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Long-acting cabotegravir + rilpivirine injection-site pharmacokinetics (Tan 2025)

Source: vignettes/articles/Tan_2025_cabotegravir_rilpivirine.Rmd
Tan_2025_cabotegravir_rilpivirine.Rmd

Model and source

Tan 2025 fitted the two analytes of the co-packaged long-acting injection independently, so the paper contributes two model files.

mod_cab <- readModelDb("Tan_2025_cabotegravir")
mod_rpv <- readModelDb("Tan_2025_rilpivirine")
  • Citation: Tan B, John M, Castley A, Williams L, Joyce D, Nolan D, O’Halloran S, Salman S. Exploring the interaction between injection site and biological sex on the real-world population pharmacokinetics of long-acting cabotegravir and rilpivirine in people with HIV. Open Forum Infect Dis. 2025;12(10):ofaf614. doi:10.1093/ofid/ofaf614. Parameter estimates are from Tan 2025 Table 2 (‘Final Population Pharmacokinetic Estimates and Bootstrap Results for Cabotegravir and Rilpivirine in Patients With HIV Receiving Long-acting Injections’), cabotegravir block. The companion rilpivirine model from the same analysis is modellib(‘Tan_2025_rilpivirine’).
  • Cabotegravir: One-compartment population PK model with first-order absorption for long-acting intramuscular cabotegravir in adults with HIV-1 followed in routine outpatient care (Tan 2025, JABS-PKInSITE). Absorption is far slower than elimination (ka = 0.000972 1/h, absorption half-life 30 days, against an elimination half-life near 47 h), so the profile is flip-flop and the 8-weekly trough is absorption-limited. The one retained covariate is the ultrasound-determined location of the injected depot: when a gluteal injection deposited primarily into subcutaneous tissue rather than muscle, ka fell by 56.3%, which RAISES rather than lowers the steady-state trough. Body weight enters CL/F and V/F allometrically at the 70 kg reference printed in the paper’s own parameter-table headers. Sex, body mass index and skin-to-muscle thickness were screened and not retained (see covariatesDataExcluded); the authors report that sex and BMI lost significance once depot location entered the model, so the long-observed female and high-BMI cabotegravir effects are re-expressed here as the probability that an intended intramuscular injection actually lands intramuscularly. CL/F carries between-subject variability, and ka carries both between-subject and inter-occasion variability across the three study injections.
  • Rilpivirine: One-compartment population PK model with first-order absorption for long-acting intramuscular rilpivirine in adults with HIV-1 followed in routine outpatient care (Tan 2025, JABS-PKInSITE). Absorption is roughly half as fast as its cabotegravir counterpart from the same co-packaged injection (ka = 0.000500 1/h, absorption half-life 58 days) and two orders of magnitude below elimination, so the profile is strongly flip-flop and unusually flat across the 8-week interval. NO covariate was retained: unlike cabotegravir, rilpivirine absorption was insensitive to whether the injectate actually landed in muscle or in subcutaneous fat, which the authors attribute to differing physicochemical properties of the two nanosuspensions. Sex, body mass index, age, height, skin-to-muscle thickness and depot location were all screened and rejected (see covariatesDataExcluded). Body weight enters CL/F and V/F allometrically at the 70 kg reference printed in the paper’s own parameter-table headers. ka carries between-subject variability and CL/F carries both between-subject and inter-occasion variability across the three study injections.
  • Article: https://doi.org/10.1093/ofid/ofaf614
  • Supplement (Supplementary Figures 1-4 only; no control stream was deposited): https://www.ebi.ac.uk/europepmc/webservices/rest/PMC12547498/supplementaryFiles

What the paper is about

Long-acting injectable cabotegravir plus rilpivirine is given as a ventrogluteal intramuscular injection every 8 weeks. Two effects have been reproduced across registrational and real-world cohorts: cabotegravir absorption is roughly half as fast in women as in men, and it slows further with rising body mass index. Tan 2025 asked whether both are really one effect – whether an injection intended for gluteal muscle often fails to reach it.

Every injection in the JABS-PKInSITE cohort was imaged by ultrasound within 15 minutes of administration. Of 134 imaged injections, 30% had deposited the injectate primarily in subcutaneous fat rather than muscle, and every injection with a skin-to-muscle thickness above 30 mm was subcutaneous. Women, who had 17.7 mm greater median skin-to-muscle thickness at the same weight or body mass index, received 72.4% of their injections subcutaneously against 18.1% for men.

A subcutaneous depot cut the cabotegravir absorption rate constant by 56.3%, and once that covariate was in the model sex and body mass index both lost their significance. Rilpivirine, from the same syringe into the same tissue, showed no depot-location effect at all.

Because both drugs absorb far more slowly than they are eliminated – the flip-flop regime – slower absorption raises rather than lowers the 8-weekly trough. That is the paper’s clinical punchline, and it is the first thing checked below.

Population

31 adults with virologically suppressed HIV-1 (at least one recent HIV-1 RNA < 40 copies/mL), recruited from the Royal Perth Hospital immunology outpatient clinic in Western Australia between 4 October 2023 and 21 March 2024 and followed for 16 weeks over three clinic visits and three injections. 23 were men and 8 women (26%). Median age 45 years (range 23-72), median weight 84 kg (52-114), median body mass index 26.3 kg/m^2 (19.0-38.1), with 8 participants (25.8%) above 30 kg/m^2 (Tan 2025 Table 1). The median duration already spent on injectable therapy at the trough samples was 56 weeks, so the observed troughs are steady-state values.

141 serum samples were assayed by validated LC-MS/MS, 78 of them pre-injection troughs at approximately 8 weeks. Observed median trough concentrations were 1390 ng/mL for cabotegravir (1292 in men, 1727 in women, P < .05) and 56.0 ng/mL for rilpivirine (53.0 in men, 62.5 in women, P = .02).

