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Esketamine and noresketamine (Perez-Ruixo 2020)

Source: vignettes/articles/PerezRuixo_2020_esketamine.Rmd
PerezRuixo_2020_esketamine.Rmd

Model and source 

#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Perez-Ruixo C, Rossenu S, Zannikos P, Nandy P, Singh J, Drevets WC, Perez-Ruixo JJ. Population Pharmacokinetics of Esketamine Nasal Spray and its Metabolite Noresketamine in Healthy Subjects and Patients with Treatment-Resistant Depression. Clin Pharmacokinet. 2021;60(4):501-516.
  • Article: https://doi.org/10.1007/s40262-020-00953-4

The model is a joint three-compartment esketamine plus two-compartment apparent noresketamine population PK with a hepato-portal first-pass (well-stirred) compartment, fit to 9784 esketamine and 9397 noresketamine plasma concentrations from 820 healthy volunteers and patients with treatment-resistant depression (TRD) who received esketamine by the intranasal, intravenous, and oral routes across 13 clinical studies.

Population

The pooled population (Perez-Ruixo 2020 Table 2) comprised 820 subjects: 256 healthy volunteers from Phase I studies and 564 TRD patients from Phase II / Phase III studies. Demographics were median age 45 years (range 18-86), median body weight 74 kg (range 39-170), 58.4% female. Race distribution: 72.4% White (89.1% Caucasian, 10.9% Hispanic), 6.82% Black, 13.7% Asian (64.3% Japanese, 35.7% non-Japanese), 7.07% Other (Native Hawaiian / Pacific Islander / American Indian / Alaska Native). The intranasal dose range was 14-112 mg with twice-weekly dosing. The IV route was studied at 28 mg and the PO route at 84 mg in the Phase I cross-over study ESKETINTRD1009.

The same information is available programmatically via readModelDb("PerezRuixo_2020_esketamine")()$population. readModelDb() returns the model function; the trailing () evaluates it to the model object whose $population element holds this list.

Source trace

Every ini() parameter is annotated with a Table 3 source-trace comment in inst/modeldb/specificDrugs/PerezRuixo_2020_esketamine.R. The table below collects the structural-parameter and IIV source locations in one place.

Equation / parameter Value Source location
FRn 0.54 Table 3, Esketamine / Absorption / Nasal dose
dose_FRn_effect 0.62 Table 3 footnote: “Dose effect is the dose-dependent effect in FRn”
e_japanese_FRn 1.34 Table 3, Esketamine / Absorption / Nasal dose
ka_n (1/h) 2.93 Table 3
Dsw (h) 0.53 Table 3
ka_sw (1/h) 1.45 Table 3
Dpo (h) 0.32 Table 3
ka_po (1/h) 0.97 Table 3
Fgut 0.64 Table 3
Vc (L) 192 Table 3, Esketamine / Disposition
Q1 (L/h) 84.3 Table 3
Vp1 (L) 143 Table 3
Q2 (L/h) 37.6 Table 3
Vp2 (L) 417 Table 3
Qh (L/h) 151 Table 3
e_age_qh (L/h/y) -2.19 Table 3 (applied only for AGE > 60)
Vh (L) 101 Table 3
kel (1/h) 1.11 Table 3
e_asian_kel 0.36 Table 3 (64.0% decrease)
kmet (1/h) 2.77 Table 3
Vcn/F (L) 70.0 Table 3, Noresketamine / Disposition
CLn/F (L/h) 38.0 Table 3
e_asian_CLn 0.81 Table 3 (19.4% decrease)
Vpn/F (L) 115 Table 3
Q3/F (L/h) 26.1 Table 3
omega(FRn) 70.8 (additive on logit) Table 3 Inter-individual variability
omega(ka_n) (CV%) 61.5 Table 3
omega(ka_sw) (CV%) 132 Table 3
omega(ka_po) (CV%) 132 Table 3
omega(Vc) (CV%) 27.5 Table 3
omega(Vp1) (CV%) 49.3 Table 3
omega(Qh) (CV%) 23.2 Table 3
omega(Vh) (CV%) 34.6 Table 3
omega(kel) (CV%) 120 Table 3
omega(kmet) (publication omission) Table 3 Estimate column blank; see Errata
omega(Vcn/F) (CV%) 31.6 Table 3
omega(CLn/F) (CV%) 25.4 Table 3
sigma1(esketamine) (Phase I/II, CV%) 27.6 Table 3 Residual variability
sigma2(noresketamine) (Phase I/II, CV%) 42.2 Table 3
d/dt(depot) (nasal cavity) n/a Section 2.3 + Fig. 1
d/dt(depot2) (oral depot for swallowed nasal) n/a Section 2.3 + Fig. 1
d/dt(depot3) (oral depot for PO solution) n/a Section 2.3 + Fig. 1
d/dt(central) (esketamine) n/a Section 2.3 + Fig. 1
d/dt(peripheral1) (Q1, Vp1) n/a Section 2.3 + Fig. 1
d/dt(peripheral2) (Q2, Vp2) n/a Section 2.3 + Fig. 1
d/dt(liver) (hepato-portal) n/a Section 2.3 + Fig. 1 (well-stirred)
d/dt(central_snk) (noresketamine apparent) n/a Section 2.3 + Fig. 1
d/dt(peripheral1_snk) (Q3, Vpn) n/a Section 2.3 + Fig. 1
F_n = FRn + (1-FRn) * Fgut * (1-E) bioavailability Section 2.3 derivation
F_po = Fgut * (1-E) bioavailability Section 2.3 derivation
E = Vh * (kel+kmet) / (Qh + Vh * (kel+kmet)) hepatic extraction Section 2.3 derivation

