 * 70,
             treatment = "single 40 mg/kg"),
  amt ~ time | treatment + id,
  doseu = "mg"
)
intervals_typ <- data.frame(
  start      = 0,
  end        = Inf,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE
)
nca_typ <- suppressWarnings(PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj_typ, dose_obj_typ, intervals = intervals_typ)
))
typ_tbl <- as.data.frame(nca_typ$result) |>
  select(PPTESTCD, PPORRES)
knitr::kable(
  typ_tbl,
  digits = 3,
  caption = "Typical-value NCA after a single 40 mg/kg IV infusion in a phase I 70-kg subject (CRCL = 100 mL/min)."
)
Typical-value NCA after a single 40 mg/kg IV infusion in a phase I 70-kg subject (CRCL = 100 mL/min).
PPTESTCD PPORRES
cmax 375.000
tmax 0.500
tlast 72.000
clast.obs 0.626
lambda.z 0.063
r.squared 1.000
adj.r.squared 1.000
lambda.z.time.first 64.750
lambda.z.time.last 72.000
lambda.z.n.points 30.000
clast.pred 0.625
half.life 11.012
span.ratio 0.658
aucinf.obs NA

The published phase I mean half-life of 7-8 hours is the comparator against the half.life row above.

Assumptions and deviations

  • The phase II SCD residual error magnitudes (addSd_study201, propSd_study201) and the phase I magnitudes (addSd_phase1, propSd_phase1) are estimated separately in Tammara 2017 Table 1. The model file selects between them per observation via the STUDY_RIV201 indicator. Simulations targeting the SCD population use STUDY_RIV201 = 1, which selects propSd = 0.232, addSd = 0.165 ug/mL.
  • Tammara 2017 expresses CRCL in raw mL/min (Cockcroft-Gault for adults, Schwartz with BSA adjustment for children to give an absolute mL/min value), not normalised to 1.73 m^2. The canonical CRCL covariate accepts both conventions; this model file’s covariateData[[CRCL]]$units is "mL/min" to flag the non-BSA-normalised use.
  • Body weight and CRCL distributions for the virtual cohort are approximated from the figures in the paper (Figure 2 for weight, Figure 4 for creatinine clearance in adults). The exact baseline demographics table for the integrated dataset is not reproduced in the publication.
  • The Cavg,ss distribution figure uses the closed-form Cavg,ss = (dose / tau) / CL_i per subject, matching the paper’s approach (“Cavg,ss simulations did not contain residual error as they reflect a model-based summary measure across the whole dosing interval”).
  • The model does not encode the pediatric (6-11 year) demographic extrapolation from the CDC growth charts and the Hoste creatinine relationship that the paper develops for its simulation exercise. Users extrapolating to younger pediatric populations must supply the appropriate WT, CRCL covariate values themselves; the structural model and the SCD hyperfiltration effect are assumed by the paper to apply unchanged in younger children.
  • No eta correlation structure was reported in Table 1; the six IIV terms are encoded as independent log-normal random effects.