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Oseltamivir (Kamal 2013)

Source: vignettes/articles/Kamal_2013_oseltamivir.Rmd
Kamal_2013_oseltamivir.Rmd

Model and source

  • Citation: Kamal MA, Van Wart SA, Rayner CR, Subramoney V, Reynolds DK, Bulik CC, Smith PF, Bhavnani SM, Ambrose PG, Forrest A. Population pharmacokinetics of oseltamivir: pediatrics through geriatrics. Antimicrob Agents Chemother. 2013;57(8):3470-3477. doi:10.1128/AAC.02438-12
  • Description: Joint parent-metabolite population PK model for oral oseltamivir (prodrug, OP) and its active metabolite oseltamivir carboxylate (OC) in 390 subjects aged 1 to 78 years pooled from 13 clinical trials (healthy adults, influenza-inoculated and naturally infected adults, healthy geriatric subjects, renally impaired adults, and healthy and infected pediatric subjects 1 to 18 years). Oseltamivir is described by a two-compartment model with first-order absorption and first-order conversion to OC (CLp/F treated as the OP-to-OC conversion clearance under the assumption of complete metabolism; <5% of prodrug is excreted unchanged renally). OC is described by a one-compartment model with first-order elimination. All clearance and volume terms are apparent (conditioned on oral bioavailability F; OC terms additionally on the fraction metabolized fm, assumed 1). Covariates: body weight as a power function on OP CLp/F, OC CLm/F, and OC Vcm/F (allometric-style exponents estimated, not fixed); creatinine clearance (BSA-normalized to 1.73 m^2) as a power function on OC CLm/F; and age as a linear (additive) term on OC Vcm/F. Inter-individual variability is exponential on all seven structural parameters, with two off-diagonal covariances (CLp/F with CLm/F, and Vp/F with Vcm/F). Residual error is proportional only for oseltamivir (40.5% CV reduced CCV model) and combined additive plus proportional for OC (14.0% CV proportional + 17.9 ng/mL additive SD).
  • Article: https://doi.org/10.1128/AAC.02438-12

The model is a joint two-compartment oseltamivir (prodrug, OP) plus one-compartment oseltamivir carboxylate (OC) population PK model with direct first-order conversion of OP to OC and full hepatic metabolism (< 5 % of prodrug eliminated unchanged in urine; OC predominantly cleared renally by glomerular filtration and tubular secretion). All clearance and volume terms are apparent (conditioned on the absorbed fraction F for the prodrug; OC terms are additionally conditioned on the fraction metabolised to OC, assumed 1). Body weight is a power covariate on the prodrug CLp/F and on both OC parameters CLm/F and Vcm/F; creatinine clearance is a power covariate on CLm/F; age is a linear additive term on Vcm/F. Inter-individual variability is exponential on all seven structural parameters with two off-diagonal covariances on the eta scale: (etalcl, etalcl_oc) and (etalvp, etalvc_oc). Residual error is proportional only for OP (40.5 % CV) and combined additive plus proportional for OC (14.0 % CV + 17.9 ng/mL).

Population

Kamal 2013 Table 1 describes a pooled dataset of 390 subjects from 13 clinical trials (8 adult, 4 paediatric, 1 geriatric, and 1 renal impairment study). The pooled cohort spans age 1 to 78 years (median 21), weight 8 to 115 kg (median 64.5), and creatinine clearance 13.9 to 178 mL/min/1.73 m^2 (median 95.1), with 241 males and 149 females (38.2 % female). Subjects span normal renal function (N = 297 with CRCL >= 80) through mild (N = 73 with CRCL 50-80), moderate (N = 19 with CRCL 30-49), and severe (N = 1 with CRCL < 30) renal dysfunction. Disease state is a mix of healthy volunteers and naturally / experimentally influenza-infected subjects; no PK difference between infected and non-infected subjects was detected (Kamal 2013 Results page 3473).

Subjects received single or repeated oral doses of oseltamivir ranging from 20 to 1,000 mg; the standard influenza treatment regimen is 75 mg every 12 hours for 5 days. Paediatric subjects ages 1-12 received 2 mg/kg twice daily by suspension; ages 1-2 received 30 mg and ages 3-5 received 45 mg as single doses in a healthy-paediatric sub-study. The analysis dataset contained 3,881 oseltamivir concentrations and 4,402 OC concentrations (Kamal 2013 Results page 3471). LLOQs were 1 ng/mL for OP and 8.8 ng/mL for OC; only 3 records below LLOQ were excluded, so no likelihood-based BQL handling was needed.

