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PF-04236921 (Li 2018)

Source: vignettes/articles/Li_2018_PF04236921.Rmd
Li_2018_PF04236921.Rmd

Model and source

  • Citation: Li C, Shoji S, Beebe J. Pharmacokinetics and C-reactive protein modelling of anti-interleukin-6 antibody (PF-04236921) in healthy volunteers and patients with autoimmune disease. Br J Clin Pharmacol. 2018;84(9):2059-2074. doi:10.1111/bcp.13641
  • Description: Integrated population PK and indirect-response PK/PD model for the anti-interleukin-6 monoclonal antibody PF-04236921 in healthy volunteers and adults with rheumatoid arthritis, Crohn’s disease, or systemic lupus erythematosus (Li 2018). Two-compartment IV/SC PK with first-order absorption and linear elimination from the central compartment; disease-stratified linear clearance and PD parameters; PF-04236921 inhibits the zero-order CRP synthesis rate of an indirect-response model.
  • Article: https://doi.org/10.1111/bcp.13641

PF-04236921 is a fully-human anti-interleukin-6 monoclonal antibody developed by Pfizer. The Li 2018 paper integrates pharmacokinetic and PK/PD data from five Phase 1 / Phase 2 trials covering healthy volunteers, rheumatoid arthritis, Crohn’s disease, and systemic lupus erythematosus into a single popPK and indirect-response PK/PD model on serum C-reactive protein (CRP).

Population

The pooled analysis dataset included 392 subjects across five clinical studies:

  • B0151001 (Phase 1 single ascending IV dose, healthy volunteers, n = 36)
  • B0151004 (Phase 1 single 200 mg SC dose, healthy volunteers, n = 10)
  • B0151002 (Phase 1 multiple ascending IV dose, rheumatoid arthritis on background methotrexate, n = 31)
  • B0151003 (Phase 2 proof-of-concept SC dose-ranging, moderate-to-severe Crohn’s disease refractory to anti-TNF, n = 178)
  • B0151006 (Phase 2 proof-of-concept SC dose-ranging, active generalized systemic lupus erythematosus, n = 138)

Baseline demographics summarised from Li 2018 Table 2 (p2065): pooled-cohort median body weight 72 kg (range 30-157 kg), albumin 4.0 g/dL (2.3-5.0 g/dL), creatinine clearance 113 mL/min (47.0-329 mL/min), and baseline CRP varying across cohorts from a median of 0.9 mg/L in healthy volunteers to 19.4 mg/L in CD subjects. The pooled cohort is approximately 48 percent female.

The same population summary is available programmatically via readModelDb("Li_2018_PF04236921")$population.

Source trace

In-file source-trace comments live next to every ini() entry in inst/modeldb/specificDrugs/Li_2018_PF04236921.R. The table below collects them in one place.