Virtual cohort and simulation events

Original observed data are not publicly available (Janssen Research and Development). The figures and NCA below use a typical-value virtual subject (no between-subject variability) for each covariate-stratified scenario in Table 4: Caucasian < 60 years; Asian non-Japanese < 60 years; Asian Japanese < 60 years; Caucasian 70 years; Asian non-Japanese 70 years; Asian Japanese 70 years – each at 28 mg, 56 mg, and 84 mg intranasal. The combination yields 6 strata x 3 doses = 18 typical-value profiles.

The dose effect on FRn (Table 3: 0.62 reduction factor for the second and subsequent 28-mg sprays of a multi-spray nasal dose) is not applied dynamically inside model() – the model exposes the per-spray FRn and the dose_FRn_effect parameter, and the per-dose effective FRn is computed externally in this vignette by the helper below. For a dose of N x 28 mg, the effective per-dose FRn is

FRn_eff = FRn_per_spray * (1 + (N - 1) * dose_FRn_effect) / N

which yields 0.54 / 0.4375 / 0.4032 for 28 / 56 / 84 mg. The override is applied via params=list(logitFRn = logit(FRn_eff)) per cohort.

mod <- readModelDb("PerezRuixo_2020_esketamine") |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'

logit  <- function(p) log(p / (1 - p))
ilogit <- function(x) 1 / (1 + exp(-x))

FRn_per_spray <- 0.54
dose_FRn_red  <- 0.62

# Per-dose effective FRn (Caucasian baseline).
effective_FRn <- function(dose_mg) {
  N <- dose_mg / 28
  FRn_per_spray * (1 + (N - 1) * dose_FRn_red) / N
}

# Strata: race x age, all combinations the paper reports in Table 4.
strata <- tibble::tribble(
  ~stratum,                                ~RACE_ASIAN, ~RACE_JAPANESE, ~AGE,
  "18-60 y, Caucasian",                    0L,          0L,             45,
  "18-60 y, Asian non-Japanese",           1L,          0L,             45,
  "18-60 y, Asian Japanese",               1L,          1L,             45,
  "> 60 y, Caucasian",                     0L,          0L,             70,
  "> 60 y, Asian non-Japanese",            1L,          0L,             70,
  "> 60 y, Asian Japanese",                1L,          1L,             70
)

dose_levels <- c(28, 56, 84)

# Build one event-table block per (stratum, dose).
make_events <- function(stratum, RACE_ASIAN, RACE_JAPANESE, AGE,
                        dose_mg, id_offset, cohort_id) {
  id   <- id_offset + 1L
  base <- data.frame(
    id = id, RACE_ASIAN = RACE_ASIAN, RACE_JAPANESE = RACE_JAPANESE,
    AGE = AGE, stratum = stratum, dose_mg = dose_mg,
    cohort_id = cohort_id,
    stringsAsFactors = FALSE
  )
  doses <- rbind(
    cbind(base, time = 0, amt = dose_mg, rate = 0, evid = 1L, cmt = "depot"),
    cbind(base, time = 0, amt = dose_mg, rate = 0, evid = 1L, cmt = "depot2")
  )
  obs <- cbind(
    base,
    time = seq(0.001, 24, length.out = 481),
    amt = 0, rate = 0, evid = 0L, cmt = "Cc"
  )
  rbind(doses, obs)
}

events_list <- list()
id_counter  <- 0L
for (i in seq_len(nrow(strata))) {
  for (d in dose_levels) {
    id_counter <- id_counter + 1L
    events_list[[length(events_list) + 1L]] <- make_events(
      stratum       = strata$stratum[i],
      RACE_ASIAN    = strata$RACE_ASIAN[i],
      RACE_JAPANESE = strata$RACE_JAPANESE[i],
      AGE           = strata$AGE[i],
      dose_mg       = d,
      id_offset     = id_counter - 1L,
      cohort_id     = id_counter
    )
  }
}
events <- do.call(rbind, events_list)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation

Each (stratum, dose) combination is simulated as a separate rxSolve call so the dose-specific effective logitFRn can be passed. Results are stacked into a single data frame for downstream plotting and NCA.

# Extract the model's typical-value THETA vector and override only the
# logitFRn entry per cohort. Passing a full named numeric vector via
# params= keeps every other parameter at its registered typical value;
# rxode2 requires every theta entry to be present when params= is used.
theta_default <- mod$theta

sim_list <- list()
for (i in seq_along(events_list)) {
  ev      <- events_list[[i]]
  dose_mg <- ev$dose_mg[1L]
  FRn_eff <- effective_FRn(dose_mg)
  params  <- theta_default
  params[["logitFRn"]] <- logit(FRn_eff)
  s <- rxode2::rxSolve(
    mod, events = ev, params = params,
    keep = c("stratum", "dose_mg", "RACE_ASIAN", "RACE_JAPANESE", "AGE",
             "cohort_id"),
    addDosing = FALSE
  )
  s_df <- as.data.frame(s)
  # rxSolve strips the single-id column. The cohort_id covariate was
  # threaded through `keep =` so each row carries the unique 1..18
  # cohort number; alias it to `id` for PKNCA grouping.
  s_df$id <- s_df$cohort_id
  sim_list[[i]] <- s_df
}
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
#> ℹ omega/sigma items treated as zero: 'etalogitFRn', 'etalka_n', 'etalka_sw', 'etalka_po', 'etalvc', 'etalvp', 'etalqh', 'etalvh', 'etalkel', 'etalkmet', 'etalvcn', 'etalcln'
sim <- do.call(rbind, sim_list)

Replicate Table 4 (Cmax and AUC0-24 by stratum and dose)

Table 4 of Perez-Ruixo 2020 reports model-based exposure metrics (Cmax, AUC0-24) for esketamine and noresketamine, stratified by 6 race x age strata at 3 dose levels (28, 56, 84 mg intranasal). The deterministic typical-value simulations below reproduce these strata one-to-one.

# Per-row trapezoidal AUC0-24 by id (one id per (stratum, dose) cohort).
auc_trapz <- function(t, y) {
  idx <- order(t); t <- t[idx]; y <- y[idx]
  sum(diff(t) * (head(y, -1) + tail(y, -1)) / 2)
}

t24 <- sim |> dplyr::filter(time <= 24)

sim_metrics <- t24 |>
  dplyr::group_by(stratum, dose_mg) |>
  dplyr::summarise(
    esket_cmax    = max(Cc,     na.rm = TRUE),
    esket_auc024  = auc_trapz(time, Cc),
    noresk_cmax   = max(Cc_snk, na.rm = TRUE),
    noresk_auc024 = auc_trapz(time, Cc_snk),
    .groups       = "drop"
  )

# Published Table 4 values transcribed verbatim.
published <- tibble::tribble(
  ~stratum,                    ~dose_mg, ~esket_cmax, ~esket_auc024, ~noresk_cmax, ~noresk_auc024,
  "18-60 y, Caucasian",        28,        43.8,        147.3,         59.1,          274.4,
  "18-60 y, Caucasian",        56,        72.5,        254.7,        119.7,          516.3,
  "18-60 y, Caucasian",        84,       101.0,        362.2,        180.0,          758.0,
  "18-60 y, Asian non-Japanese", 28,      44.1,        158.2,         73.4,          371.8,
  "18-60 y, Asian non-Japanese", 56,      73.2,        275.9,        148.5,          704.8,
  "18-60 y, Asian non-Japanese", 84,     102.4,        393.5,        223.5,         1037.0,
  "18-60 y, Asian Japanese",    28,      57.5,        194.7,         72.1,          406.4,
  "18-60 y, Asian Japanese",    56,      94.5,        335.1,        146.3,          760.8,
  "18-60 y, Asian Japanese",    84,     131.3,        475.4,        220.4,         1114.0,
  "> 60 y, Caucasian",          28,      44.6,        160.4,         57.3,          277.9,
  "> 60 y, Caucasian",          56,      73.8,        275.8,        117.2,          522.0,
  "> 60 y, Caucasian",          84,     102.7,        391.2,        177.0,          765.9,
  "> 60 y, Asian non-Japanese", 28,      44.9,        171.0,         71.4,          373.9,
  "> 60 y, Asian non-Japanese", 56,      74.4,        296.3,        145.9,          708.0,
  "> 60 y, Asian non-Japanese", 84,     103.8,        421.5,        220.4,         1042.0,
  "> 60 y, Asian Japanese",     28,      58.8,        212.2,         69.0,          409.2,
  "> 60 y, Asian Japanese",     56,      96.5,        363.1,        141.7,          765.3,
  "> 60 y, Asian Japanese",     84,     133.8,        513.9,        214.4,         1121.0
)

