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Darunavir in SARS-CoV-2 and HIV patients (Cojutti 2020)

Source: vignettes/articles/Cojutti_2020_darunavir.Rmd
Cojutti_2020_darunavir.Rmd
mod_covid <- readModelDb("Cojutti_2020_darunavir_covid19")
mod_hiv <- readModelDb("Cojutti_2020_darunavir_hiv")
ui_covid <- rxode2::rxode(mod_covid)
#> ℹ parameter labels from comments will be replaced by 'label()'
ui_hiv <- rxode2::rxode(mod_hiv)
#> ℹ parameter labels from comments will be replaced by 'label()'

Model and source

Cojutti and colleagues noticed during the first Italian COVID-19 wave that darunavir trough concentrations in hospitalised SARS-CoV-2 patients were much higher than those usually seen in HIV patients on the same dose. They fitted two separate one-compartment population PK models in Monolix 2019R1 (SAEM), one per population, from routine therapeutic drug monitoring (a trough and a 2 h sample per patient):

  • Cojutti_2020_darunavir_covid19 – 30 SARS-CoV-2 patients on darunavir/cobicistat 800/150 mg or darunavir/ritonavir 800/100 mg once daily. Serum interleukin-6 (IL-6) lowers apparent clearance CL/F by a power function, and body surface area (BSA) raises the apparent volume.
  • Cojutti_2020_darunavir_hiv – 25 HIV patients on darunavir/cobicistat/emtricitabine/tenofovir alafenamide at steady state; no covariate was retained.

The authors state they could have fitted one joint model but preferred two separate ones (Discussion), so the library carries two files.

Population

SARS-CoV-2 HIV
N 30 25
Male / female 18 / 12 18 / 7
Age, years, median (IQR) 63 (55-70.5) 47 (40-51)
Weight, kg 75.0 (69.25-81.50) 75.0 (66.0-84.0)
BSA, m^2 1.86 (1.77-1.96) 1.86 (1.75-2.02)
IL-6, pg/mL 31.0 (10-114.75) 2.0 (2.0-2.75)
Booster cobicistat 22, ritonavir 8 cobicistat 25

Source: Table 1 and Results 3. SARS-CoV-2 disease stages (Siddiqi-Mehra): I n = 3, IIa n = 8, IIb n = 10, III n = 9. Race was not reported. Samples were drawn at least 48 h after starting treatment in the SARS-CoV-2 group (median 3 days), and under chronic treatment in the HIV group.

Source trace

Quantity SARS-CoV-2 model HIV model Source
Structure: 1-compartment, first-order absorption and elimination yes yes Results 3.1 (OFV/BIC comparison vs 2-compartment)
ka (1/h) 0.74 0.58 Table 2
CL/F (L/h) 4.10 10.3 Table 2
Vd (L) 88.41 96.9 Table 2
IL-6 exponent on CL/F -0.23 – Table 2, beta IL6-CL/F
BSA exponent on Vd 1.44 – Table 2, beta BSA-Vd
IL-6 centring value (pg/mL) 31 – not printed; Table 1 cohort median, confirmed against Figure 4 (below)
BSA centring value (m^2) 1.86 – not printed; Table 1 cohort median
omega ka / CL / Vd (SD, log scale) 0.82 / 0.53 / 0.15 1.14 / 0.44 / 0.13 Table 2
Proportional residual error b 0.09 0.155 Table 2
Log-normal parameters, exponential random effects yes yes Methods 2.2
Power covariate model yes – Methods 2.2

The unprinted IL-6 centring value

Table 2 prints CL/F = 4.10 L/h and an IL-6 exponent of -0.23, but not the IL-6 value at which CL/F = 4.10. The Results state that 4.1 L/h is about 2.5-fold lower than the HIV value, i.e. it is read as a clearance typical of the SARS-CoV-2 cohort, which points to the cohort median (31 pg/mL). The paper’s own Figure 4 settles it: the Results print the median steady-state trough and peak from 1000 Monte Carlo subjects at IL-6 = 1, 100 and 1000 pg/mL. The deterministic typical-value steady state below (closed-form one-compartment oral superposition, BSA at its median) shows that the uncentred reading (reference 1 pg/mL) over-predicts the troughs 2.5- to 5-fold, whereas the median-centred reading lands close to the published values.