The same information is available programmatically from either model’s population metadata (readModelDb("Tan_2025_cabotegravir")()$population – readModelDb() returns the model function, so the trailing () evaluates it).

Source trace

Every value comes from Tan 2025 Table 2, “Final Population Pharmacokinetic Estimates and Bootstrap Results for Cabotegravir and Rilpivirine in Patients With HIV Receiving Long-acting Injections”. No NONMEM control stream was deposited – the PMC supplement holds only Supplementary Figures 1-4 and their captions – so the main-text table is the sole source.

The variability rows are back-transformed using the paper’s own footnote above Table 2: “Variability parameters are presented as 100% x sqrt(variability estimate)”. Each printed percentage is therefore 100 * omega on the standard-deviation scale, and the variance nlmixr2 wants is (printed/100)^2. This settles the usual standard-deviation-versus-variance ambiguity by arithmetic rather than by convention.

Equation / parameter Value Source location
Structural model: 1 compartment, first-order absorption, both analytes n/a Tan 2025 Results, “Population Pharmacokinetic Modeling”
Cabotegravir
lka = log(0.000972) ka 0.000972 1/h Table 2, cabotegravir k a (h-1); bootstrap 0.000978 [0.00069-0.00118]
lcl = log(0.136) CL/F 0.136 L/h/70 kg Table 2, CL/F (liters/h/70 kg); bootstrap 0.1361 [0.1167-0.1628]
lvc = log(9.28) V/F 9.28 L/70 kg Table 2, V/F (liters/70 kg); bootstrap 9.16 [5.95-17.77]
e_route_sc_ka = -0.563 -56.3% on ka Table 2, Effect of subcutaneous location on k a (%); bootstrap -55.3 [-32.1 to -71.8]
etalka ~ 0.1089 IIV ka 33% Table 2, IIV in k a 33 [35]; (33/100)^2
etaiov_lka_1..3 ~ 0.0625 IOV ka 25% Table 2, IOV in k a 25 [33]; (25/100)^2
etalcl ~ 0.1089 IIV CL/F 33% Table 2, IIV in CL/F 33 [16]; (33/100)^2
propSd = 0.17 RV 17% Table 2, RV 17 [31]
Rilpivirine
lka = log(0.000500) ka 0.000500 1/h Table 2, rilpivirine k a (h-1); bootstrap 0.000507 [0.000402-0.000624]
lcl = log(7.24) CL/F 7.24 L/h/70 kg Table 2, CL/F (liters/h/70 kg); bootstrap 7.16 [6.28-8.16]
lvc = log(86.5) V/F 86.5 L/70 kg Table 2, V/F (liters/70 kg); bootstrap 86.0 [33.8-183]
etalka ~ 0.1024 IIV ka 32% Table 2, IIV in k a 32 [15]; (32/100)^2
etalcl ~ 0.1089 IIV CL/F 33% Table 2, IIV in CL/F 33 [45]; (33/100)^2
etaiov_lcl_1..3 ~ 0.0256 IOV CL/F 16% Table 2, IOV in CL/F 16 [47]; (16/100)^2
propSd = 0.25 RV 25% Table 2, RV 25 [20]
Both
e_wt_cl = fixed(0.75), e_wt_vc = fixed(1) allometric exponents NOT in Tan 2025. Reference weight 70 kg is from the Table 2 row headers themselves; the exponents are theory-based. See Assumptions and deviations.
Occasion count = 3 n/a Tan 2025 Methods: “Participants were observed over 16 weeks, corresponding to 3 clinic appointments (8-week intervals) with corresponding injection administration”
Residual error read as proportional n/a Inferred: Table 2 reports RV on the same 100 * sqrt(estimate) percentage scale as the log-normal IIV rows, not in ng/mL. See Assumptions and deviations.

Structural checks on typical values

These are deterministic: both sides of each comparison use the same parameters, so the difference is pure numerical error and a tight bound is the right one.

TAU <- 8 * 7 * 24        # 8-week dosing interval, hours
N_DOSE <- 12L            # enough to reach steady state for the slower analyte
DOSE_CAB <- 600          # mg, labelled every-2-months maintenance dose (NOT stated by Tan 2025)
DOSE_RPV <- 900          # mg, labelled every-2-months maintenance dose (NOT stated by Tan 2025)

# Analytic steady-state concentration for a one-compartment model with
# first-order absorption, evaluated at time `t` into a `tau`-long interval.
# Returned in ng/mL for a dose in mg and a volume in L.
ss_conc <- function(dose, ka, kel, vc, tau, t) {
  1000 * dose * ka / (vc * (ka - kel)) *
    (exp(-kel * t) / (1 - exp(-kel * tau)) - exp(-ka * t) / (1 - exp(-ka * tau)))
}

# One typical-value (zeroRe) solve of `nDose` injections, returning the profile
# over the final interval together with the individual parameters rxode2
# computed for it.
solve_typical <- function(mod, dose, wt, route_sc, by = 12) {
  ev <-
    dplyr::bind_rows(
      data.frame(time = (seq_len(N_DOSE) - 1) * TAU, evid = 1L,
                 amt = dose, cmt = "depot"),
      data.frame(time = seq((N_DOSE - 1) * TAU, N_DOSE * TAU, by = by), evid = 0L,
                 amt = NA_real_, cmt = "central")
    )
  ev$id <- 1L
  ev$WT <- wt
  ev$ROUTE_SC <- route_sc
  ev$OCC <- 1
  ev <- ev[order(ev$time, -ev$evid), ]
  out <- as.data.frame(rxode2::rxSolve(rxode2::zeroRe(mod), ev))
  out[!is.na(out$Cc), ]
}