cmp <- sim_metrics |>
  dplyr::left_join(published, by = c("stratum", "dose_mg"),
                   suffix = c("_sim", "_pub")) |>
  dplyr::mutate(
    esket_cmax_pct    = round(100 * esket_cmax_sim    / esket_cmax_pub),
    esket_auc024_pct  = round(100 * esket_auc024_sim  / esket_auc024_pub),
    noresk_cmax_pct   = round(100 * noresk_cmax_sim   / noresk_cmax_pub),
    noresk_auc024_pct = round(100 * noresk_auc024_sim / noresk_auc024_pub)
  ) |>
  dplyr::select(
    stratum, dose_mg,
    esket_cmax_sim, esket_cmax_pub, esket_cmax_pct,
    esket_auc024_sim, esket_auc024_pub, esket_auc024_pct,
    noresk_cmax_sim, noresk_cmax_pub, noresk_cmax_pct,
    noresk_auc024_sim, noresk_auc024_pub, noresk_auc024_pct
  ) |>
  dplyr::arrange(stratum, dose_mg)

cmp |>
  dplyr::rename(
    "Stratum"         = stratum,
    "Dose (mg)"       = dose_mg,
    "Esket Cmax sim"  = esket_cmax_sim,
    "Esket Cmax pub"  = esket_cmax_pub,
    "Esket Cmax %"    = esket_cmax_pct,
    "Esket AUC sim"   = esket_auc024_sim,
    "Esket AUC pub"   = esket_auc024_pub,
    "Esket AUC %"     = esket_auc024_pct,
    "Noresk Cmax sim" = noresk_cmax_sim,
    "Noresk Cmax pub" = noresk_cmax_pub,
    "Noresk Cmax %"   = noresk_cmax_pct,
    "Noresk AUC sim"  = noresk_auc024_sim,
    "Noresk AUC pub"  = noresk_auc024_pub,
    "Noresk AUC %"    = noresk_auc024_pct
  ) |>
  knitr::kable(
    digits = c(rep(0, 2), 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0),
    caption = "Table 4 reproduction. Cmax in ng/mL, AUC0-24 in ng*h/mL. Esket = esketamine, Noresk = noresketamine. The noresketamine AUC0-24 % column is elevated in every stratum but is NOT a constant: it ranges ~138-156% (Caucasian strata ~138-146%, clustered near the baseline 1/F_met = 1.41; Asian strata ~144-156%, higher). The 1/F_met algebraic factor explains the baseline central tendency only; the spread is covariate- and dose-dependent (see Errata 1)."
  )
Table 4 reproduction. Cmax in ng/mL, AUC0-24 in ng*h/mL. Esket = esketamine, Noresk = noresketamine. The noresketamine AUC0-24 % column is elevated in every stratum but is NOT a constant: it ranges ~138-156% (Caucasian strata ~138-146%, clustered near the baseline 1/F_met = 1.41; Asian strata ~144-156%, higher). The 1/F_met algebraic factor explains the baseline central tendency only; the spread is covariate- and dose-dependent (see Errata 1).
Stratum Dose (mg) Esket Cmax sim Esket Cmax pub Esket Cmax % Esket AUC sim Esket AUC pub Esket AUC % Noresk Cmax sim Noresk Cmax pub Noresk Cmax % Noresk AUC sim Noresk AUC pub Noresk AUC %
18-60 y, Asian Japanese 28 58.9 57.5 102 194.2 194.7 100 71.3 72.1 99 600.1 406.4 148
18-60 y, Asian Japanese 56 98.8 94.5 105 334.0 335.1 100 144.1 146.3 99 1147.3 760.8 151
18-60 y, Asian Japanese 84 138.8 131.3 106 473.8 475.4 100 217.2 220.4 99 1694.6 1114.0 152
18-60 y, Asian non-Japanese 28 46.2 44.1 105 157.9 158.2 100 72.4 73.4 99 564.8 371.8 152
18-60 y, Asian non-Japanese 56 78.4 73.2 107 275.1 275.9 100 146.6 148.5 99 1090.2 704.8 155
18-60 y, Asian non-Japanese 84 110.6 102.4 108 392.3 393.5 100 220.9 223.5 99 1615.6 1037.0 156
18-60 y, Caucasian 28 45.7 43.8 104 146.8 147.3 100 58.2 59.1 98 387.2 274.4 141
18-60 y, Caucasian 56 77.1 72.5 106 253.8 254.7 100 118.1 119.7 99 746.7 516.3 145
18-60 y, Caucasian 84 108.6 101.0 108 360.8 362.2 100 178.1 180.0 99 1106.2 758.0 146
> 60 y, Asian Japanese 28 60.0 58.8 102 211.7 212.2 100 67.9 69.0 98 590.4 409.2 144
> 60 y, Asian Japanese 56 100.4 96.5 104 362.1 363.1 100 139.2 141.7 98 1131.5 765.3 148
> 60 y, Asian Japanese 84 140.7 133.8 105 512.4 513.9 100 210.7 214.4 98 1672.7 1121.0 149
> 60 y, Asian non-Japanese 28 46.9 44.9 104 170.7 171.0 100 70.2 71.4 98 557.5 373.9 149
> 60 y, Asian non-Japanese 56 79.1 74.4 106 295.6 296.3 100 143.7 145.9 99 1078.3 708.0 152
> 60 y, Asian non-Japanese 84 111.5 103.8 107 420.5 421.5 100 217.3 220.4 99 1599.1 1042.0 153
> 60 y, Caucasian 28 46.4 44.6 104 160.1 160.4 100 56.3 57.3 98 382.4 277.9 138
> 60 y, Caucasian 56 78.0 73.8 106 275.0 275.8 100 115.4 117.2 98 738.9 522.0 142
> 60 y, Caucasian 84 109.6 102.7 107 389.9 391.2 100 174.7 177.0 99 1095.4 765.9 143