The same information is available programmatically via readModelDb("Kamal_2013_oseltamivir")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Kamal_2013_oseltamivir.R. The table below collects them in one place for review; all values come from Kamal 2013 Table 2 (final-estimate column).

Equation / parameter Value Source location
ka (OP absorption) 0.775 1/h Table 2 row ‘ka’ (3.74 % SEM)
CLp/F (OP apparent CL at 70 kg) 519 L/h Table 2 row ‘CLp/F coefficient’ (3.99 % SEM)
Vcp/F (OP apparent Vc) 421 L Table 2 row ‘Vcp/F’ (6.05 % SEM)
CLd/F (OP apparent Q) 120 L/h Table 2 row ‘CLd/F’ (4.95 % SEM)
Vp/F (OP apparent peripheral V) 2,800 L Table 2 row ‘Vp/F’ (7.46 % SEM)
CLm/F (OC apparent CL at 70 kg, CRCL 95) 20.7 L/h Table 2 row ‘CLm/F coefficient’ (3.36 % SEM)
Vcm/F (OC apparent V at 70 kg, age 21) 238 L Table 2 row ‘Vcm/F coefficient’ (5.16 % SEM)
Power of WT on CLp/F 0.838 Table 2 row ‘Power of WT’ under CLp/F
Power of WT on CLm/F 0.560 Table 2 row ‘Power of WT’ under CLm/F
Power of CRCL on CLm/F 0.487 Table 2 row ‘Power of CL CR’
Power of WT on Vcm/F 0.830 Table 2 row ‘Power of WT’ under Vcm/F (18.7 % SEM)
Linear slope of age on Vcm/F -2.25 L/year Table 2 row ‘Slope of age’ (31.2 % SEM)
omega^2(ka) 30.7 % CV Table 2 row ‘omega^2 for ka’
omega^2(CLp/F) 42.1 % CV Table 2 row ‘omega^2 for CLp/F’
omega^2(Vcp/F) 69.3 % CV Table 2 row ‘omega^2 for Vcp/F’
omega^2(CLd/F) 62.1 % CV Table 2 row ‘omega^2 for CLd/F’
omega^2(Vp/F) 63.7 % CV Table 2 row ‘omega^2 for Vp/F’
omega^2(CLm/F) 38.3 % CV Table 2 row ‘omega^2 for CLm/F’
omega^2(Vcm/F) 65.3 % CV Table 2 row ‘omega^2 for Vcm/F’
Cov(CLp/F, CLm/F) 0.0987 (r^2 = 0.372) Table 2 row ‘Covariance (CLp/F, CLm/F)’
Cov(Vp/F, Vcm/F) 0.218 (r^2 = 0.274) Table 2 row ‘Covariance (Vp/F, Vcm/F)’
sigma_CCV(OP) 40.5 % CV Table 2 row ‘sigma^2 CCV for oseltamivir’
sigma_CCV(OC) 14.0 % CV Table 2 row ‘sigma^2 CCV for OC’
sigma_ADD(OC) 17.9 ng/mL = 0.0179 mg/L Table 2 row ‘sigma^2 ADD for OC’
ODE: d/dt(depot) = -ka * depot n/a Figure 1 schematic (page 3472)
ODE: d/dt(central) = ka * depot - kel * central - k12 * central + k21 * peripheral1 n/a Figure 1 schematic; Methods ‘Structural model development’ page 3471
ODE: d/dt(peripheral1) = k12 * central - k21 * peripheral1 n/a Figure 1 schematic
ODE: d/dt(central_oc) = kel * central - kel_oc * central_oc n/a Figure 1 schematic (‘direct conversion of oseltamivir to OC’); Discussion page 3473 (‘oseltamivir is completely converted to the OC metabolite’)

Virtual cohort

Original observed data are not publicly available. Simulations below use typical-value covariate combinations that match the published Figure 4 cohorts (deterministic replication), and a 200-subject stochastic virtual cohort approximating the pooled trial demographics (Table 1 of the source paper) for the VPC.

set.seed(2013L)
mod <- rxode2::rxode(readModelDb("Kamal_2013_oseltamivir"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typical <- rxode2::zeroRe(mod)
ref_age  <- 21
ref_wt   <- 70
ref_crcl <- 95

Replicate published figures

Figure 1 – Schematic

Kamal 2013 Figure 1 (page 3472) is a schematic of the two-compartment prodrug plus one-compartment metabolite structure with first-order absorption and first-order OP -> OC conversion. The structure is reproduced directly by the ODE block in inst/modeldb/specificDrugs/Kamal_2013_oseltamivir.R.

