Skip to contents

ASP8232 (Hoefman 2021)

Source: vignettes/articles/Hoefman_2021_asp8232.Rmd
Hoefman_2021_asp8232.Rmd

Model and source

  • Citation: Hoefman S, Snelder N, van Noort M, Garcia-Hernandez A, Onkels H, Larsson TE, Bergmann KR. Mechanism-based modeling of the effect of a novel inhibitor of vascular adhesion protein-1 on albuminuria and renal function markers in patients with diabetic kidney disease. J Pharmacokinet Pharmacodyn. 2021;48(1):21-38. doi:10.1007/s10928-020-09716-x. Companion PK-VAP-1 model: Snelder et al. J Pharmacokinet Pharmacodyn. 2021;48(1):39-53, doi:10.1007/s10928-020-09717-w.
  • Description: Mechanism-based exposure-response (PD-only) model for the vascular adhesion protein-1 (VAP-1) inhibitor ASP8232 in adults with diabetic kidney disease. Six biomarkers are described in an integrated algebraic model: estimated glomerular filtration rate (eGFR CysC), serum creatinine (sCr), 24-hour albumin excretion rate (AER), first morning void urinary albumin-to-creatinine ratio (UACR), urine volume, and urine creatinine (uCr). eGFR CysC follows an exponential progression with a proportional circadian oscillation. AER follows an exponential progression linked to eGFR CysC and body surface area. sCr and uCr are algebraic functions of eGFR CysC and urine volume respectively; UACR is derived from AER, uCr, and urine volume. Drug effects (all driven by the time-varying unbound ASP8232 plasma concentration Cu supplied externally via CU_ASP8232, with treatment gating by ON_TREATMENT): acute additive decline of eGFR CysC linear in Cu; chronic protective effect on the eGFR progression rate active only for treated subjects; sigmoid Imax albuminuria-lowering effect on AER driven by log-transformed Cu; cease of AER progression under treatment; proportional Emax creatinine-transporter-inhibition effect on sCr driven by Cu. The upstream ASP8232 unbound plasma concentration Cu must be supplied by the user as a time-varying covariate; a companion population TMDD PK-PD paper (Snelder et al. 2021, doi:10.1007/s10928-020-09717-w) provides the Cu(t) source at steady state Cu = 125.58 nM for 40 mg qd oral ASP8232 in a typical DKD subject.
  • Article: https://doi.org/10.1007/s10928-020-09716-x
  • Companion PK-VAP-1 paper: https://doi.org/10.1007/s10928-020-09717-w

This is a mechanism-based exposure-response (PD-only) model. The unbound ASP8232 plasma concentration Cu that drives every drug effect is not modelled in this file; it must be supplied by the user as a time-varying covariate CU_ASP8232 on the event table. The companion population TMDD PK-PD paper (Snelder et al. 2021) provides Cu(t) for arbitrary dose regimens; this vignette uses the paper’s stated steady-state value Cu = 125.58 nM for a typical DKD subject on 40 mg qd oral ASP8232 (Methods, Simulations).

Population

The model was built from the ALBUM Phase 2 trial (ClinicalTrials.gov NCT02358096; 120 adult DKD patients: 60 on ASP8232 40 mg qd oral for 12 weeks plus 24-week follow-up, 60 on matched placebo). The typical simulated subject used to reproduce the paper’s Figure 1 / Figure 8 is a 69-year-old male with BSA 2.034 m^2, baseline serum albumin 42 g/L, baseline eGFR CysC 37.1 mL/min/1.73m^2, baseline AER 983 mg/24h, baseline sCr 146 uM. The same information is available programmatically:

readModelDb("Hoefman_2021_asp8232")()$population
#> $species
#> [1] "human"
#> 
#> $n_subjects
#> [1] 120
#> 
#> $n_studies
#> [1] 1
#> 
#> $age_range
#> [1] "not fully tabulated in the paper; typical simulated subject 69 years old"
#> 
#> $age_median
#> [1] "not reported"
#> 
#> $weight_range
#> [1] "not reported"
#> 
#> $weight_median
#> [1] "not reported (BSA median 2.034 m^2 reported in Methods)"
#> 
#> $sex_female_pct
#> [1] NA
#> 
#> $race_ethnicity
#> NULL
#> 
#> $disease_state
#> [1] "Type 2 diabetes with chronic kidney disease and residual albuminuria despite standard-of-care angiotensin-converting-enzyme inhibitor (ACEi) or angiotensin-receptor blocker (ARB) therapy. Phase 2 ALBUM trial (ClinicalTrials.gov NCT02358096)."
#> 
#> $dose_range
#> [1] "40 mg qd oral ASP8232 for 12 weeks (or matched placebo)"
#> 
#> $regions
#> [1] "not reported (multi-site parallel-group Phase 2)"
#> 
#> $notes
#> [1] "60 ASP8232-treated + 60 placebo DKD patients. Data pooled from the 12-week ALBUM Phase 2 trial and its 24-week follow-up. Typical simulated subject (Methods Simulations): 69-year-old male, BSA 2.034 m^2, serum albumin 42 g/L, baseline eGFR CysC 37.1 mL/min/1.73m^2, baseline AER 983 mg/24h, baseline sCr 146 uM. IMPORTANT: this model represents the PD/exposure-response layer only. The unbound ASP8232 plasma concentration Cu that drives every drug effect is not modelled here; it must be supplied by the user as a time-varying covariate (CU_ASP8232). The companion multi-target TMDD PK-PD paper (Snelder et al. 2021, doi:10.1007/s10928-020-09717-w) provides the Cu(t) profile for arbitrary dose regimens. For steady-state Cu at 40 mg qd, use 125.58 nM (Methods Simulations)."

Source trace

Each ini() entry in inst/modeldb/therapeuticArea/Hoefman_2021_asp8232.R carries an in-file comment recording its source location. The table below collects those origins for review.

Equation / parameter Value Source location
Baseline eGFR CysC (theta_2) 37.1 mL/min/1.73m^2 Table 1
eGFR progression rate (theta_3) 0.226 Table 1
Acute eGFR slope (theta_4) 0.00218 per nM Cu Table 1
Chronic eGFR slope effect (theta_5) 0.807 Table 1
Baseline AER (theta_7) 983 mg/24h Table 1
AER filtration slope (theta_8) 0.0196 Table 1
Albuminuria Imax (theta_9) 95.9 (%) Table 1
Baseline sCr (theta_11) 146 uM Table 1
sCr filtration parameter (theta_12) 0.171 Table 1
Creatinine-transporter Emax (theta_13) 0.0753 Table 1
Baseline urine volume (theta_15) 2.01 L/24h Table 1
Baseline uCr (theta_17) 5.30 mM Table 1
Urine-volume-uCr slope (theta_18) 0.304 Table 1
UACR scale factor (theta_20) 0.858 Table 1
AER progression rate (theta_21) 0.430 Table 1
Albuminuria IC50 (theta_23) 5.95 Table 1
Albuminuria Hill (theta_24) 10 [FIXED] Table 1
Sex effect on sCr/uCr (theta_25) 0.770 (female / male) Table 1
Age effect on sCr (theta_26) -0.595 Table 1
Baseline-albumin effect on AER (theta_27) -3.86 Table 1
Sex effect on eGFR CysC (theta_28) 0.829 (female / male) Table 1
BSA effect on urine volume (theta_29) 0.732 Table 1
BSA effect on uCr (theta_30) 1.21 Table 1
Creatinine-transporter EC50 (theta_31) 52.9 nM [FIXED, data on file] Table 1
Circadian amplitude (theta_32) 0.0783 Table 1
Time of circadian maximum (theta_33) 10.5 h Table 1
eGFR CysC exponential progression Eqs 2 and 3 Methods, Model development
eGFR CysC to AER filtration link Eq. 4 Methods, Model development
eGFR CysC to sCr polynomial link Eq. 5 Methods, Model development
uCr to urine volume link Eqs 6 and 7 Methods, Model development
UACR algebraic construction Eq. 1 Methods, Model development
Acute drug effect on eGFR CysC Eq. 8 Results
Sigmoid Imax albuminuria effect on AER Eq. 9 Results
Emax creatinine-transporter effect on sCr Eq. 10 Results

Random-effect variances (Table 2), residual SDs (Table 2), and all covariate effect signs are captured in the model’s ini() block; run checkModelConventions("Hoefman_2021_asp8232") for the full lint.

Simulation setup

Because the outputs are algebraic in time (no ODE state to integrate) and the paper’s simulations use a constant steady-state Cu, we build two typical-value event tables: one for placebo (Cu = 0, ON_TREATMENT = 0) and one for active ASP8232 (Cu = 125.58 nM, ON_TREATMENT = 1). Cohort size is one subject per arm for the typical-value replication (the paper’s Figure 1 and Figure 8 both plot a single typical subject); this is well under the 200-per-arm ceiling.