Equation / parameter Value Source location
lcl (HV reference CL) log(0.00546 L/h) Table 3A theta_CL,HV (p2068)
e_ra_cl, e_cd_cl, e_sle_cl log-ratios on HV CL Table 3A theta_CL,RA/CD/SLE (p2068)
lvc log(3.03 L) Table 3A theta_Vc
lq log(0.0245 L/h) Table 3A theta_Q
lvp log(3.58 L) Table 3A theta_Vp
lka log(0.00607 1/h) Table 3A theta_ka
lfdepot log(1) fixed Results “Final PK model” p2063 (“F fixed to 100 percent”)
e_wt_cl, e_wt_vc, e_wt_q, e_wt_vp power exponents Table 3A theta_BWT_on_* (ref 72 kg, p2064 PK equation)
e_alb_cl, e_crcl_cl, e_crp_cl power exponents Table 3A (ref 4.0 g/dL ALB, 113 mL/min CRCL, 7.6 mg/L CRP)
e_sex_cl 0.862 multiplier Table 3A theta_SEX_on_CL (paper Eq. (theta)^(SEX-1))
q_vc_scale 2.73 Table 3A theta_IIV_on_Q; paper Eq. eta_Q = theta * eta_Vc
IIV block (CL, Vc, Vp) omega^2 = (CV/100)^2 Table 3A footnote b on p2069
lbase, e_*_base typical BLCRP per cohort Table 3B theta_BLCRP,HV/RA/CD/SLE (p2068)
e_alb_base -3.69 Table 3B theta_ALB_on_BLCRP
lic50, e_*_ic50 typical IC50 per cohort Table 3B IC50,HV/RA/CD/SLE
logitimax, e_*_logitimax typical Imax per cohort Table 3B Imax,HV/RA/CD/SLE (Imax = exp(theta_Imax)/(1 + exp(theta_Imax)))
e_alb_logitimax -1.53 power exp (logit scale) Table 3B theta_ALB_on_Imax
lkout log(0.0238 1/h) Table 3B theta_Kout
lgamma log(1) fixed Table 3B theta_gamma,HV/RA/CD = 1 fix
e_sle_gamma log(1.55) Table 3B theta_gamma,SLE
IIV block (BLCRP, Imax) + IC50 omega^2 = (CV/100)^2 Table 3B footnote d on p2069
PK residual expSd 0.179 Table 3A pooled patient CV (RA/CD/SLE)
PD residual expSd_CRP 0.453 Table 3B residual CV (45.3 percent)
ODE: 2-cmt PK + first-order absorption n/a Results “Final PK model” p2063 + paper Eq. p2064
ODE: indirect response on CRP n/a Methods “Final PK/PD model” p2062, p2066

Virtual cohort

The original observed concentrations are not publicly available. The figures below use deterministic typical-value simulations from the published parameter estimates (between-subject variability zeroed out via rxode2::zeroRe()) running one representative dose level per cohort.

Reference covariate values for the typical subject (Li 2018 Methods, p2064 and Supplemental Figure S3 caption): BWT 72 kg, ALB 4.0 g/dL, CRCL 113 mL/min, CRP 1.16 / 7.81 / 15.5 / 2.42 mg/L for HV / RA / CD / SLE respectively, male.

set.seed(2018)

mod_full <- rxode2::rxode2(readModelDb("Li_2018_PF04236921"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typ  <- rxode2::zeroRe(mod_full)

# Observation grid (in hours) -- 0 to 60 weeks
obs_times <- sort(unique(c(
  seq(0,   28,   by = 1),
  seq(28,  168,  by = 4),
  seq(168, 720,  by = 12),
  seq(720, 60 * 168, by = 24)
)))

make_cohort <- function(id, label, route, doses_mg, dose_times_h,
                        WT, SEXF, ALB, CRCL, CRP,
                        DIS_RA, DIS_CD, DIS_SLE) {
  cmt_dose <- if (route == "iv") "central" else "depot"
  ev <- rxode2::et()
  for (k in seq_along(doses_mg)) {
    ev <- rxode2::et(ev,
                     amt  = doses_mg[k],
                     cmt  = cmt_dose,
                     evid = 1L,
                     time = dose_times_h[k])
  }
  # Sample Cc at every time on the grid; sample CRP_pred at the same grid.
  ev <- rxode2::et(ev, obs_times, cmt = "Cc")
  ev <- rxode2::et(ev, obs_times, cmt = "CRP_pred")
  ev <- as.data.frame(ev)
  ev$id      <- id
  ev$cohort  <- label
  ev$WT      <- WT
  ev$SEXF    <- SEXF
  ev$ALB     <- ALB
  ev$CRCL    <- CRCL
  ev$CRP     <- CRP
  ev$DIS_RA  <- DIS_RA
  ev$DIS_CD  <- DIS_CD
  ev$DIS_SLE <- DIS_SLE
  ev
}