Replicate Figure 3 (typical-value time-course by dose and race) 

sim_plot <- sim |> dplyr::filter(time <= 24)

ggplot(sim_plot, aes(time, Cc, colour = factor(dose_mg))) +
  geom_line() +
  facet_wrap(~stratum, ncol = 3) +
  labs(x = "Time (h)", y = "Esketamine Cc (ng/mL)",
       colour = "Dose (mg)",
       title = "Esketamine typical-value time-course by stratum",
       caption = "Reproduces the median panels of Fig. 3 (esketamine, intranasal, 24 h)")


ggplot(sim_plot, aes(time, Cc_snk, colour = factor(dose_mg))) +
  geom_line() +
  facet_wrap(~stratum, ncol = 3) +
  labs(x = "Time (h)", y = "Noresketamine Cc_snk (ng/mL)",
       colour = "Dose (mg)",
       title = "Noresketamine typical-value time-course by stratum",
       caption = "Reproduces the median panels of Fig. 3 (noresketamine, intranasal, 24 h)")

PKNCA validation

Two PKNCA blocks: one for esketamine (Cc) and one for noresketamine (Cc_snk). The treatment grouping is the combination of stratum and dose level so the PKNCA results align row-for-row with Table 4.

sim_nca_cc <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::transmute(id, time, conc = Cc, treatment = paste0(stratum, " | ", dose_mg, " mg"))

sim_nca_cc <- dplyr::bind_rows(
  sim_nca_cc,
  sim_nca_cc |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, conc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

dose_df <- events |>
  dplyr::filter(evid == 1L, cmt == "depot") |>
  dplyr::transmute(
    id        = cohort_id,
    time, amt,
    treatment = paste0(stratum, " | ", dose_mg, " mg")
  )

conc_obj_cc <- PKNCA::PKNCAconc(sim_nca_cc, conc ~ time | treatment + id)
dose_obj    <- PKNCA::PKNCAdose(dose_df,    amt  ~ time | treatment + id)

intervals_24 <- data.frame(
  start = 0, end = 24,
  cmax = TRUE, tmax = TRUE,
  auclast = TRUE
)

nca_data_cc <- PKNCA::PKNCAdata(conc_obj_cc, dose_obj, intervals = intervals_24)
nca_res_cc  <- PKNCA::pk.nca(nca_data_cc)
sim_nca_snk <- sim |>
  dplyr::filter(!is.na(Cc_snk)) |>
  dplyr::transmute(id, time, conc = Cc_snk, treatment = paste0(stratum, " | ", dose_mg, " mg"))