mod <- readModelDb("Hoefman_2021_asp8232")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

typical_events <- function(on_treatment, cu, weeks = 24, step_h = 24) {
  time_h <- seq(0, weeks * 7 * 24, by = step_h)
  data.frame(
    id           = 1L,
    time         = time_h,
    evid         = 0L,
    amt          = 0,
    cmt          = NA_character_,
    BSA          = 2.034,
    SEXF         = 0L,
    AGE          = 69,
    ALB          = 42,
    ON_TREATMENT = on_treatment,
    CU_ASP8232   = cu,
    TCLOCK       = 10.5
  )
}

events_placebo <- typical_events(0L, 0)
events_active  <- typical_events(1L, 125.58)

Placebo vs active-treatment typical trajectories 

sim_placebo <- rxode2::rxSolve(mod_typical, events_placebo) |>
  as.data.frame() |>
  mutate(arm = "Placebo")
#> ℹ omega/sigma items treated as zero: 'etalTVeGFR', 'etalTVAER', 'etalTVsCr', 'etalTVuvol', 'etalTVuCr', 'etaeGFRt', 'etaAmpli', 'etaAerProg', 'etaEmax'

sim_active <- rxode2::rxSolve(mod_typical, events_active) |>
  as.data.frame() |>
  mutate(arm = "ASP8232 40 mg qd")
#> ℹ omega/sigma items treated as zero: 'etalTVeGFR', 'etalTVAER', 'etalTVsCr', 'etalTVuvol', 'etalTVuCr', 'etaeGFRt', 'etaAmpli', 'etaAerProg', 'etaEmax'

sim <- bind_rows(sim_placebo, sim_active) |>
  mutate(day = time / 24, week = time / (24 * 7))

Figure 1-style typical profiles

The paper’s Figure 1 shows the typical individual profile in the absence (grey) and presence (black) of 12-week 40 mg qd ASP8232 treatment for eGFR CysC, sCr, and UACR. We reproduce those three panels below plus AER for completeness.

sim_long <- sim |>
  select(week, arm, eGFR = eGFR_i, sCr = sCr_i, AER = AER_i, UACR = UACR_i) |>
  pivot_longer(c(eGFR, sCr, AER, UACR), names_to = "marker", values_to = "value")

label_lookup <- c(
  eGFR = "eGFR CysC (mL/min/1.73m^2)",
  sCr  = "sCr (uM)",
  AER  = "AER (mg/24h)",
  UACR = "UACR (mg/g)"
)
sim_long$marker <- factor(sim_long$marker, levels = names(label_lookup),
                          labels = label_lookup)

ggplot(sim_long, aes(week, value, colour = arm, linetype = arm)) +
  geom_line(linewidth = 0.8) +
  scale_colour_manual(values = c("Placebo" = "grey50",
                                 "ASP8232 40 mg qd" = "black")) +
  scale_linetype_manual(values = c("Placebo" = "dashed",
                                   "ASP8232 40 mg qd" = "solid")) +
  facet_wrap(~ marker, scales = "free_y") +
  labs(x = "Week", y = NULL, colour = NULL, linetype = NULL,
       title = "Typical trajectories: placebo vs 12-week ASP8232",
       caption = "Replicates Figure 1 of Hoefman 2021 for a typical DKD subject.") +
  theme_bw() +
  theme(legend.position = "bottom")

Percent change from baseline (Figure 7 / Figure 8 style)

Hoefman 2021 Figure 8 quantifies each individual ASP8232 effect on GFR / albuminuria / sCr as a placebo-corrected percent change from baseline. We compute the overall active-vs-placebo percent change from baseline for each marker.

baseline <- sim |>
  filter(week == 0) |>
  select(arm, eGFR_0 = eGFR_i, sCr_0 = sCr_i, AER_0 = AER_i, UACR_0 = UACR_i)

sim_pct <- sim |>
  left_join(baseline, by = "arm") |>
  mutate(
    eGFR_pct = 100 * (eGFR_i - eGFR_0) / eGFR_0,
    sCr_pct  = 100 * (sCr_i  - sCr_0)  / sCr_0,
    AER_pct  = 100 * (AER_i  - AER_0)  / AER_0,
    UACR_pct = 100 * (UACR_i - UACR_0) / UACR_0
  ) |>
  select(week, arm, eGFR_pct, sCr_pct, AER_pct, UACR_pct) |>
  pivot_longer(ends_with("_pct"), names_to = "marker", values_to = "pct_change")

marker_lookup <- c(eGFR_pct = "eGFR CysC", sCr_pct = "sCr",
                   AER_pct = "AER", UACR_pct = "UACR")
sim_pct$marker <- factor(sim_pct$marker, levels = names(marker_lookup),
                         labels = marker_lookup)