Figure 4A – Renal-impairment impact on OC at steady state

Kamal 2013 Figure 4A (page 3474) plots typical population mean OC concentration-time profiles at steady state for a 40-year-old, 70 kg subject receiving the standard influenza-treatment regimen (75 mg every 12 h for 5 days) at CRCL = 120, 80, 50, and 30 mL/min/1.73 m^2. The paper reports that the CRCL = 30 subject shows “an approximate 2-fold increase in OC exposure relative to a subject with normal renal function (CRCL of 120)”.

dose_times <- seq(0, 108, by = 12)  # ten 12-hourly doses over 5 days
obs_times  <- sort(unique(c(seq(0, 132, by = 0.5), dose_times)))

make_typical <- function(id_offset, AGE, WT, CRCL, label) {
  doses <- tibble(
    id = id_offset + 1L, time = dose_times, evid = 1L,
    amt = 75, cmt = "depot"
  )
  obs <- tibble(
    id = id_offset + 1L, time = obs_times, evid = 0L,
    amt = 0, cmt = "Cc"
  )
  bind_rows(doses, obs) |>
    mutate(AGE = AGE, WT = WT, CRCL = CRCL, group = label) |>
    arrange(time, desc(evid))
}

crcl_panels <- bind_rows(
  make_typical(0L,    AGE = 40, WT = 70, CRCL = 120, label = "CRCL 120"),
  make_typical(100L,  AGE = 40, WT = 70, CRCL =  80, label = "CRCL 80"),
  make_typical(200L,  AGE = 40, WT = 70, CRCL =  50, label = "CRCL 50"),
  make_typical(300L,  AGE = 40, WT = 70, CRCL =  30, label = "CRCL 30")
)
stopifnot(!anyDuplicated(unique(crcl_panels[, c("id", "time", "evid")])))

sim_crcl <- rxode2::rxSolve(mod_typical, events = crcl_panels,
                            keep = c("group", "AGE", "WT", "CRCL")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalcl_oc', 'etalvp', 'etalvc_oc', 'etalka', 'etalvc', 'etalq'
#> Warning: multi-subject simulation without without 'omega'

sim_crcl_ss <- sim_crcl |>
  filter(time >= 108, time <= 132) |>
  mutate(t_in_interval = time - 108,
         group = factor(group, levels = c("CRCL 120","CRCL 80","CRCL 50","CRCL 30")))

ggplot(sim_crcl_ss, aes(t_in_interval, Cc_oc, colour = group)) +
  geom_line(linewidth = 0.7) +
  scale_y_continuous(name = "OC concentration (mg/L)") +
  scale_x_continuous(name = "Time after morning dose at steady state (h)",
                     breaks = seq(0, 24, 6)) +
  labs(colour = NULL,
       title = "Figure 4A: typical OC profile at steady state by renal function",
       subtitle = "40-year-old, 70 kg, 75 mg q12h x 5 days") +
  theme_minimal()
Replicates Figure 4A of Kamal 2013 (renal-function impact on OC PK at steady state).

Replicates Figure 4A of Kamal 2013 (renal-function impact on OC PK at steady state). 

auc24 <- sim_crcl_ss |>
  group_by(group) |>
  summarise(AUC_0_24 = PKNCA::pk.calc.auc(Cc_oc, t_in_interval,
                                          method = "linear"),
            Cmax     = max(Cc_oc),
            .groups = "drop")
ref_120 <- auc24 |> filter(group == "CRCL 120")
auc24 <- auc24 |>
  mutate(AUC_ratio_vs_120 = AUC_0_24 / ref_120$AUC_0_24,
         Cmax_ratio_vs_120 = Cmax / ref_120$Cmax)
knitr::kable(auc24, digits = 3,
             caption = "Simulated steady-state OC AUC0-24 and Cmax for the Figure 4A panels, with ratios versus CRCL 120 (paper reports an ~2-fold increase in OC exposure for CRCL 30 vs 120).")
Simulated steady-state OC AUC0-24 and Cmax for the Figure 4A panels, with ratios versus CRCL 120 (paper reports an ~2-fold increase in OC exposure for CRCL 30 vs 120).
group AUC_0_24 Cmax AUC_ratio_vs_120 Cmax_ratio_vs_120
CRCL 120 4.555 0.348 1.000 1.000
CRCL 80 5.785 0.406 1.270 1.167
CRCL 50 7.612 0.489 1.671 1.405
CRCL 30 10.197 0.603 2.239 1.733