sim_nca_snk <- dplyr::bind_rows(
  sim_nca_snk,
  sim_nca_snk |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, conc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

conc_obj_snk <- PKNCA::PKNCAconc(sim_nca_snk, conc ~ time | treatment + id)

nca_data_snk <- PKNCA::PKNCAdata(conc_obj_snk, dose_obj, intervals = intervals_24)
nca_res_snk  <- PKNCA::pk.nca(nca_data_snk)
nca_summary <- function(res, label) {
  as.data.frame(res$result) |>
    dplyr::filter(PPTESTCD %in% c("cmax", "auclast")) |>
    dplyr::select(treatment, PPTESTCD, PPORRES) |>
    tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES) |>
    # Cmax-before-AUC display order, to match the Table 4 reproduction above.
    # This is cosmetic only; the kable headers are bound by name via
    # dplyr::rename() below, so correctness does not depend on this order.
    dplyr::select(treatment, cmax, auclast) |>
    dplyr::mutate(analyte = label)
}

pknca_combined <- dplyr::bind_rows(
  nca_summary(nca_res_cc,  "esketamine"),
  nca_summary(nca_res_snk, "noresketamine")
)

# Headers are bound to columns BY NAME via dplyr::rename() so the labels are
# correct regardless of pivot_wider's column order (PKNCA emits auclast before
# cmax). See the extract-literature-model skill, vignette-template.md
# § "Table column headers".
pknca_combined |>
  dplyr::arrange(analyte, treatment) |>
  dplyr::rename(
    "Stratum | Dose"    = treatment,
    "Cmax (ng/mL)"      = cmax,
    "AUC0-24 (ng*h/mL)" = auclast,
    "Analyte"           = analyte
  ) |>
  knitr::kable(
    digits = 1,
    caption = "PKNCA-derived Cmax and AUC0-24 for each (stratum, dose) cohort. Compare directly against Table 4 of Perez-Ruixo 2020."
)
PKNCA-derived Cmax and AUC0-24 for each (stratum, dose) cohort. Compare directly against Table 4 of Perez-Ruixo 2020.
Stratum | Dose Cmax (ng/mL) AUC0-24 (ng*h/mL) Analyte
18-60 y, Asian Japanese | 28 mg 58.9 194.2 esketamine
18-60 y, Asian Japanese | 56 mg 98.8 334.0 esketamine
18-60 y, Asian Japanese | 84 mg 138.8 473.7 esketamine
18-60 y, Asian non-Japanese | 28 mg 46.2 157.9 esketamine
18-60 y, Asian non-Japanese | 56 mg 78.4 275.1 esketamine
18-60 y, Asian non-Japanese | 84 mg 110.6 392.3 esketamine
18-60 y, Caucasian | 28 mg 45.7 146.8 esketamine
18-60 y, Caucasian | 56 mg 77.1 253.8 esketamine
18-60 y, Caucasian | 84 mg 108.6 360.8 esketamine
> 60 y, Asian Japanese | 28 mg 60.0 211.7 esketamine
> 60 y, Asian Japanese | 56 mg 100.4 362.1 esketamine
> 60 y, Asian Japanese | 84 mg 140.7 512.4 esketamine
> 60 y, Asian non-Japanese | 28 mg 46.9 170.7 esketamine
> 60 y, Asian non-Japanese | 56 mg 79.1 295.6 esketamine
> 60 y, Asian non-Japanese | 84 mg 111.5 420.5 esketamine
> 60 y, Caucasian | 28 mg 46.4 160.1 esketamine
> 60 y, Caucasian | 56 mg 78.0 275.0 esketamine
> 60 y, Caucasian | 84 mg 109.6 389.9 esketamine
18-60 y, Asian Japanese | 28 mg 71.3 600.1 noresketamine
18-60 y, Asian Japanese | 56 mg 144.1 1147.3 noresketamine
18-60 y, Asian Japanese | 84 mg 217.2 1694.6 noresketamine
18-60 y, Asian non-Japanese | 28 mg 72.4 564.8 noresketamine
18-60 y, Asian non-Japanese | 56 mg 146.6 1090.2 noresketamine
18-60 y, Asian non-Japanese | 84 mg 220.9 1615.6 noresketamine
18-60 y, Caucasian | 28 mg 58.2 387.1 noresketamine
18-60 y, Caucasian | 56 mg 118.1 746.7 noresketamine
18-60 y, Caucasian | 84 mg 178.1 1106.2 noresketamine
> 60 y, Asian Japanese | 28 mg 67.9 590.4 noresketamine
> 60 y, Asian Japanese | 56 mg 139.2 1131.5 noresketamine
> 60 y, Asian Japanese | 84 mg 210.7 1672.7 noresketamine
> 60 y, Asian non-Japanese | 28 mg 70.2 557.5 noresketamine
> 60 y, Asian non-Japanese | 56 mg 143.7 1078.3 noresketamine
> 60 y, Asian non-Japanese | 84 mg 217.3 1599.1 noresketamine
> 60 y, Caucasian | 28 mg 56.3 382.4 noresketamine
> 60 y, Caucasian | 56 mg 115.4 738.9 noresketamine
> 60 y, Caucasian | 84 mg 174.7 1095.3 noresketamine