events <- bind_rows(
  make_cohort(1L, "HV-IV (700 mg single IV)",  "iv",
              doses_mg = 700,  dose_times_h = 0,
              WT = 72, SEXF = 0, ALB = 4.5, CRCL = 116, CRP = 0.9,
              DIS_RA = 0, DIS_CD = 0, DIS_SLE = 0),
  make_cohort(2L, "HV-SC (200 mg single SC)",  "sc",
              doses_mg = 200,  dose_times_h = 0,
              WT = 72, SEXF = 0, ALB = 4.5, CRCL = 123, CRP = 0.8,
              DIS_RA = 0, DIS_CD = 0, DIS_SLE = 0),
  make_cohort(3L, "RA-IV (250 mg IV Q4W x 3)", "iv",
              doses_mg = c(250, 250, 250),  dose_times_h = c(0, 28*24, 56*24),
              WT = 61, SEXF = 1, ALB = 4.2, CRCL = 93.3, CRP = 7.4,
              DIS_RA = 1, DIS_CD = 0, DIS_SLE = 0),
  make_cohort(4L, "CD-SC (200 mg SC at Day 1, Week 4)", "sc",
              doses_mg = c(200, 200),  dose_times_h = c(0, 4 * 7 * 24),
              WT = 70, SEXF = 1, ALB = 4.0, CRCL = 110, CRP = 19.4,
              DIS_RA = 0, DIS_CD = 1, DIS_SLE = 0),
  make_cohort(5L, "SLE-SC (200 mg SC at Day 1, Week 8, Week 16)", "sc",
              doses_mg = c(200, 200, 200),  dose_times_h = c(0, 8 * 7 * 24, 16 * 7 * 24),
              WT = 73, SEXF = 1, ALB = 3.9, CRCL = 119, CRP = 2.9,
              DIS_RA = 0, DIS_CD = 0, DIS_SLE = 1)
)

Simulation 

sim <- rxode2::rxSolve(mod_typ, events = events, keep = c("cohort"))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalka', 'etalbase', 'etalogitimax', 'etalic50'
#> Warning: multi-subject simulation without without 'omega'
sim_df <- as.data.frame(sim)

Replicate published figures

The published PK time courses (paper Figure 1a) show multi-exponential decay following the IV doses and a flatter SC profile reflecting the slow absorption rate (ka = 0.00607 1/h, absorption half-life ~ 5 days). The simulated typical profiles below reproduce that qualitative shape.

sim_df |>
  dplyr::filter(time > 0, Cc > 0) |>
  ggplot(aes(time / (24 * 7), Cc, colour = cohort)) +
  geom_line(linewidth = 0.6) +
  scale_y_log10() +
  labs(
    x = "Time (weeks)",
    y = "PF-04236921 concentration (ng/mL)",
    title = "Figure 1a-equivalent: typical-value PK by cohort",
    caption = "Replicates the qualitative dose-route stratification in Figure 1a of Li 2018."
  ) +
  theme_minimal() +
  theme(legend.position = "bottom")

The published CRP response (paper Figure 1b) shows a delayed CRP reduction relative to PF-04236921 Cmax (the paper notes a ~5-day delay) followed by recovery as drug is cleared. Note: the CRP curve below uses the cohort-specific baseline CRP value as the steady-state pre-dose CRP (CRP(0) = BLCRP), and the simulated CRP returns toward that baseline after drug elimination.

sim_df |>
  ggplot(aes(time / (24 * 7), CRP_pred, colour = cohort)) +
  geom_line(linewidth = 0.6) +
  scale_y_log10() +
  labs(
    x = "Time (weeks)",
    y = "CRP (mg/L)",
    title = "Figure 1b-equivalent: typical-value CRP response by cohort",
    caption = "Replicates the qualitative CRP reduction pattern in Figure 1b of Li 2018."
  ) +
  theme_minimal() +
  theme(legend.position = "bottom")

PKNCA validation

NCA for the single-dose cohorts (HV-IV 700 mg and HV-SC 200 mg). The multi-dose cohorts (RA, CD, SLE) accumulate concentration across dosing intervals and are not directly comparable to a single-dose NCA.

sim_nca <- sim_df |>
  dplyr::filter(time > 0, !is.na(Cc), Cc > 0,
                cohort %in% c("HV-IV (700 mg single IV)",
                              "HV-SC (200 mg single SC)")) |>
  dplyr::distinct(id, time, .keep_all = TRUE) |>
  dplyr::transmute(id = as.integer(id), time = time / 24, Cc = Cc, treatment = cohort)

dose_df <- events |>
  dplyr::filter(evid == 1, id %in% c(1L, 2L)) |>
  dplyr::transmute(id = as.integer(id), time = time / 24, amt = amt,
                   treatment = cohort)

