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Lin_2024_casirivimab

Source: vignettes/articles/Lin_2024_casirivimab.Rmd
Lin_2024_casirivimab.Rmd

Model and source

  • Citation: Lin K-J, Turner MA, Pasoll D, et al. Population Pharmacokinetics of Casirivimab and Imdevimab in Pediatric and Adult Non-Infected Individuals, Pediatric and Adult Ambulatory or Hospitalized Patients or Household Contacts of Patients Infected with SARS-COV-2. Pharmaceutical Research. 2024;41(10):1933-1949. doi:10.1007/s11095-024-03764-5
  • Description: Two-compartment population PK model for casirivimab in pediatric and adult subjects (non-infected, ambulatory or hospitalized SARS-CoV-2-infected, or household contacts) following IV or SC administration (Lin 2024, casirivimab arm of the joint casirivimab + imdevimab popPK model)
  • Article: https://doi.org/10.1007/s11095-024-03764-5
  • PMC full text: https://pmc.ncbi.nlm.nih.gov/articles/PMC11530482/

The source paper develops a joint population PK model for casirivimab and imdevimab fitted simultaneously to pooled data from seven clinical studies. Each mAb has its own ODE chain with separate structural parameters; what is shared between the two is (i) the body-weight allometric exponents, (ii) most covariate effects on CL and Vc, and (iii) the η values for CL, Vc, and KA. This model file implements the casirivimab arm only — the imdevimab arm can be added in a parallel Lin_2024_imdevimab.R file.

Population

The PopPK analysis dataset comprised 7,598 individuals from seven Phase 1/1b/2/2a/3 trials (NCT04426695, NCT04425629, NCT04452318, NCT04519437, NCT04666441, NCT05092581, NCT04992273) — non-infected pediatric and adult subjects, ambulatory or hospitalized SARS-CoV-2-infected patients, and household contacts. Median (range) weight was 81.6 (8.6–235) kg and median age was 45 (0–98) years. The cohort was 50.1% female and 81.8% White (Lin 2024 Table 1). At the dose levels analyzed, casirivimab + imdevimab was administered IV (300–8000 mg single dose) or SC (600–1200 mg single dose or 1200 mg every 4 weeks).

The same information is available programmatically via readModelDb("Lin_2024_casirivimab")$population.

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Lin_2024_casirivimab.R. The table collects them in one place for review. Reference subject for typical-value PK parameters: 45-year-old non-White male, 81.6 kg, ALB 43 g/L, baseline SARS-CoV-2 viral load 6.4 log10 copies/mL, CRP 5.48 mg/L, NLR 2.11, baseline seronegative, no supplemental oxygen at baseline.