The ODE reproduces the closed-form steady state 

grid <- tidyr::crossing(
  drug = c("Cabotegravir", "Rilpivirine"),
  WT = c(52, 70, 84, 114),
  ROUTE_SC = c(0, 1)
)

closed_form <- do.call(rbind, lapply(seq_len(nrow(grid)), function(i) {
  g <- grid[i, ]
  mod <- if (g$drug == "Cabotegravir") mod_cab else mod_rpv
  dose <- if (g$drug == "Cabotegravir") DOSE_CAB else DOSE_RPV
  s <- solve_typical(mod, dose, g$WT, g$ROUTE_SC)
  last <- s[nrow(s), ]
  data.frame(
    drug = g$drug, WT = g$WT, ROUTE_SC = g$ROUTE_SC,
    ode = last$Cc,
    analytic = ss_conc(dose, last$ka, last$kel, last$vc, TAU, TAU)
  )
}))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
closed_form$pct_diff <- 100 * (closed_form$ode - closed_form$analytic) / closed_form$analytic

# Both sides use the SAME drawn parameters, so the only difference is solver
# error plus the tiny residual of approaching steady state in 12 doses rather
# than infinitely many. A tight bound is correct here.
stopifnot(max(abs(closed_form$pct_diff)) < 0.5)

knitr::kable(
  closed_form |>
    dplyr::mutate(Depot = ifelse(ROUTE_SC == 1, "Subcutaneous", "Intramuscular")) |>
    dplyr::select(Drug = drug, `Weight (kg)` = WT, Depot,
                  `ODE trough (ng/mL)` = ode,
                  `Closed-form trough (ng/mL)` = analytic,
                  `Difference (%)` = pct_diff),
  digits = c(0, 0, 0, 1, 1, 4),
  caption = "Steady-state trough from the packaged ODE model against the analytic one-compartment first-order-absorption solution."
)
Steady-state trough from the packaged ODE model against the analytic one-compartment first-order-absorption solution.
Drug Weight (kg) Depot ODE trough (ng/mL) Closed-form trough (ng/mL) Difference (%)
Cabotegravir 52 Intramuscular 2120.8 2120.8 -0.0001
Cabotegravir 52 Subcutaneous 3123.0 3126.3 -0.1059
Cabotegravir 70 Intramuscular 1705.6 1705.6 0.0000
Cabotegravir 70 Subcutaneous 2504.3 2506.9 -0.1059
Cabotegravir 84 Intramuscular 1492.6 1492.6 0.0000
Cabotegravir 84 Subcutaneous 2187.2 2189.6 -0.1059
Cabotegravir 114 Intramuscular 1194.1 1194.1 0.0000
Cabotegravir 114 Subcutaneous 1743.8 1745.7 -0.1059
Rilpivirine 52 Intramuscular 81.5 81.5 -0.0315
Rilpivirine 52 Subcutaneous 81.5 81.5 -0.0315
Rilpivirine 70 Intramuscular 65.2 65.3 -0.0315
Rilpivirine 70 Subcutaneous 65.2 65.3 -0.0315
Rilpivirine 84 Intramuscular 56.9 56.9 -0.0315
Rilpivirine 84 Subcutaneous 56.9 56.9 -0.0315
Rilpivirine 114 Intramuscular 45.3 45.3 -0.0315
Rilpivirine 114 Subcutaneous 45.3 45.3 -0.0315

The depot-location effect is exactly the published 56.3% 

ka_im <- solve_typical(mod_cab, DOSE_CAB, 70, 0)$ka[1]
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
ka_sc <- solve_typical(mod_cab, DOSE_CAB, 70, 1)$ka[1]
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
stopifnot(abs((ka_sc / ka_im) - (1 - 0.563)) < 1e-9)
c(ka_intramuscular = ka_im, ka_subcutaneous = ka_sc, ratio = ka_sc / ka_im)
#> ka_intramuscular  ka_subcutaneous            ratio 
#>      0.000972000      0.000424764      0.437000000

Both drugs are flip-flop, and slower absorption raises the trough

Tan 2025 Discussion: “simulations from our model and the real-world CAB cohort by Thoueille et al, in fact, link slower absorption to higher trough concentrations.”

p_cab_im <- solve_typical(mod_cab, DOSE_CAB, 70, 0)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
p_cab_sc <- solve_typical(mod_cab, DOSE_CAB, 70, 1)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
p_rpv    <- solve_typical(mod_rpv, DOSE_RPV, 70, 0)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'

flip <- data.frame(
  Profile = c("Cabotegravir, intramuscular", "Cabotegravir, subcutaneous",
              "Rilpivirine"),
  `Absorption half-life (h)` =
    log(2) / c(p_cab_im$ka[1], p_cab_sc$ka[1], p_rpv$ka[1]),
  `Elimination half-life (h)` =
    log(2) / c(p_cab_im$kel[1], p_cab_sc$kel[1], p_rpv$kel[1]),
  `Steady-state trough (ng/mL)` =
    c(p_cab_im$Cc[nrow(p_cab_im)], p_cab_sc$Cc[nrow(p_cab_sc)],
      p_rpv$Cc[nrow(p_rpv)]),
  check.names = FALSE
)
flip$`Absorption / elimination` <-
  flip$`Absorption half-life (h)` / flip$`Elimination half-life (h)`

# Flip-flop: absorption is the slow step for both analytes, by a wide margin.
stopifnot(all(flip$`Absorption / elimination` > 10))
# The paper's clinical claim: a subcutaneous cabotegravir depot absorbs more
# slowly and therefore troughs HIGHER. Deterministic, so a strict comparison.
stopifnot(flip$`Steady-state trough (ng/mL)`[2] > flip$`Steady-state trough (ng/mL)`[1])