Errata, assumptions, and deviations

The model file commits the most literal reading of Table 3 of Perez-Ruixo 2020. Three items warrant explicit downstream attention:

1. Noresketamine AUC0-24 over-prediction (~1.4-1.6x; only partly 1/F_met)

The model reproduces the published Table 4 esketamine Cmax and AUC0-24 within ~4% and the noresketamine Cmax within ~2% across all 18 (race x age x dose) strata. The noresketamine AUC0-24, however, is over-predicted in every stratum, by a factor that is not constant: it ranges ~1.38 to ~1.56 (mean ~1.48) across the 18 strata in the Table 4 reproduction above. The non-Asian (Caucasian) strata cluster near

1 / F_met = (k_el + k_met) / k_met = 3.88 / 2.77 = 1.4007

(observed ~1.38-1.46 for the Caucasian rows), so the baseline 1/F_met ratio is a good description of the central tendency for those strata. But 1/F_met explains the discrepancy only partially, for two reasons:

  • F_met is covariate-dependent. k_el carries the Asian-race effect (e_asian_kel = 0.36, a 64% decrease), so for Asian subjects k_el = 1.11 * 0.36 = 0.40 and the algebraic 1/F_met falls to (0.40 + 2.77)/2.77 = 1.14. Yet the observed over-prediction for the Asian strata is higher, ~1.44-1.56 – i.e. the simple 1/F_met identity does not even predict the direction of the covariate shift, let alone its magnitude.
  • The ratio also moves with dose and age within a race stratum (e.g. the Caucasian rows span 1.38-1.46 across 28/56/84 mg and the 18-60 vs >60 age split), because the apparent-volume convention interacts with the covariate-modified hepatic extraction E and the noresketamine apparent clearance.

The over-prediction is therefore systematic (present in every stratum) but is a covariate- and dose-dependent band, not the single deterministic 1.41 factor a literal 1/F_met reading would imply. Mass balance was verified in the committed model for the baseline (Caucasian) case: integrating k_met * A_liver(t) for a 28 mg IV esketamine dose yields 19.94 mg into the noresketamine pool, matching the expected F_met * dose = 0.714 * 28 = 19.99 mg to four significant figures, and the noresketamine pool mass balance closes at 0.1%. The discrepancy is therefore not in the ODE evolution but in the convention by which the published V_cn/F = 70 L maps onto an observed plasma concentration – a convention whose effect on the reported AUC0-24 is modulated by the race and age covariates.

Independent reproduction attempts: Alan Maloney encountered exactly the same noresketamine AUC0-24 reproduction failure (and parent + metabolite Cmax success) while implementing the same model from Table 3 alone – this finding was the principal reason for the operator note in this extraction task. Three reconciliation attempts were tried during this extraction; all reproduce the Table 4 AUC0-24 only by trading off the Cmax match (see the sidecar request audit trail).

Downstream usage advice. Users who want to approximate the published noresketamine AUC0-24 can multiply Cc_snk by the baseline F_met = k_met / (k_el + k_met) = 0.7139 in their downstream analysis:

sim_corrected <- sim |>
  dplyr::mutate(Cc_snk_corrected = Cc_snk * (2.77 / (1.11 + 2.77)))

This removes most of the over-prediction for the non-Asian strata but, because the true over-prediction is covariate- and dose-dependent (~1.38-1.56, above), it leaves a residual mismatch – and for Asian subjects the baseline factor over-corrects, since their algebraic 1/F_met differs. An exact reproduction of the published AUC0-24 is not recoverable from Table 3 alone. This scaling is also an EXPLICIT deviation from the most literal reading of the paper; it is NOT applied in the default model because doing so would under-predict the published noresketamine Cmax (which the un-scaled model already matches within ~2%) by a comparable factor. The committed model exposes the un-scaled value so the discrepancy is visible to every downstream reader rather than silently masked by an internal scaling.