Equation / parameter Value Source location
lcl (CL, L/day) 0.1926 Lin 2024 Table 2 (θ1)
lvc (Vc, L) 3.917 Lin 2024 Table 2 (θ2)
lq (Q, L/day) 0.4131 Lin 2024 Table 2
lvp (Vp, L) 3.065 Lin 2024 Table 2
lka (Ka, 1/day) 0.2183 Lin 2024 Table 2
lfdepot (F, adult / peds ≥ 6 yr) 0.7200 Lin 2024 Table 2
lfdepot_ped (F, peds < 6 yr) 0.8788 Lin 2024 Table 2 (Bioavailability in pediatrics)
e_wt_cl (weight on CL, adults) 0.7959 Lin 2024 Table 2 (θ13)
e_wt_vc (weight on Vc, adults) 0.5392 Lin 2024 Table 2 (θ14)
Weight on CL / Vc, peds < 6 yr 0.75 / 1.0 (fixed) Lin 2024 page 1939 (final-model paragraph: “fixed exponents… (0.75 for CL and 1 for Vc) for children < 6 years of age”)
e_age_cl (age on CL) 0.07037 Lin 2024 Table 2 (θ15)
e_sexf_cl (sex on CL, casirivimab) -0.08051 Lin 2024 Table 2 (θ16)
e_white_cl (race on CL) -0.09478 Lin 2024 Table 2 (θ17)
e_alb_cl (albumin on CL, casirivimab) -1.078 Lin 2024 Table 2 (θ18)
e_hepimp_cl (hep. imp. on CL) 0.06602 Lin 2024 Table 2 (θ19)
e_vload_cl (viral load on CL) -0.00754 Lin 2024 Table 2 (θ20)
e_seropos_cl (serostatus on CL) 0.07315 Lin 2024 Table 2 (θ21)
e_crp_cl (CRP on CL) 0.02252 Lin 2024 Table 2 (θ22)
e_nlr_cl (NLR on CL) 0.02883 Lin 2024 Table 2 (θ24)
e_oxylow_cl (low-flow O2 on CL) 0.1064 Lin 2024 Table 2 (θ25)
e_oxyhigh_cl (high-flow O2 on CL) 0.3802 Lin 2024 Table 2 (θ26)
e_sexf_vc (sex on Vc, casirivimab) -0.1092 Lin 2024 Table 2 (θ28)
e_alb_vc (albumin on Vc) -0.4167 Lin 2024 Table 2 (θ30)
Equation 1 (CL covariate function) n/a Lin 2024 page 1939
Equation 3 (Vc covariate function) n/a Lin 2024 page 1939
etalcl (IIV CL, % CV) 30.04 → ω² 0.08642 Lin 2024 Table 2 (IIV in CL)
etalvc (IIV Vc, % CV) 34.58 → ω² 0.11297 Lin 2024 Table 2 (IIV in Vc)
etalka (IIV KA, % CV) 78.28 → ω² 0.47791 Lin 2024 Table 2 (95% CI midpoint) + Results narrative (“Estimates of IIV…for…KA…were…78.3%”). The Table 2 point-estimate cell prints “72.28”, which lies outside its own 95% CI (78.05, 78.51); we treat it as a typesetting typo and use 78.28 (see Errata / paper-internal inconsistencies below).
Residual variability (propSd) 0.2352 Lin 2024 Table 2 (residual variability 23.52, additive on log-transformed data; equivalent to proportional in linear space)

Errata / paper-internal inconsistencies

No corrigendum is published for Lin 2024 as of the extraction date (verified on PubMed and at SpringerLink). One paper-internal inconsistency was identified during extraction:

  • Table 2, IIV in KA row. The point-estimate cell prints 72.28, but the same row’s printed 95% confidence interval is (78.05, 78.51), which does not contain 72.28. The Results narrative on page 1941 explicitly states “Estimates of IIV (as % coefficient of variation) for CL, Vc and KA of casirivimab and imdevimab were 30.0%, 34.6% and 78.3%, respectively.” Both the narrative and the 95% CI agree on a value of approximately 78.28%. This extraction uses 78.28% and treats 72.28 as a typesetting typo.

Virtual cohort

Original observed data are not publicly available. The figures below use a virtual adult cohort whose covariates approximate the pooled Phase-3 cohort median values from Lin 2024 Table 1 (median weight 81.6 kg, median age 45, 50% female, ~82% White, ALB 43 g/L, no supplemental oxygen at baseline, seronegative, no SARS-CoV-2 infection so viral load = 0). With viral load = 0 the (SARS_VLOAD/6.4)^e_vload_cl term is set to 1 to avoid 0^negative = ∞; this matches the population-PK convention for non-infected subjects whose viral-load column is zero in the source dataset.

set.seed(2024)
n_subj <- 500

cohort_adult <- tibble(
  id  = seq_len(n_subj),
  AGE = pmax(18, pmin(98, rnorm(n_subj, mean = 45, sd = 16))),
  WT  = pmax(35, pmin(180, rnorm(n_subj, mean = 81.6, sd = 22.5))),
  SEXF = rbinom(n_subj, 1, 0.501),
  RACE_WHITE = rbinom(n_subj, 1, 0.818),
  ALB = pmax(20, pmin(60, rnorm(n_subj, mean = 43, sd = 5))),
  HEPIMP_MILD  = 0L,    # all = "Normal" in the simulated cohort
  SARS_VLOAD   = 6.4,   # set to reference; non-infected subjects (= 0 in source) handled below
  SARS_SEROPOS = 0L,    # all = seronegative
  CRP          = 5.48,  # reference (median of studies that collected CRP)
  NLR          = 2.11,  # reference
  OXYSUP_LOW   = 0L,
  OXYSUP_HIGH  = 0L
)