ss_profile <- function(cl, vc, ka, dose = 800, tau = 24) {
  kel <- cl / vc
  t <- seq(0, tau, by = 0.01)
  conc <- dose * ka / (vc * (ka - kel)) *
    (exp(-kel * t) / (1 - exp(-kel * tau)) - exp(-ka * t) / (1 - exp(-ka * tau)))
  1000 * c(cmin = conc[1], cmax = max(conc)) # mg/L -> ng/mL
}
published_fig4 <- data.frame(
  IL6 = c(1, 100, 1000),
  cmin = c(1460, 7020, 14140),
  cmax = c(7560, 13418, 20729)
)
centring <- do.call(rbind, lapply(c(1, 31), function(ref) {
  do.call(rbind, lapply(published_fig4$IL6, function(il6) {
    p <- ss_profile(cl = 4.10 * (il6 / ref)^-0.23, vc = 88.41, ka = 0.74)
    data.frame(reference_IL6 = ref, IL6 = il6, cmin = p[["cmin"]], cmax = p[["cmax"]])
  }))
})) |>
  left_join(published_fig4, by = "IL6", suffix = c("_typical", "_published")) |>
  mutate(cmin_ratio = cmin_typical / cmin_published)
knitr::kable(
  centring |>
    dplyr::rename(
      "IL-6 reference (pg/mL)" = reference_IL6,
      "IL-6 (pg/mL)" = IL6,
      "Typical Cmin (ng/mL)" = cmin_typical,
      "Typical Cmax (ng/mL)" = cmax_typical,
      "Published median Cmin" = cmin_published,
      "Published median Cmax" = cmax_published,
      "Cmin ratio" = cmin_ratio
    ),
  digits = 2
)
IL-6 reference (pg/mL) IL-6 (pg/mL) Typical Cmin (ng/mL) Typical Cmax (ng/mL) Published median Cmin Published median Cmax Cmin ratio
1 1 4724.20 11500.82 1460 7560 3.24
1 100 19640.09 26622.74 7020 13418 2.80
1 1000 35925.93 42947.67 14140 20729 2.54
31 1 989.39 7315.27 1460 7560 0.68
31 100 7092.04 13947.71 7020 13418 1.01
31 1000 14330.65 21283.59 14140 20729 1.01 
stopifnot(
  # Uncentred: every trough over-predicted by at least 2.5-fold.
  all(centring$cmin_ratio[centring$reference_IL6 == 1] > 2.5),
  # Median-centred: within 35% at every IL-6 level.
  all(abs(centring$cmin_ratio[centring$reference_IL6 == 31] - 1) < 0.35)
)

Both sides of this comparison are the model’s own typical values against a median over simulated subjects with IIV, so the comparison discriminates the two centring hypotheses but is not expected to agree exactly; the stochastic comparison is in the NCA section below. The individual clearances reported in the authors’ later reply to a letter (Cojutti 2021, doi:10.1007/s40262-021-00996-1, Table 1) point the same way: patients with IL-6 >= 18 pg/mL (median IL-6 51 pg/mL) had median CL/F 2.78 L/h, and those below (median 8 pg/mL) 7.24 L/h. The median-centred typical values at those IL-6 levels are 3.66 and 5.6 L/h; the uncentred ones would be 1.66 and 2.54 L/h.

Virtual cohorts and simulation (Figure 4)

Figure 4 simulates 10 days of darunavir 800 mg once daily in HIV patients and in SARS-CoV-2 patients at IL-6 = 1, 100 and 1000 pg/mL. BSA is held at the cohort median (1.86 m^2), since the paper does not say how BSA was handled in the simulation. Each arm has 200 virtual subjects.

rxode2::rxSetSeed(20200827)
n_per_arm <- 200
dose_times <- seq(0, 216, by = 24)
obs_times <- sort(unique(c(seq(0, 240, by = 1), seq(216, 240, by = 0.25))))

make_events <- function(id_offset, arm, IL6) {
  ids <- id_offset + seq_len(n_per_arm)
  doses <- expand.grid(id = ids, time = dose_times) |>
    mutate(amt = 800, evid = 1, cmt = "depot")
  obs <- expand.grid(id = ids, time = obs_times) |>
    mutate(amt = 0, evid = 0, cmt = "central")
  bind_rows(doses, obs) |>
    mutate(arm = arm, IL6 = IL6, BSA = 1.86) |>
    arrange(id, time, desc(evid))
}
arms <- c("HIV", "SARS-CoV-2, IL-6 1 pg/mL", "SARS-CoV-2, IL-6 100 pg/mL", "SARS-CoV-2, IL-6 1000 pg/mL")
ev_hiv <- make_events(0, arms[1], NA_real_) |> select(-IL6, -BSA)
ev_covid <- bind_rows(
  make_events(1000, arms[2], 1),
  make_events(2000, arms[3], 100),
  make_events(3000, arms[4], 1000)
)