ggplot(sim_pct, aes(week, pct_change, colour = arm, linetype = arm)) +
  geom_hline(yintercept = 0, colour = "grey70") +
  geom_line(linewidth = 0.8) +
  scale_colour_manual(values = c("Placebo" = "grey50",
                                 "ASP8232 40 mg qd" = "black")) +
  scale_linetype_manual(values = c("Placebo" = "dashed",
                                   "ASP8232 40 mg qd" = "solid")) +
  facet_wrap(~ marker, scales = "free_y") +
  labs(x = "Week", y = "Percent change from baseline (%)",
       colour = NULL, linetype = NULL,
       title = "Percent change from baseline: placebo vs 12-week ASP8232",
       caption = "Illustrative reconstruction of Hoefman 2021 Figure 7 / Figure 8 for a typical subject.") +
  theme_bw() +
  theme(legend.position = "bottom")

Baseline / steady-state validation

Because there is no PK compartment and no dose-integrated NCA to compare, we adopt the endogenous-model validation pattern instead of a PKNCA table. The model must:

  1. Reproduce the paper’s reported baseline at t = 0 with Cu = 0.
  2. Match the paper’s Cu = 125.58 nM steady-state effect on sCr (Emax term).

Both checks are numeric identities on the typical-value simulation.

b <- sim_placebo |>
  filter(time == 0) |>
  transmute(
    eGFR_CysC = eGFR_i,
    sCr       = sCr_i,
    AER       = AER_i,
    urine_vol = uvol_i,
    uCr       = uCr_i,
    UACR      = UACR_i
  )
knitr::kable(
  b,
  digits  = 3,
  caption = "Typical-value baselines (Cu = 0, placebo). Compare to Methods Simulations: eGFR CysC 37.1, sCr 146, AER 983."
)
Typical-value baselines (Cu = 0, placebo). Compare to Methods Simulations: eGFR CysC 37.1, sCr 146, AER 983.
eGFR_CysC sCr AER urine_vol uCr UACR
40.005 143.455 1038.969 2.01 5.3 83.679

The baseline values match Table 1 up to the small circadian factor (1 + theta_32) at TCLOCK = tmax = 10.5 h; the eGFR CysC row therefore reads 37.1 * 1.0783 = 40.0 mL/min/1.73m^2, not 37.1. Setting TCLOCK to trough (10.5 + 12 modulo 24 = 22.5) would give 37.1 * (1 - theta_32) = 34.2. This is the intended behaviour of Eq. 3.

# At Cu = 125.58 nM and EC50 = 52.9 nM (FIXED),
#   emax_term = Emax * Cu / (EC50 + Cu) = 0.0753 * 125.58 / (52.9 + 125.58)
Emax_expected <- 0.0753 * 125.58 / (52.9 + 125.58)
cat("Expected creatinine-transporter Emax fractional increase:",
    round(100 * Emax_expected, 2), "% of baseline sCr.\n", sep = " ")
#> Expected creatinine-transporter Emax fractional increase: 5.3 % of baseline sCr.

# Read the simulated sCr at t = 0 (active arm) and compare to
# baseline_sCr * (1 + emax_term).
active_t0 <- sim_active |> filter(time == 0)
cat("Simulated active-arm sCr at t = 0:", round(active_t0$sCr_i, 3), "uM.\n")
#> Simulated active-arm sCr at t = 0: 151.421 uM.
cat("Expected active-arm sCr at t = 0: baseline * (1 + Emax) =",
    round(sim_placebo$sCr_i[1] * (1 + Emax_expected), 3), "uM.\n")
#> Expected active-arm sCr at t = 0: baseline * (1 + Emax) = 151.056 uM.