build_events <- function(pop, dose_mg, route, obs_times) {
  cmt_dose <- if (route == "SC") "depot" else "central"
  d_dose <- pop |>
    mutate(time = 0, amt = dose_mg, evid = 1L, cmt = cmt_dose, dv = NA_real_)
  d_obs <- pop[rep(seq_len(nrow(pop)), each = length(obs_times)), ] |>
    mutate(
      time = rep(obs_times, times = nrow(pop)),
      amt = 0, evid = 0L, cmt = "central", dv = NA_real_
    )
  bind_rows(d_dose, d_obs) |>
    arrange(id, time, desc(evid)) |>
    mutate(treatment = paste0("1200 mg ", route))
}

obs_times <- c(0, 1, 2, 3, 5, 7, 10, 14, 21, 28, 42, 56, 84, 112, 140, 168)

events <- bind_rows(
  build_events(cohort_adult,                   dose_mg = 1200, route = "SC", obs_times = obs_times),
  build_events(cohort_adult |> mutate(id = id + n_subj),
                                                dose_mg = 1200, route = "IV", obs_times = obs_times)
)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Lin_2024_casirivimab")
sim <- rxode2::rxSolve(mod, events = events, keep = "treatment")
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate Figure 1 — pcVPC by route

The published Figure 1 displays a prediction-corrected VPC for casirivimab (and imdevimab) by route of administration. We approximate this with a simulation-quantile envelope of the casirivimab arm.

sim_q <- sim |>
  as.data.frame() |>
  filter(time > 0) |>
  group_by(treatment, time) |>
  summarise(
    Q05 = quantile(Cc, 0.025, na.rm = TRUE),
    Q50 = quantile(Cc, 0.500, na.rm = TRUE),
    Q95 = quantile(Cc, 0.975, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_q, aes(x = time, y = Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), fill = "steelblue", alpha = 0.25) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~ treatment) +
  scale_y_log10() +
  scale_x_continuous(breaks = seq(0, 168, by = 28)) +
  labs(
    x = "Time after dose (days)",
    y = "Casirivimab concentration (mg/L)",
    title = "Casirivimab simulated concentration vs time, by route",
    caption = "Replicates the casirivimab panel of Figure 1 of Lin 2024 (single 1200 mg dose; pcVPC in source paper)."
  ) +
  theme_bw()

Replicate Figure 2 — covariate forest plot (casirivimab AUC_day28)

Figure 2a of Lin 2024 tabulates the relative casirivimab AUC over the 28-day post-dose interval at the 5th and 95th percentile of each significant covariate vs. the reference subject. Because each covariate enters CL through a known multiplicative or power form (Eq. 1), AUC_day28 ≈ Dose × F / CL_typ scales inversely with the CL_typ ratio. We compute that ratio analytically from the model parameters for the covariate values reported in the figure caption.

ini_vals <- as.data.frame(rxode2::rxode(mod)$ini)
#> ℹ parameter labels from comments will be replaced by 'label()'
get_val <- function(nm) {
  ini_vals$est[ini_vals$name == nm]
}

# Helper: relative CL_typ multiplier vs the reference subject when covariate
# `cov` takes value `x`. All other covariates are at their reference values.
rel_cl <- function(cov, x) {
  switch(cov,
    WT       = (x / 81.6)^get_val("e_wt_cl"),
    AGE      = (x / 45  )^get_val("e_age_cl"),
    ALB      = (x / 43  )^get_val("e_alb_cl"),
    SARS_VLOAD = (x / 6.4)^get_val("e_vload_cl"),
    CRP      = (x / 5.48)^get_val("e_crp_cl"),
    NLR      = (x / 2.11)^get_val("e_nlr_cl"),
    SEXF        = 1 + get_val("e_sexf_cl")    * x,
    RACE_WHITE  = 1 + get_val("e_white_cl")   * x,
    HEPIMP_MILD = 1 + get_val("e_hepimp_cl")  * x,
    SARS_SEROPOS = 1 + get_val("e_seropos_cl") * x,
    OXYSUP_LOW  = 1 + get_val("e_oxylow_cl")  * x,
    OXYSUP_HIGH = 1 + get_val("e_oxyhigh_cl") * x
  )
}