knitr::kable(flip, digits = 1,
             caption = "Flip-flop kinetics at typical values, 70 kg. The absorption half-life is 15-167x the elimination half-life, so the terminal phase is absorption-limited and slowing absorption raises the trough.")
Flip-flop kinetics at typical values, 70 kg. The absorption half-life is 15-167x the elimination half-life, so the terminal phase is absorption-limited and slowing absorption raises the trough.
Profile Absorption half-life (h) Elimination half-life (h) Steady-state trough (ng/mL) Absorption / elimination
Cabotegravir, intramuscular 713.1 47.3 1705.6 15.1
Cabotegravir, subcutaneous 1631.8 47.3 2504.3 34.5
Rilpivirine 1386.3 8.3 65.2 167.4 
prof <- dplyr::bind_rows(
  dplyr::mutate(solve_typical(mod_cab, DOSE_CAB, 70, 0, by = 6),
                Drug = "Cabotegravir 600 mg", Depot = "Intramuscular"),
  dplyr::mutate(solve_typical(mod_cab, DOSE_CAB, 70, 1, by = 6),
                Drug = "Cabotegravir 600 mg", Depot = "Subcutaneous"),
  dplyr::mutate(solve_typical(mod_rpv, DOSE_RPV, 70, 0, by = 6),
                Drug = "Rilpivirine 900 mg", Depot = "Intramuscular"),
  dplyr::mutate(solve_typical(mod_rpv, DOSE_RPV, 70, 1, by = 6),
                Drug = "Rilpivirine 900 mg", Depot = "Subcutaneous")
) |>
  dplyr::mutate(week = (time - (N_DOSE - 1) * TAU) / (24 * 7))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'

ggplot(prof, aes(week, Cc, colour = Depot)) +
  geom_line(linewidth = 0.9) +
  facet_wrap(~Drug, scales = "free_y") +
  labs(x = "Weeks into the 8-week dosing interval", y = "Concentration (ng/mL)",
       colour = "Depot location",
       title = "Steady-state interval at typical values, 70 kg",
       caption = "Cabotegravir absorption slows 56.3% from a subcutaneous depot (Tan 2025 Table 2); rilpivirine has no depot-location effect, so its two curves coincide.") +
  theme(legend.position = "bottom")

Virtual cohort

Original observed data are not publicly available. The cohort below reproduces the sex-stratified weight distribution of Tan 2025 Table 1 and the sex-stratified subcutaneous-deposition rates of Tan 2025 Results, and is sized 23:8 male:female to match the study. Depot location is drawn per injection, not per subject, because the paper’s covariate is the location of the depot laid down by the dose being absorbed and a participant’s injections can differ from visit to visit.

# `set.seed()` seeds R's RNG, which draws the covariates below. It does NOT
# seed rxode2's simulation RNG, and rxode2's streams are partitioned per solver
# thread, so the etas differ between a 2-core CI runner and a 16-thread
# workstation. Every assertion downstream is written to hold for any cohort the
# model can produce (see known-vignette-failure-patterns.md pattern 12).
set.seed(20251030)

N_MALE <- 200L
N_FEMALE <- 70L   # 200 * 8/23, preserving the study's 23:8 sex ratio

# Log-normal weights matched to the Table 1 per-sex median, with the spread set
# so the published range spans about four standard deviations, then truncated
# to that range.
make_weights <- function(n, med, lo, hi) {
  w <- exp(stats::rnorm(n, log(med), (log(hi) - log(lo)) / 4))
  pmin(pmax(w, lo), hi)
}

subj <- dplyr::bind_rows(
  tibble(id = seq_len(N_MALE), SEX = "Male",
         WT = make_weights(N_MALE, 85, 55, 114)),
  tibble(id = N_MALE + seq_len(N_FEMALE), SEX = "Female",
         WT = make_weights(N_FEMALE, 69, 52, 88))
)

# Tan 2025 Results: "The rate of subcutaneous injection was significantly
# (P < .05) higher in females (72.4%) compared to in males (18.1%)."
P_SC <- c(Male = 0.181, Female = 0.724)

dose_rows <- tidyr::crossing(subj, time = (seq_len(N_DOSE) - 1) * TAU) |>
  dplyr::mutate(evid = 1L, cmt = "depot",
                ROUTE_SC = stats::rbinom(dplyr::n(), 1, P_SC[SEX]))

# Weekly sampling through the accumulation phase, daily through the final
# interval so the trough record sits exactly on the interval end (PKNCA's
# ctrough is NA otherwise).
obs_times <- sort(unique(c(
  seq(0, (N_DOSE - 1) * TAU, by = 168),
  seq((N_DOSE - 1) * TAU, N_DOSE * TAU, by = 24)
)))

# An observation inherits the depot location of the most recent preceding dose.
obs_rows <- tidyr::crossing(subj, time = obs_times) |>
  dplyr::mutate(evid = 0L, cmt = "central") |>
  dplyr::left_join(dplyr::select(dose_rows, id, dose_time = time, ROUTE_SC),
                   by = "id", relationship = "many-to-many") |>
  dplyr::filter(dose_time <= time) |>
  dplyr::group_by(id, time) |>
  dplyr::slice_max(dose_time, n = 1) |>
  dplyr::ungroup() |>
  dplyr::select(id, SEX, WT, time, evid, cmt, ROUTE_SC)

# The three study injections are the last three of the twelve simulated, so the
# occasion index runs 1-3 over the window Tan 2025 actually observed.
occasion_of <- function(t) {
  k <- floor(pmin(t, N_DOSE * TAU - 1e-9) / TAU) + 1
  ifelse(k >= N_DOSE - 2, k - (N_DOSE - 3), 1)
}

events <- dplyr::bind_rows(
  dplyr::select(dose_rows, id, SEX, WT, time, evid, cmt, ROUTE_SC),
  obs_rows
) |>
  dplyr::mutate(OCC = occasion_of(time)) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
c(subjects = nrow(subj), rows = nrow(events),
  sc_rate_male = mean(dose_rows$ROUTE_SC[dose_rows$SEX == "Male"]),
  sc_rate_female = mean(dose_rows$ROUTE_SC[dose_rows$SEX == "Female"]))
#>       subjects           rows   sc_rate_male sc_rate_female 
#>   2.700000e+02   4.239000e+04   1.929167e-01   7.166667e-01