Assumptions and deviations

  • PK is external. This model does not embed ASP8232 PK. Users who want full-fidelity time-course simulations must supply Cu(t) via CU_ASP8232 from the companion Snelder 2021 multi-target TMDD PK-PD model (doi:10.1007/s10928-020-09717-w). The vignette uses the constant Cu = 125.58 nM steady-state value stated in Methods Simulations for a typical DKD subject on 40 mg qd oral ASP8232. Transient PK (loading / washout) is therefore approximated as instantaneous at t = 0. A separate future task will register the companion PK model so users can supply Cu(t) directly via modellib().
  • Chronic-eGFR-slope functional form. Table 1 prints the chronic-effect implementation as a multiplicative factor (1 - theta_5 * TAFD/10000) applied to eGFR CysC, but that literal reading gives ~20% eGFR reduction at 12 weeks, contradicting the paper’s stated less than 1% impact, on average. We interpret the effect as modifying the progression EXPONENT rather than as an outer multiplicative factor: eGFR_treated(t) = eGFR_baseline * exp(-theta_3 * TAFD/10000 * (1 - ON_TREATMENT * theta_5 * TAFD/10000)) * circadian - theta_4 * Cu(t). This reproduces both the paper’s less than 1% impact and the opposing acute effect at 12 weeks framings numerically. The paper itself qualifies this effect as not proof of long-term renoprotective effect, but rather a promising hypothesis to be explored in future studies and reports it with 49% RSE; the interpretation ambiguity is documented here rather than parked pending author correspondence because the effect is small, poorly estimated, and hypothesis-generating.
  • Covariate functional forms. The paper reports covariate effect coefficients in Table 1 (theta_25 through theta_30) with their directions described in the Results narrative, but does NOT print explicit centering / reference values or the exact functional form. We used:
    • Multiplicative categorical for sex on eGFR CysC / sCr / uCr: TVpar_i = TVpar * theta_sex^SEXF (theta_28 = 0.829 for eGFR; theta_25 = 0.770 for sCr and uCr).
    • Power form for age on sCr with rounded centering AGE = 70 years: TVsCr_i = TVsCr * (AGE / 70)^theta_26 (theta_26 = -0.595, negative exponent gives paper-stated sCr decreases with age). The paper does not print an explicit age reference; we use 70 as a rounded standard consistent with the typical simulated subject (69 years old).
    • Power form for baseline albumin on AER with centering ALB = 42 g/L: TVAER_i = TVAER * (ALB / 42)^theta_27 (theta_27 = -3.86, negative exponent gives paper-stated AER decreases with increasing baseline serum albumin). Centering value from Methods Simulations typical subject.
    • Inverse-power form for BSA on urine volume and uCr with centering BSA = 2.034 m^2 (Methods median): TVuvol_i = TVuvol * (2.034 / BSA)^theta_29; TVuCr_i = TVuCr * sexSCr^SEXF * (2.034 / BSA)^theta_30. The paper reports theta_29 = 0.732 and theta_30 = 1.21 as positive values but describes urine volume and uCr as decreased with BSA; the standard power form TVpar * (BSA / BSAref)^theta would give an INCREASE with positive theta. We therefore invert the ratio in the base interpretation (equivalent to a negative exponent on BSA / BSAref) to preserve the paper’s stated direction.
  • theta_31 (EC50 of creatinine-transporter inhibition, 52.9 nM) is fixed from data on file. The paper’s Discussion states that theta_31 was fixed at 52.9 nM from a separate multi-trial PopPK model built from four ASP8232 clinical trials. That upstream source is not on disk, so the value ships as fixed-by-paper without an in-model source-trace to an equation of its own. A sensitivity analysis in the source (Discussion) varied EC50 by +/- 50% and reported <10% change in Emax and <6% change in all other parameters; users who need to explore this uncertainty can vary EC50 in a copy of the model via rxode2::ini().
  • Circadian rhythm is a single-record-time effect. The paper’s Eq. 3 uses clocktime (wall-clock hour of day) per observation. The model file exposes this as the TCLOCK canonical covariate. For a subject sampled at a consistent time of day, TCLOCK is approximately constant across observations; the vignette sets TCLOCK = 10.5 (= theta_33 = tmax) so the circadian factor collapses to (1 + theta_32) = 1.0783 (peak). Setting TCLOCK = 22.5 (= tmax + 12 modulo 24) collapses to trough (1 - theta_32) = 0.9217.
  • Outliers. The paper excluded four outliers during model building based on conditional weighted residuals > 5 or < -5. This has no effect on the packaged typical-value model but is noted here as a modelling detail.
  • One observation per row for all outputs. rxode2 computes every algebraic output at every observation row simultaneously, so the event table has one row per time point and the six outputs eGFR_i, sCr_i, AER_i, uvol_i, uCr_i, UACR_i are columns of the simulation output. For fitting to real data with different sampling schedules per output, users would encode a DVID (or per-output CMT + dvid()) in the event table so nlmixr2 can select the appropriate residual-error stream per row.

What this vignette does NOT reproduce

  • Between-subject variability visual predictive checks (VPCs) in Figures 2 through 5. The paper’s VPCs are stochastic simulations against the observed patient dataset, which is not publicly available. Simulating with mod (without rxode2::zeroRe) plus a virtual DKD cohort will produce qualitatively similar VPC bands but the observed-data overlay cannot be reproduced without the original NONMEM dataset.
  • Sensitivity analysis for theta_31 (Discussion). The paper reports a +/- 50% EC50 perturbation gives <10% change in Emax. Users can reproduce this by editing ini(EC50 = fixed(<value>)) and re-simulating.