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

intervals <- data.frame(
  start       = 0,
  end         = 60 * 7,  # day
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.0416667) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0416667) is not allowed
knitr::kable(
  as.data.frame(nca_res$result),
  caption = "Simulated NCA parameters for single-dose HV cohorts (time in days, Cc in ng/mL)."
)
Simulated NCA parameters for single-dose HV cohorts (time in days, Cc in ng/mL).
treatment id start end PPTESTCD PPORRES exclude
HV-IV (700 mg single IV) 1 0 420 cmax 2.288549e+05 NA
HV-IV (700 mg single IV) 1 0 420 tmax 4.166670e-02 NA
HV-IV (700 mg single IV) 1 0 420 tlast 4.200000e+02 NA
HV-IV (700 mg single IV) 1 0 420 clast.obs 2.309266e+02 NA
HV-IV (700 mg single IV) 1 0 420 lambda.z 1.438510e-02 NA
HV-IV (700 mg single IV) 1 0 420 r.squared 9.999131e-01 NA
HV-IV (700 mg single IV) 1 0 420 adj.r.squared 9.999129e-01 NA
HV-IV (700 mg single IV) 1 0 420 lambda.z.time.first 6.000000e+00 NA
HV-IV (700 mg single IV) 1 0 420 lambda.z.time.last 4.200000e+02 NA
HV-IV (700 mg single IV) 1 0 420 lambda.z.n.points 4.430000e+02 NA
HV-IV (700 mg single IV) 1 0 420 clast.pred 2.296649e+02 NA
HV-IV (700 mg single IV) 1 0 420 half.life 4.818513e+01 NA
HV-IV (700 mg single IV) 1 0 420 span.ratio 8.591863e+00 NA
HV-IV (700 mg single IV) 1 0 420 aucinf.obs NA Requesting an AUC range starting (0) before the first measurement (0.0416667) is not allowed
HV-SC (200 mg single SC) 2 0 420 cmax 2.425841e+04 NA
HV-SC (200 mg single SC) 2 0 420 tmax 1.050000e+01 NA
HV-SC (200 mg single SC) 2 0 420 tlast 4.200000e+02 NA
HV-SC (200 mg single SC) 2 0 420 clast.obs 6.859067e+01 NA
HV-SC (200 mg single SC) 2 0 420 lambda.z 1.447610e-02 NA
HV-SC (200 mg single SC) 2 0 420 r.squared 9.999851e-01 NA
HV-SC (200 mg single SC) 2 0 420 adj.r.squared 9.999851e-01 NA
HV-SC (200 mg single SC) 2 0 420 lambda.z.time.first 1.100000e+01 NA
HV-SC (200 mg single SC) 2 0 420 lambda.z.time.last 4.200000e+02 NA
HV-SC (200 mg single SC) 2 0 420 lambda.z.n.points 4.290000e+02 NA
HV-SC (200 mg single SC) 2 0 420 clast.pred 6.880709e+01 NA
HV-SC (200 mg single SC) 2 0 420 half.life 4.788204e+01 NA
HV-SC (200 mg single SC) 2 0 420 span.ratio 8.541825e+00 NA
HV-SC (200 mg single SC) 2 0 420 aucinf.obs NA Requesting an AUC range starting (0) before the first measurement (0.0416667) is not allowed

Comparison against published expectations

Li 2018 reports key descriptive PK metrics in the Results and Discussion rather than in a side-by-side single-dose NCA table:

  • SC absorption peak: paper p2065 notes Cmax was reached at approximately 120 hours (5 days) post-dose following a single 200 mg SC administration in study B0151004; the simulated Tmax above for HV-SC should fall in the same range.
  • Terminal half-life: paper p2070 reports approximately 32-39 days in healthy / RA / SLE subjects from the beta-phase elimination rate constant; the simulated half.life for HV-IV should fall in that range.
  • Dose-normalized AUCinf: paper p2065 reports geometric mean of 262,050 ng/h/mL per mg for SC 200 mg in B0151004. The simulated typical AUCinf for HV-SC divided by 200 mg gives a comparable reference value.
  • Per-cohort typical CRP: pre-dose typical CRP equals the cohort-specific BLCRP from Table 3B (1.16 / 7.81 / 15.5 / 2.42 mg/L for HV / RA / CD / SLE), and the simulated CRP_pred at time 0 should match these.