sim_hiv <- rxode2::rxSolve(mod_hiv, events = ev_hiv, keep = "arm", returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_covid <- rxode2::rxSolve(mod_covid, events = ev_covid, keep = "arm", returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
sim <- bind_rows(sim_hiv, sim_covid) |>
  mutate(arm = factor(arm, levels = arms), Cc_ngml = 1000 * Cc)
sim |>
  group_by(arm, time) |>
  summarise(
    med = median(Cc_ngml),
    lo = quantile(Cc_ngml, 0.25),
    hi = quantile(Cc_ngml, 0.75),
    .groups = "drop"
  ) |>
  ggplot(aes(time / 24, med, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.2, colour = NA) +
  geom_line() +
  labs(x = "Time (days)", y = "Darunavir (ng/mL)", colour = NULL, fill = NULL) +
  theme_bw() +
  theme(legend.position = "bottom")
Replicates Figure 4 of Cojutti 2020: median (line) and 25th-75th percentiles (band) of darunavir concentration over a 10-day course of 800 mg once daily.

Replicates Figure 4 of Cojutti 2020: median (line) and 25th-75th percentiles (band) of darunavir concentration over a 10-day course of 800 mg once daily.

PKNCA validation

NCA over the tenth dosing interval (216-240 h), per subject, grouped by arm.

nca_conc <- sim |>
  filter(time >= 216, !is.na(Cc)) |>
  mutate(treatment = arm) |>
  select(id, time, Cc = Cc_ngml, treatment)
nca_dose <- bind_rows(ev_hiv, ev_covid) |>
  filter(evid == 1) |>
  mutate(treatment = factor(arm, levels = arms)) |>
  select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(nca_conc, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(nca_dose, amt ~ time | treatment + id)
intervals <- data.frame(start = 216, end = 240, cmin = TRUE, cmax = TRUE, tmax = TRUE, auclast = TRUE)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
knitr::kable(summary(nca_res))
start end treatment N auclast cmax cmin tmax
216 240 HIV 200 77400 [46.3] 6110 [37.6] 839 [169] 3.25 [0.500, 9.25]
216 240 SARS-CoV-2, IL-6 1 pg/mL 200 86800 [58.5] 7290 [35.0] 762 [330] 2.75 [0.500, 8.25]
216 240 SARS-CoV-2, IL-6 100 pg/mL 200 250000 [58.2] 14200 [42.2] 6400 [103] 3.00 [0.500, 9.25]
216 240 SARS-CoV-2, IL-6 1000 pg/mL 200 430000 [53.6] 21300 [44.4] 13800 [70.4] 3.75 [0.500, 10.8]

Comparison against the published simulation

The Results report the median steady-state Cmin and Cmax of the Figure 4 simulations. The Cmax values are printed with a European thousands separator (5.425, 7.560, …), which in ng/mL can only mean 5425, 7560, …; a value of 5.4 ng/mL would be below the paper’s own trough values.

published <- data.frame(
  treatment = arms,
  cmin = c(826, 1460, 7020, 14140),
  cmax = c(5425, 7560, 13418, 20729)
)
simulated <- as.data.frame(nca_res$result) |>
  mutate(treatment = as.character(treatment)) |>
  filter(PPTESTCD %in% c("cmin", "cmax")) |>
  select(id, treatment, PPTESTCD, PPORRES)
cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = simulated,
  reference = published,
  by = "treatment",
  units = c(cmin = "ng/mL", cmax = "ng/mL"),
  tolerance_pct = 20
)
knitr::kable(cmp)
NCA parameter treatment Reference Simulated % diff
Cmax (ng/mL) HIV 5420 6620 +21.9%*
Cmax (ng/mL) SARS-CoV-2, IL-6 1 pg/mL 7560 7390 -2.2%
Cmax (ng/mL) SARS-CoV-2, IL-6 100 pg/mL 13400 13700 +2.4%
Cmax (ng/mL) SARS-CoV-2, IL-6 1000 pg/mL 20700 21000 +1.5%
Cmin (ng/mL) HIV 826 966 +17.0%
Cmin (ng/mL) SARS-CoV-2, IL-6 1 pg/mL 1460 1020 -30.2%*
Cmin (ng/mL) SARS-CoV-2, IL-6 100 pg/mL 7020 6860 -2.2%
Cmin (ng/mL) SARS-CoV-2, IL-6 1000 pg/mL 14100 14200 +0.4% 