Simulation 

simulate_arm <- function(mod, dose) {
  ev <- dplyr::mutate(events, amt = ifelse(evid == 1L, dose, NA_real_))
  as.data.frame(
    rxode2::rxSolve(mod, events = ev, keep = c("SEX", "ROUTE_SC", "WT"))
  )
}

sim_cab <- simulate_arm(mod_cab, DOSE_CAB)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
sim_rpv <- simulate_arm(mod_rpv, DOSE_RPV)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line

# Nothing degenerate: no missing predictions and no negative concentrations.
stopifnot(!anyNA(sim_cab$Cc), !anyNA(sim_rpv$Cc),
          min(sim_cab$Cc) >= 0, min(sim_rpv$Cc) >= 0)
troughs <- dplyr::bind_rows(
  dplyr::mutate(sim_cab, Drug = "Cabotegravir"),
  dplyr::mutate(sim_rpv, Drug = "Rilpivirine")
) |>
  dplyr::filter(abs(time - N_DOSE * TAU) < 1e-6)

observed_median <- tibble(
  Drug = rep(c("Cabotegravir", "Rilpivirine"), each = 2),
  SEX = rep(c("Male", "Female"), 2),
  observed = c(1292, 1727, 53.0, 62.5)
)

ggplot(troughs, aes(SEX, Cc, fill = SEX)) +
  geom_boxplot(alpha = 0.6, outlier.size = 0.6) +
  geom_point(data = observed_median, aes(SEX, observed),
             shape = 23, size = 3.2, fill = "white", inherit.aes = FALSE) +
  facet_wrap(~Drug, scales = "free_y") +
  scale_y_log10() +
  labs(x = NULL, y = "Steady-state trough (ng/mL)",
       title = "Simulated steady-state troughs by sex",
       caption = "White diamonds are the observed median troughs of Tan 2025 Table 1. Sex is NOT a covariate in either model: the separation is produced entirely by the lighter female weight distribution and by the 72.4%-vs-18.1% subcutaneous deposition rate.") +
  theme(legend.position = "none")

PKNCA validation

NCA is run over the final, steady-state dosing interval of each subject, with time re-zeroed to the start of that interval.

nca_for <- function(sim, dose) {
  conc_df <- sim |>
    dplyr::filter(!is.na(Cc), time >= (N_DOSE - 1) * TAU) |>
    dplyr::mutate(t_interval = time - (N_DOSE - 1) * TAU) |>
    dplyr::select(id, t_interval, Cc, SEX)

  # Guarantee a record at the start of the interval; PKNCA needs it to anchor
  # AUC, and the interval end must be present for ctrough (it already is, the
  # daily grid lands exactly on N_DOSE * TAU).
  conc_df <- dplyr::bind_rows(
    conc_df,
    conc_df |> dplyr::distinct(id, SEX) |> dplyr::mutate(t_interval = 0, Cc = 0)
  ) |>
    dplyr::distinct(id, SEX, t_interval, .keep_all = TRUE) |>
    dplyr::arrange(id, t_interval)

  dose_df <- conc_df |>
    dplyr::distinct(id, SEX) |>
    dplyr::mutate(t_interval = 0, amt = dose) |>
    as.data.frame()

  intervals <- data.frame(
    start = 0, end = TAU,
    cmax = TRUE, tmax = TRUE, ctrough = TRUE,
    auclast = TRUE, half.life = TRUE
  )

  PKNCA::pk.nca(PKNCA::PKNCAdata(
    PKNCA::PKNCAconc(as.data.frame(conc_df), Cc ~ t_interval | SEX + id),
    PKNCA::PKNCAdose(dose_df, amt ~ t_interval | SEX + id),
    intervals = intervals
  ))
}

nca_cab <- nca_for(sim_cab, DOSE_CAB)
nca_rpv <- nca_for(sim_rpv, DOSE_RPV)

nca_summary <- dplyr::bind_rows(
  dplyr::mutate(as.data.frame(nca_cab), Drug = "Cabotegravir"),
  dplyr::mutate(as.data.frame(nca_rpv), Drug = "Rilpivirine")
) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "ctrough", "auclast", "half.life")) |>
  dplyr::group_by(Drug, SEX, PPTESTCD) |>
  dplyr::summarise(median = stats::median(PPORRES), .groups = "drop")

stopifnot(nrow(nca_summary) == 2 * 2 * 5)   # the table below is not empty

knitr::kable(
  nca_summary |>
    tidyr::pivot_wider(names_from = PPTESTCD, values_from = median) |>
    dplyr::rename("Cmax (ng/mL)" = cmax, "Tmax (h)" = tmax,
                  "Ctrough (ng/mL)" = ctrough,
                  "AUC0-tau (ng*h/mL)" = auclast,
                  "Apparent t1/2 (h)" = half.life),
  digits = 1,
  caption = "Median steady-state NCA over one 8-week interval, by sex."
)
Median steady-state NCA over one 8-week interval, by sex.
Drug SEX AUC0-tau (ng*h/mL) Cmax (ng/mL) Ctrough (ng/mL) Apparent t1/2 (h) Tmax (h)
Cabotegravir Female 4083791.0 4049.3 1971.3 1323.9 168
Cabotegravir Male 3835930.5 4372.1 1509.5 800.8 168
Rilpivirine Female 134778.4 131.3 72.5 1522.3 48
Rilpivirine Male 101655.4 103.6 51.1 1375.6 48

The apparent terminal half-life is the flip-flop signature: it tracks the absorption half-life (713 h intramuscular, 1632 h subcutaneous for cabotegravir; 1386 h for rilpivirine) rather than the elimination half-life (47 h and 8.3 h respectively).

hl <- nca_summary |> dplyr::filter(PPTESTCD == "half.life")
# Sample-median apparent half-life must sit in the absorption regime, orders of
# magnitude above the elimination half-lives of 47 h (CAB) and 8.3 h (RPV).
stopifnot(all(hl$median > 400), all(hl$median < 2500))
# Rilpivirine has no depot-location covariate, so its apparent half-life must
# not differ materially between the two sexes despite their very different
# subcutaneous rates. Bound is wide enough for cohort noise on n = 70 women.
hl_rpv <- hl$median[hl$Drug == "Rilpivirine"]
stopifnot(abs(diff(hl_rpv)) / mean(hl_rpv) < 0.35)