Assumptions and deviations

  • Residual error. Li 2018 estimated separate log-normal residual variance for HV.IV (CV 10.7 percent), HV.SC (CV 28.3 percent), and the pooled patient cohort RA/CD/SLE (CV 17.9 percent), with an additional IIV(eta_error) = 40.1 percent multiplying the per-subject residual SD on the PK side. The packaged model collapses this three-group residual structure to the pooled-patient single value (expSd = 0.179) and drops the IIV-on-residual layer because nlmixr2’s log-normal error model assumes a single residual SD per output. The same simplification applies to the PD residual (single expSd_CRP = 0.453, no IIV-on-residual). Downstream simulations under the packaged model are slightly less variable than the paper’s NONMEM fits.

  • Disease-cohort parameter encoding. The paper estimated theta_CL, theta_BLCRP, theta_IC50, and theta_Imax separately for each of the four cohorts (HV, RA, CD, SLE) as independent THETAs. The packaged model re-expresses this as a HV-reference structural value plus three log-shift covariate-effect parameters keyed on DIS_RA, DIS_CD, and DIS_SLE. The numerical typical values for each cohort match the paper’s Table 3A and Table 3B exactly when only one indicator is 1 (the cohorts are non-overlapping). The encoding is mathematically equivalent to the paper’s per-cohort THETAs but presents a cleaner covariate-effect interface.

  • Imax covariate form. The paper’s Eq. (p2066) writes theta_prime_Imax = theta_Imax * (ALB / 4.0)^theta_ALB_on_Imax, i.e. the ALB effect is multiplicative on the LOGIT-scale parameter rather than additive. The packaged model encodes this multiplicative form verbatim; it differs from the more common “additive on logit” convention. For ALB at the reference 4.0 g/dL the multiplier is 1 and the cohort-specific Imax matches the published value.

  • Eta_Q derived from eta_Vc. The paper writes eta_Q = theta_IIV_on_Q * eta_Vc (a derived random effect rather than an independent draw). The packaged model encodes this with a fixed-effect scalar q_vc_scale = 2.73 applied to etalvc inside the Q parameterisation, matching the paper’s structural form. This avoids the singular 4x4 covariance matrix that would result from forcing eta_Q to be 100 percent correlated with eta_Vc inside the IIV block.

  • CRP units. The covariate column CRP and the model state effect (output CRP_pred) are both in mg/L per the paper’s Table 2 reporting. The paper’s Methods section reports the LLOQ in mg/dL (1 mg/dL = 10 mg/L); this model file’s covariate notes flag the mg/L convention explicitly.

  • Creatinine clearance units. Li 2018 Table 2 reports CLcr in “mL/min” without the BSA normalisation that the canonical CRCL register entry defaults to (mL/min/1.73 m^2). The packaged model carries the raw mL/min unit and documents the deviation in covariateData[[CRCL]]$notes so that a downstream user supplies the same convention.

  • Bioavailability. SC F was fixed to 1 in the paper’s base model (Results, p2063), supported by comparable dose-normalised AUCinf estimates between IV and SC at similar doses. The packaged model encodes this as lfdepot <- fixed(log(1)).

  • Placebo / baseline drift. The paper found placebo-arm CRP time courses were approximately constant (Supplemental Figure S1) and the model assumes a constant pre-treatment CRP equal to BLCRP. No placebo / baseline-drift term is in the packaged model.

  • Typical-value figures vs VPCs. The published Figure 1 (panels a and b) shows observed-data medians and the published Figure 4 shows prediction-corrected VPCs. The reproductions in this vignette use the typical patient (random effects zeroed via rxode2::zeroRe()) at one representative dose per cohort – enough to reproduce the qualitative dose-route stratification but not the within-cohort variability or the dose-range richness of the published figures.