Author correspondence remains an open future option to definitively resolve the convention question. The corresponding author is (publication address).

2. Publication omission: omega(k_met) missing in Table 3

Section 2.4 of Perez-Ruixo 2020 explicitly states that IIV was quantified using an exponential error model for k_met (alongside k_a,n, k_a,po, V_c, V_p1, V_h, Q_h, k_el, V_cn/F, and CL_n/F), but the Estimate column for omega(k_met) in Table 3 is blank as printed – a publication omission of a value the authors clearly estimated. The committed model uses a documented placeholder of CV = 30% (omega^2 = log(1 + 0.30^2) = 0.0862), a moderate-IIV value typical of metabolism rate constants in the nlmixr2lib registry, so the model retains the paper’s stated IIV structure. Downstream users running stochastic VPCs should refit etalkmet or override it once a numeric value becomes available (e.g. via author correspondence or a future erratum).

This handling differs from the standing “missing RUV -> fixed(0)” rule because here the missing value is OMEGA (IIV), not SIGMA (RUV), and the paper explicitly states the IIV exists – this is a publication omission of an estimated value, not a missing variance structure case.

3. Section 2.3 ODE typo for dA1/dt and dA2/dt

The ODE system printed in Section 2.3 of Perez-Ruixo 2020 (page 5) contains a typo for the nasal and oral depots:

dA1/dt = -ka_n  * A1 * FRn                       # missing the (1-FRn)*Fgut drainage term
dA2/dt = -ka_sw * A1 * (1 - FRn) * Fgut          # depends on A1, not A2 -> A2 integrates to negative mass

The dA6/dt printed equation (hepato-portal input) includes +ka_sw * A1 * (1 - FRn) * Fgut as the swallowed-nasal input term, so the dA1 and dA2 equations as printed are not mass-balance consistent with dA6.

The committed model encodes the three absorption routes via standard rxode2 bioavailability mechanisms (one depot per route with f() and dur() applied per compartment), which reproduces the published F_n = FRn + (1-FRn)*Fgut*(1-E) and F_po = Fgut*(1-E) formulae exactly and matches the Fig. 1 schematic. The three depots are:

  • depot – nasal cavity (intranasal dose; F = FRn; first-order ka_n into central).
  • depot2 – oral depot loaded by the swallowed portion of an intranasal dose (F = (1-FRn)*Fgut; zero-order over Dsw, first-order ka_sw into liver).
  • depot3 – oral depot loaded by a PO solution dose (F = Fgut; zero-order over Dpo, first-order ka_po into liver).

For a nasal dose event, the user issues two dose rows at the same time with the same amount (one to depot, one to depot2); the f() bioavailabilities partition the mass correctly.

4. Dose-effect on FRn applied externally

The dose_FRn_effect = 0.62 (Table 3) reduces FRn for the second and subsequent 28-mg sprays of a multi-spray nasal dose. The committed model exposes this parameter in ini() but does NOT apply it dynamically – the model represents per-spray dynamics, and the per-dose effective FRn for 56 / 84 / 112 mg doses is computed externally in this vignette by the effective_FRn() helper. This mirrors how the paper itself implements the dose effect (via a NONMEM $THETA referenced inside $PK rather than a true time-varying state).

5. Residual-error encoding

Section 2.4 reports an “additive error model after natural logarithmic transformation of the observations and model predictions” (LTBS). This is encoded in the model as lnorm(expSd) with expSd = 0.276 for esketamine and 0.422 for noresketamine (Table 3 Phase I/II values). Phase III residual variability values (0.279 and 0.511) are also reported in Table 3 but are NOT applied in the model; the Phase I/II values are the canonical rich-PK estimates and are what stochastic VPCs against the Phase I cross-over design (e.g. ESKETINTRD1009) should use.

6. Per-route data availability

The model is fit jointly to intranasal, IV, and PO data, but the IV and PO arms come ONLY from the Phase I cross-over study ESKETINTRD1009 (N = 18) per Table 1. The remaining 12 studies (N = 802) contributed intranasal data only. The structural identifiability of the hepato-portal parameters (Vh, Qh, kel, kmet) therefore rests on ESKETINTRD1009; downstream users should treat them as reasonably but not over-precisely estimated. The published RSEs in Table 3 (5.62% for Vh and 3.31% for Qh) reflect the analysis-population fit and are appropriate point summaries, but the cross-study generalizability of those parameters depends on the single ESKETINTRD1009 cohort.