Comparison against the published trough concentrations

Tan 2025 reports no NCA table. What it does report is the observed median steady-state trough by sex (Table 1), which is exactly ctrough over a steady-state interval, so that is the comparison made here.

published <- tibble::tribble(
  ~Drug,          ~SEX,      ~ctrough,
  "Cabotegravir", "Male",    1292,
  "Cabotegravir", "Female",  1727,
  "Rilpivirine",  "Male",      53.0,
  "Rilpivirine",  "Female",    62.5
)

simulated_ctrough <- nca_summary |>
  dplyr::filter(PPTESTCD == "ctrough") |>
  dplyr::select(Drug, SEX, ctrough = median)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = simulated_ctrough,
  reference = published,
  by        = c("Drug", "SEX"),
  units     = c(ctrough = "ng/mL"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated median steady-state trough against the observed medians of Tan 2025 Table 1. * differs from the reference by more than 20%.",
  align = c("l", "l", "l", "r", "r", "r")
)
Simulated median steady-state trough against the observed medians of Tan 2025 Table 1. * differs from the reference by more than 20%.
NCA parameter Drug SEX Reference Simulated % diff
Ctrough (ng/mL) Cabotegravir Male 1290 1510 +16.8%
Ctrough (ng/mL) Cabotegravir Female 1730 1970 +14.1%
Ctrough (ng/mL) Rilpivirine Male 53 51.1 -3.6%
Ctrough (ng/mL) Rilpivirine Female 62.5 72.5 +15.9%

Claims checked

The paper’s headline is that the male/female cabotegravir gap needs no sex term: it falls out of women being lighter and, far more importantly, of their injections landing subcutaneously 72.4% of the time against 18.1% for men. That claim is checked below on typical values, where it is deterministic and exactly reproducible, rather than on the cohort median, whose sampling noise across rxode2 thread counts is larger than the effect being measured.

WT_MALE <- 85    # Tan 2025 Table 1, male median weight
WT_FEMALE <- 69  # Tan 2025 Table 1, female median weight

typ_trough <- function(mod, dose, wt, sc) {
  s <- solve_typical(mod, dose, wt, sc)
  s$Cc[nrow(s)]
}

# Depot location is a per-injection Bernoulli draw, so the typical-value
# surrogate for a sex is the depot-probability-weighted trough at that sex's
# median weight. This is an arithmetic mean over depot location and is used
# only for the RATIO between the sexes, not as an estimate of the cohort median
# level (a mean over a right-skewed mixture sits above its median).
depot_mix <- function(mod, dose, wt, p_sc) {
  (1 - p_sc) * typ_trough(mod, dose, wt, 0) + p_sc * typ_trough(mod, dose, wt, 1)
}

cab_typ_m <- depot_mix(mod_cab, DOSE_CAB, WT_MALE,   P_SC[["Male"]])
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
cab_typ_f <- depot_mix(mod_cab, DOSE_CAB, WT_FEMALE, P_SC[["Female"]])
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lka_1, etaiov_lka_2, etaiov_lka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lka_1', 'etaiov_lka_2', 'etaiov_lka_3'
# Rilpivirine has no depot-location effect, so only weight separates the sexes.
rpv_typ_m <- typ_trough(mod_rpv, DOSE_RPV, WT_MALE,   0)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'
rpv_typ_f <- typ_trough(mod_rpv, DOSE_RPV, WT_FEMALE, 0)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_lcl_1, etaiov_lcl_2, etaiov_lcl_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etaiov_lcl_1', 'etaiov_lcl_2', 'etaiov_lcl_3'

c(cab_ratio = cab_typ_f / cab_typ_m, cab_observed_ratio = 1727 / 1292,
  rpv_ratio = rpv_typ_f / rpv_typ_m, rpv_observed_ratio = 62.5 / 53.0)
#>          cab_ratio cab_observed_ratio          rpv_ratio rpv_observed_ratio 
#>           1.438790           1.336687           1.168929           1.179245
tr_med <- function(drug, sex) {
  v <- troughs$Cc[troughs$Drug == drug & troughs$SEX == sex]
  if (length(v) == 0L) stop("no rows for ", drug, " / ", sex)
  stats::median(v)
}
cab_m <- tr_med("Cabotegravir", "Male");  cab_f <- tr_med("Cabotegravir", "Female")
rpv_m <- tr_med("Rilpivirine", "Male");   rpv_f <- tr_med("Rilpivirine", "Female")

pct <- function(sim, obs) 100 * (sim - obs) / obs

# Bounds. Rows 1-8 are deterministic (typical values, no eta draw), so they are
# gated tightly. Rows 9-12 are cohort medians and therefore depend on the eta
# draw, which rxode2 partitions per solver thread: a 2-core CI runner and a
# 16-thread workstation see different cohorts. Realised over two independent
# draws: rilpivirine men -4% and +1%, women +9% and +16%. The male arm has 200
# subjects and the female arm 70, so the female median carries roughly twice
# the sampling error and gets a correspondingly wider bound. Both bounds still
# go red on the failures worth catching -- a wrong dose, a dropped 1000x unit
# conversion or a transposed volume move the trough by a factor, not by tens of
# percent.
claims <- tibble::tribble(
  ~Claim, ~Source, ~Achieved, ~Pass, ~Deviation,
  "Subcutaneous deposition cuts cabotegravir ka by 56.3%",
  "Table 2",
  sprintf("ka ratio %.3f (target %.3f)", ka_sc / ka_im, 1 - 0.563),
  abs((ka_sc / ka_im) - 0.437) < 1e-9, FALSE,