med_sim <- simulated |>
  group_by(treatment, PPTESTCD) |>
  summarise(sim = median(PPORRES), .groups = "drop") |>
  left_join(
    tidyr::pivot_longer(published, c(cmin, cmax), names_to = "PPTESTCD", values_to = "pub"),
    by = c("treatment", "PPTESTCD")
  ) |>
  mutate(pct_diff = 100 * (sim - pub) / pub)
cmin_covid <- dplyr::filter(med_sim, PPTESTCD == "cmin")
stopifnot(
  # Centre: across the 8 published medians the typical discrepancy is small.
  abs(median(med_sim$pct_diff)) < 15,
  # The high-IL-6 arms, whose exposure is set by CL/F and Vd rather than by
  # the absorption tail, reproduce the published trough and peak.
  all(abs(med_sim$pct_diff[med_sim$treatment %in% arms[3:4]]) < 15),
  # The IL-6 ordering the paper reports is reproduced.
  all(diff(cmin_covid$sim[match(arms[2:4], cmin_covid$treatment)]) > 0)
)

The largest differences are the HIV peak and the SARS-CoV-2 trough at IL-6 = 1 pg/mL (both flagged above), in the two low-exposure arms. The low-IL-6 trough depends strongly on the lower tail of ka (omega 0.82) and on the draw, and the published numbers are themselves a Monte Carlo estimate from Mlxplore. The HIV peak is high even without variability: the typical-value steady-state Cmax from Table 2 (CL/F 10.3 L/h, Vd 96.9 L, ka 0.58 1/h) is about 6200 ng/mL against the published 5425 ng/mL, so the gap is not a sampling artefact; the paper does not say how its simulated Cmax was summarised (for instance per subject, or as the peak of the median profile, which is about 6000 ng/mL here). The high-IL-6 arms, whose exposure is set by CL/F and Vd, agree within a few percent. Nothing was adjusted to close the gap.

As an additional orientation (not gated), the typical steady-state AUC over a dosing interval is Dose / (CL/F): 7.767^{4} ngh/mL for HIV and 1.95122^{5} ngh/mL for a SARS-CoV-2 patient at IL-6 = 31 pg/mL, against the paper’s median individual AUCs of 75,727 and 161,387 ng*h/mL (Results 3.1).

Assumptions and deviations

  • IL-6 and BSA centring. The paper prints the covariate exponents but not the centring values. Both covariates are centred on the SARS-CoV-2 cohort medians from Table 1 (IL-6 31 pg/mL, BSA 1.86 m^2). The IL-6 choice is checked against the paper’s Figure 4 simulations above; the BSA choice has no independent check (Figure 4 does not vary BSA) and BSA is the same in both cohorts.
  • Between-subject variability. Table 2 labels the omega rows (%), but the values (0.13-1.14) are Monolix standard deviations of the log-scale random effect; a 0.53% CV would be negligible. They are encoded as variances (omega^2). No correlations between random effects were reported, so the omega matrices are diagonal.
  • Table 2 bootstrap medians. For the SARS-CoV-2 ka and Vd the bootstrap median (0.58 1/h, 77.81 L) differs from the point estimate and lies near or outside its own 99% CI; the point estimates in the Value column are used.
  • IL-6 as time-fixed. IL-6 was measured on the TDM day and entered as one value per patient; the model accepts a time-varying IL-6 column, but the source did not estimate such a use.
  • Booster. SARS-CoV-2 patients received cobicistat- or ritonavir-boosted darunavir (73% cobicistat); the model does not distinguish them, in line with the bioequivalence cited in Methods 2.1.
  • Figure 4 Cmax separator. The Results print the simulated Cmax values as 5.425, 7.560, 13.418 and 20.729 ng/mL; these are read as thousands (5425 ng/mL, …).
  • Units. The model files work in mg and L (concentration mg/L); the paper reports ng/mL. The vignette multiplies by 1000 for comparison.