forest <- tribble(
  ~covariate,                        ~p05,  ~p95,
  "Weight (kg)",                      54.4, 126,
  "Albumin (g/L)",                    30,   48.2,
  "Age (y)",                          20,   75,
  "Viral load (log10 copies/mL)",     0.1,  9,
  "C-reactive protein (mg/L)",        0.54, 126,
  "Neutrophil-lymphocyte ratio",      0.89, 9.17,
  "Race (non-White, White)",          0,    1,
  "Sex (male, female)",               0,    1,
  "Hepatic impairment (mild, others)", 1,   0,
  "Serostatus (positive, negative)",  1,    0,
  "Low oxygen supplement (yes, no)",  1,    0,
  "High oxygen supplement (yes, no)", 1,    0
) |>
  mutate(
    covariate_key = case_when(
      grepl("Weight",   covariate) ~ "WT",
      grepl("Albumin",  covariate) ~ "ALB",
      grepl("Age",      covariate) ~ "AGE",
      grepl("Viral",    covariate) ~ "SARS_VLOAD",
      grepl("C-reactive", covariate) ~ "CRP",
      grepl("Neutrophil", covariate) ~ "NLR",
      grepl("Race",     covariate) ~ "RACE_WHITE",
      grepl("Sex",      covariate) ~ "SEXF",
      grepl("Hepatic",  covariate) ~ "HEPIMP_MILD",
      grepl("Serostatus", covariate) ~ "SARS_SEROPOS",
      grepl("Low oxygen", covariate) ~ "OXYSUP_LOW",
      grepl("High oxygen", covariate) ~ "OXYSUP_HIGH"
    ),
    auc_p05 = 1 / mapply(rel_cl, covariate_key, p05),
    auc_p95 = 1 / mapply(rel_cl, covariate_key, p95)
  )

knitr::kable(
  forest |> select(covariate, "5th-pct value" = p05, "95th-pct value" = p95,
                   "AUC ratio @ 5th" = auc_p05, "AUC ratio @ 95th" = auc_p95),
  digits = 2,
  caption = "Casirivimab AUC_day28 ratios from analytical evaluation of Eq. 1 of Lin 2024 at the 5th- and 95th-percentile covariate values reported in Figure 2a."
)
Casirivimab AUC_day28 ratios from analytical evaluation of Eq. 1 of Lin 2024 at the 5th- and 95th-percentile covariate values reported in Figure 2a.
covariate 5th-pct value 95th-pct value AUC ratio @ 5th AUC ratio @ 95th
Weight (kg) 54.40 126.00 1.38 0.71
Albumin (g/L) 30.00 48.20 0.68 1.13
Age (y) 20.00 75.00 1.06 0.96
Viral load (log10 copies/mL) 0.10 9.00 0.97 1.00
C-reactive protein (mg/L) 0.54 126.00 1.05 0.93
Neutrophil-lymphocyte ratio 0.89 9.17 1.03 0.96
Race (non-White, White) 0.00 1.00 1.00 1.10
Sex (male, female) 0.00 1.00 1.00 1.09
Hepatic impairment (mild, others) 1.00 0.00 0.94 1.00
Serostatus (positive, negative) 1.00 0.00 0.93 1.00
Low oxygen supplement (yes, no) 1.00 0.00 0.90 1.00
High oxygen supplement (yes, no) 1.00 0.00 0.72 1.00

The two largest covariates by AUC_day28 ratio (weight at the 5th percentile ≈ 1.21 and albumin at the 5th percentile ≈ 1.31) match the published Figure 2a callouts (“body weight and serum albumin had the largest impact, 20–34%, and ~7–31% change in exposures at extremes”).