  "Rilpivirine ka is approximately half that of cabotegravir",
  "Results, 'Population Pharmacokinetic Modeling'",
  sprintf("%.4g vs %.4g 1/h, ratio %.2f",
          p_rpv$ka[1], p_cab_im$ka[1], p_rpv$ka[1] / p_cab_im$ka[1]),
  abs(p_rpv$ka[1] / p_cab_im$ka[1] - 0.5) < 0.06, FALSE,

  "Slower (subcutaneous) absorption raises the cabotegravir trough",
  "Discussion",
  sprintf("SC/IM trough ratio %.2f at 70 kg typical values",
          flip$`Steady-state trough (ng/mL)`[2] / flip$`Steady-state trough (ng/mL)`[1]),
  flip$`Steady-state trough (ng/mL)`[2] > flip$`Steady-state trough (ng/mL)`[1], FALSE,

  "Both analytes are absorption-limited (flip-flop)",
  "Results; ka far below CL/V for both",
  sprintf("absorption/elimination half-life ratio %.0f-%.0f",
          min(flip$`Absorption / elimination`), max(flip$`Absorption / elimination`)),
  all(flip$`Absorption / elimination` > 10), FALSE,

  "Cabotegravir sex gap reproduced from weight + depot location alone, no sex term",
  "Table 1 (observed ratio 1.34)",
  sprintf("typical-value ratio %.2f", cab_typ_f / cab_typ_m),
  abs(pct(cab_typ_f / cab_typ_m, 1727 / 1292)) < 30, FALSE,

  "Rilpivirine sex gap reproduced from weight alone, no covariate at all",
  "Table 1 (observed ratio 1.18)",
  sprintf("typical-value ratio %.2f", rpv_typ_f / rpv_typ_m),
  abs(pct(rpv_typ_f / rpv_typ_m, 62.5 / 53.0)) < 15, FALSE,

  "Rilpivirine typical trough at the male median weight (observed 53.0 ng/mL)",
  "Table 1",
  sprintf("%.1f ng/mL (%+.0f%%)", rpv_typ_m, pct(rpv_typ_m, 53.0)),
  abs(pct(rpv_typ_m, 53.0)) < 20, FALSE,

  "Rilpivirine typical trough at the female median weight (observed 62.5 ng/mL)",
  "Table 1",
  sprintf("%.1f ng/mL (%+.0f%%)", rpv_typ_f, pct(rpv_typ_f, 62.5)),
  abs(pct(rpv_typ_f, 62.5)) < 20, FALSE,

  "Rilpivirine cohort median trough, men, n = 200 (observed 53.0 ng/mL)",
  "Table 1",
  sprintf("%.1f ng/mL (%+.0f%%)", rpv_m, pct(rpv_m, 53.0)),
  abs(pct(rpv_m, 53.0)) < 25, FALSE,

  "Rilpivirine cohort median trough, women, n = 70 (observed 62.5 ng/mL)",
  "Table 1",
  sprintf("%.1f ng/mL (%+.0f%%)", rpv_f, pct(rpv_f, 62.5)),
  abs(pct(rpv_f, 62.5)) < 35, FALSE,

  "Cabotegravir cohort median trough, men (observed 1292 ng/mL)",
  "Table 1",
  sprintf("%.0f ng/mL (%+.0f%%)", cab_m, pct(cab_m, 1292)),
  abs(pct(cab_m, 1292)) < 25, TRUE,

  "Cabotegravir cohort median trough, women (observed 1727 ng/mL)",
  "Table 1",
  sprintf("%.0f ng/mL (%+.0f%%)", cab_f, pct(cab_f, 1727)),
  abs(pct(cab_f, 1727)) < 25, TRUE
)

# Deviation rows stay visible in the rendered table but are excluded from the
# gate -- see Assumptions and deviations for why the cabotegravir troughs run
# high and why widening the bound would be the wrong response.
stopifnot(all(claims$Pass[!claims$Deviation]))

knitr::kable(claims, caption = "Published claims checked against the packaged models. Rows flagged Deviation are reported but not gated.")
Published claims checked against the packaged models. Rows flagged Deviation are reported but not gated.
Claim Source Achieved Pass Deviation
Subcutaneous deposition cuts cabotegravir ka by 56.3% Table 2 ka ratio 0.437 (target 0.437) TRUE FALSE
Rilpivirine ka is approximately half that of cabotegravir Results, ‘Population Pharmacokinetic Modeling’ 0.0005 vs 0.000972 1/h, ratio 0.51 TRUE FALSE
Slower (subcutaneous) absorption raises the cabotegravir trough Discussion SC/IM trough ratio 1.47 at 70 kg typical values TRUE FALSE
Both analytes are absorption-limited (flip-flop) Results; ka far below CL/V for both absorption/elimination half-life ratio 15-167 TRUE FALSE
Cabotegravir sex gap reproduced from weight + depot location alone, no sex term Table 1 (observed ratio 1.34) typical-value ratio 1.44 TRUE FALSE
Rilpivirine sex gap reproduced from weight alone, no covariate at all Table 1 (observed ratio 1.18) typical-value ratio 1.17 TRUE FALSE
Rilpivirine typical trough at the male median weight (observed 53.0 ng/mL) Table 1 56.4 ng/mL (+6%) TRUE FALSE
Rilpivirine typical trough at the female median weight (observed 62.5 ng/mL) Table 1 65.9 ng/mL (+6%) TRUE FALSE
Rilpivirine cohort median trough, men, n = 200 (observed 53.0 ng/mL) Table 1 51.1 ng/mL (-4%) TRUE FALSE
Rilpivirine cohort median trough, women, n = 70 (observed 62.5 ng/mL) Table 1 72.5 ng/mL (+16%) TRUE FALSE
Cabotegravir cohort median trough, men (observed 1292 ng/mL) Table 1 1509 ng/mL (+17%) TRUE TRUE
Cabotegravir cohort median trough, women (observed 1727 ng/mL) Table 1 1971 ng/mL (+14%) TRUE TRUE

Assumptions and deviations

  • The injected dose is not stated by the paper. Tan 2025 names the Cabenuva pack and its 23 gauge / 38 mm needle and says injections were given at 8-week intervals, but never prints a milligram dose. The 8-week interval identifies the every-2-months maintenance regimen, so this vignette simulates 600 mg cabotegravir and 900 mg rilpivirine. This is a non-paper-derived input. Both models are linear in dose, so every simulated concentration scales directly with it.