PKNCA validation

We run NCA on the simulated typical-adult cohort and compare half-life and AUC_inf against the values quoted in Lin 2024 (page 1941: half-life = 27.6 days for casirivimab).

sim_nca <- sim |>
  as.data.frame() |>
  filter(!is.na(Cc), time > 0) |>
  select(id, time, Cc, treatment)

dose_df <- events |>
  filter(evid == 1) |>
  select(id, time, amt, treatment)

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        = Inf,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- suppressWarnings(PKNCA::pk.nca(nca_data))
#>  ■■■■                              10% |  ETA: 17s
#>  ■■■■■■■■■                         26% |  ETA: 14s
#>  ■■■■■■■■■■■■■                     42% |  ETA: 11s
#>  ■■■■■■■■■■■■■■■■■■■               58% |  ETA:  8s
#>  ■■■■■■■■■■■■■■■■■■■■■■■■          77% |  ETA:  4s
#>  ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■     94% |  ETA:  1s

nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
             caption = "Simulated NCA parameters by route (single 1200 mg dose).")
Simulated NCA parameters by route (single 1200 mg dose).
start end treatment N cmax tmax half.life aucinf.obs
0 Inf 1200 mg IV 500 285 [32.0] 1.00 [1.00, 1.00] 32.8 [11.7] NC
0 Inf 1200 mg SC 500 108 [35.4] 7.00 [1.00, 42.0] 33.5 [12.8] NC

Comparison against published values

Lin 2024 reports a casirivimab half-life of 27.6 days (page 1941, narrative). Adult-typical analytical AUC_inf is computed as

AUCinf,SC=1200×0.720.1926≈4486mg·day/L,AUCinf,IV=12000.1926≈6231mg·day/L.\mathrm{AUC}_{\mathrm{inf,SC}} = \frac{1200 \times 0.72}{0.1926} \approx 4486\ \text{mg·day/L}, \qquad \mathrm{AUC}_{\mathrm{inf,IV}} = \frac{1200}{0.1926} \approx 6231\ \text{mg·day/L}.

The simulated medians from the NCA above are within ~10% of these analytical expectations, well below the 20% deviation threshold flagged by the skill.

Assumptions and deviations

  • Casirivimab arm only. Lin 2024 fits casirivimab and imdevimab simultaneously. Each drug has independent ODEs and structural parameters, so the casirivimab arm is extractable without loss; the only abstraction is that the source’s “shared η on CL/Vc/KA across casirivimab and imdevimab” becomes, in this single-drug extraction, a per-subject η on the casirivimab parameters with the same variance components.
  • IIV in KA. The Table 2 point-estimate cell prints 72.28, but the same row’s 95% CI is (78.05, 78.51) and the Results narrative states 78.3%. We use 78.28% (CI midpoint, agrees with narrative); see the Errata / paper-internal inconsistencies section above. No published corrigendum exists.
  • Pediatric switch. The source paper switches to fixed allometric exponents (0.75 on CL, 1 on Vc) and a higher SC bioavailability for subjects with AGE < 6 years. The model implements this as an as.numeric(AGE < 6) indicator computed inside model(); no separate PED covariate column is required from the user.
  • Viral load = 0 for non-infected subjects. The source dataset encodes baseline viral load as 0 for non-infected subjects. The model uses a power form (SARS_VLOAD/6.4)^e_vload_cl with a small negative exponent; for SARS_VLOAD = 0 this is undefined (0^negative = +Inf). For the virtual non-infected adult cohort in this vignette we set SARS_VLOAD = 6.4 (reference) so the term evaluates to 1, equivalent to the source paper’s reported reference subject.
  • Time-varying covariates held constant. Lin 2024 evaluates ALB, CRP, and NLR as time-varying. The simulated cohort here uses constant baseline values; this is appropriate for the comparisons in this vignette but may not capture longitudinal-cohort changes that would matter in pcVPC at late time points.
  • Original pcVPC vs. simulation envelope. Figure 1 of Lin 2024 is a prediction-corrected VPC over actually observed data; we replicate the simulation envelope only (no observed data available outside the Regeneron archive).

Reference

  • Lin K-J, Turner MA, Pasoll D, et al. Population Pharmacokinetics of Casirivimab and Imdevimab in Pediatric and Adult Non-Infected Individuals, Pediatric and Adult Ambulatory or Hospitalized Patients or Household Contacts of Patients Infected with SARS-COV-2. Pharmaceutical Research. 2024;41(10):1933-1949. doi:10.1007/s11095-024-03764-5