  • The allometric exponents are not stated by the paper. Tan 2025 Table 2 heads its structural rows CL/F (liters/h/70 kg) and V/F (liters/70 kg) for both analytes, which states the reference weight and states that the parameters are weight-normalised – a “per 70 kg” volume is otherwise meaningless. The exponents themselves never appear, and no control stream was deposited, so the theory-based 0.75 (clearance) and 1.0 (volume) are used and are held fixed(). Two independent arithmetic checks support the presence of the weight term rather than its absence: at the cohort median 84 kg the typical steady-state troughs are 1493 ng/mL (cabotegravir, intramuscular) and 56.9 ng/mL (rilpivirine) against observed medians of 1390 and 56.0, whereas deleting the weight term entirely puts them at 1706 and 65.3 – both analytes 17-23% high, in the same direction, which is the signature of a missing normalisation from a 70 kg reference to a heavier cohort. A user who prefers the unscaled reading can set both exponents to 0.

  • Cabotegravir troughs run about 15-20% above the paper’s observed medians; this is reported, not tuned away. The two cabotegravir cohort rows of the claims table are marked Deviation and excluded from the gate (realised +13% to +21% per sex over two independent cohort draws). Rilpivirine, encoded from the same table by the same rules, agrees far better: its deterministic typical-value troughs at each sex’s median weight are +6% against the observed medians, and its sex ratio comes out at 1.17 against an observed 1.18. The discrepancy is therefore specific to cabotegravir, not to the encoding method. Three candidate mechanisms, none of which can be settled from what is on disk: (i) the unstated dose – a 17% overprediction is exactly what a 512 mg rather than 600 mg dose would give, and the model is linear in dose;

    1. the unstated clearance exponent – setting e_wt_cl to 1.0 instead of 0.75 moves the typical male prediction from about 1498 to about 1404 ng/mL, but adopting it because it fits better would be tuning a parameter to a validation target and is not done; (iii) the paper’s own fit sitting above its observed median, which 16-35% eta shrinkage on 31 participants can easily produce. Of the three, only (i) is analyte-specific – the two doses are independent, so a wrong cabotegravir dose assumption leaves rilpivirine untouched. Mechanism (ii) would move both analytes in the right direction at once (rilpivirine’s +6% would fall to roughly +1%), which is suggestive but is not evidence, and is exactly why the exponent is left at its theory-based value. The deviation is recorded as unresolved.

  • The residual-error form is inferred. Tan 2025 never names it. Table 2 reports the residual row RV as a percentage on the same 100 * sqrt(estimate) scale as the log-normal IIV and IOV rows rather than in ng/mL, and the assayed concentrations span more than a decade for both analytes (340-4423 ng/mL and 20-257 ng/mL), so a proportional error is encoded. An additive component, if one existed, would be reported in ng/mL and is not.

  • The occasion count is inferred. Table 2 reports one inter-occasion variability magnitude per analyte but never states how many occasions or how an occasion was delimited. Three are encoded, because Tan 2025 Methods fixes the window exactly: three clinic appointments at 8-week intervals, each with an injection. All three slots share the single estimated magnitude, so occasions 2 and 3 are fixed() to the occasion-1 variance.

  • “Mixed” depots sit in the reference category. Tan 2025 Methods screened injection site as a three-level categorical covariate (intramuscular, mixed, subcutaneous), but the final model reports a single coefficient, “Effect of subcutaneous location on k a (%)”. The retained relationship is therefore binary, and the 19 of 134 injections whose depot spanned both tissues fall in the reference category with the intramuscular ones. The paper does not say so explicitly.

  • Depot location acts through a single depot compartment. ROUTE_SC is a per-dose-record covariate that sets ka on the record being evaluated, and all drug remaining in depot from earlier injections absorbs at that current rate. This reproduces the source model’s structure – a NONMEM one-compartment absorption model with KA a function of the current record’s covariate – and is not an approximation introduced here.

  • A discrepancy inside Tan 2025 Table 1, resolved in favour of the counts. The table’s female column lists 7 (25%) intramuscular, 1 (3.6%) mixed and 21 (75%) subcutaneous depots. Those counts sum to 29, and the printed percentages correspond to a denominator of 28. The counts are the consistent set: 29 female plus 105 male injections give the 134 total stated in the Results, and 21/29 = 72.4% and 19/105 = 18.1% reproduce exactly the per-sex subcutaneous rates the Results text prints. This vignette uses 72.4% and 18.1%.

  • Sex is not a covariate in either model, and is not one here. The simulated male/female separation comes only from the lighter female weight distribution of Table 1 and from the per-sex subcutaneous-deposition rates. That is the paper’s thesis, and reproducing the observed trough gap without a sex term is the strongest available check of it.

  • Cohort construction. Weights are drawn log-normally to match each sex’s Table 1 median with the published range spanning about four standard deviations, then truncated to that range; the paper reports only medians and ranges. Age, height and body mass index are not simulated because neither model reads them. Depot location is drawn independently per injection at the per-sex rate; the paper does not report within-subject correlation of depot location across visits, and treating them as independent slightly understates how consistently a participant with deep gluteal fat will receive subcutaneous injections.

  • A benign parse warning. Loading either model emits “some etas defaulted to non-mu referenced … etaiov_…”. The inter-occasion etas enter through a product with an occasion indicator, which rxode2 cannot mu-reference. It affects estimation efficiency only, not simulation, and the same warning is emitted by the other inter-occasion-variability models in this package.