Figure 4B – Weight and age impact on OC at steady state

Kamal 2013 Figure 4B (page 3474) plots typical population mean OC profiles at steady state for 18-year-old and 55-year-old subjects with CRCL 120, at weights 50, 70, and 90 kg. The paper reports “a 1.38-fold increase in the maximum OC exposure was predicted as weight increases from 50 to 90 kg for an 18-year-old subject” and that “the impact of age was also demonstrated to be negligible as evident by the fact that the maximal OC exposure increased only 1.08- to 1.17-fold between an 18-year-old and 55-year-old subject across these same weights”.

wt_age_panels <- bind_rows(
  make_typical(1000L, AGE = 18, WT = 50, CRCL = 120, label = "18y, 50 kg"),
  make_typical(1100L, AGE = 18, WT = 70, CRCL = 120, label = "18y, 70 kg"),
  make_typical(1200L, AGE = 18, WT = 90, CRCL = 120, label = "18y, 90 kg"),
  make_typical(1300L, AGE = 55, WT = 50, CRCL = 120, label = "55y, 50 kg"),
  make_typical(1400L, AGE = 55, WT = 70, CRCL = 120, label = "55y, 70 kg"),
  make_typical(1500L, AGE = 55, WT = 90, CRCL = 120, label = "55y, 90 kg")
)
stopifnot(!anyDuplicated(unique(wt_age_panels[, c("id", "time", "evid")])))

sim_wt <- rxode2::rxSolve(mod_typical, events = wt_age_panels,
                          keep = c("group", "AGE", "WT", "CRCL")) |>
  as.data.frame() |>
  mutate(group = factor(group, levels = c(
    "18y, 50 kg","18y, 70 kg","18y, 90 kg",
    "55y, 50 kg","55y, 70 kg","55y, 90 kg")),
    age_band = ifelse(AGE == 18, "18-year-old", "55-year-old"),
    wt_band  = paste0(WT, " kg"))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalcl_oc', 'etalvp', 'etalvc_oc', 'etalka', 'etalvc', 'etalq'
#> Warning: multi-subject simulation without without 'omega'

sim_wt_ss <- sim_wt |>
  filter(time >= 108, time <= 132) |>
  mutate(t_in_interval = time - 108)

ggplot(sim_wt_ss, aes(t_in_interval, Cc_oc, colour = wt_band)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~ age_band) +
  scale_y_continuous(name = "OC concentration (mg/L)") +
  scale_x_continuous(name = "Time after morning dose at steady state (h)",
                     breaks = seq(0, 24, 6)) +
  labs(colour = "Body weight",
       title = "Figure 4B: typical OC profile by weight and age (CRCL 120)",
       subtitle = "75 mg q12h x 5 days") +
  theme_minimal()
Replicates Figure 4B of Kamal 2013 (weight and age impact on OC PK at steady state).

Replicates Figure 4B of Kamal 2013 (weight and age impact on OC PK at steady state). 

wt_age_summary <- sim_wt_ss |>
  group_by(age_band, wt_band) |>
  summarise(Cmax = max(Cc_oc),
            AUC_0_24 = PKNCA::pk.calc.auc(Cc_oc, t_in_interval, method = "linear"),
            .groups = "drop")

# Within-age weight ratios (90 kg vs 50 kg).
wt_ratios <- wt_age_summary |>
  select(age_band, wt_band, Cmax) |>
  pivot_wider(names_from = wt_band, values_from = Cmax) |>
  mutate(Cmax_ratio_90_vs_50 = `90 kg` / `50 kg`)

knitr::kable(wt_ratios, digits = 3,
             caption = "Simulated steady-state OC Cmax 90 kg vs 50 kg, by age band. Paper reports 1.38-fold increase across this weight range for an 18-year-old.")
Simulated steady-state OC Cmax 90 kg vs 50 kg, by age band. Paper reports 1.38-fold increase across this weight range for an 18-year-old.
age_band 50 kg 70 kg 90 kg Cmax_ratio_90_vs_50
18-year-old 0.397 0.331 0.287 0.724
55-year-old 0.459 0.365 0.310 0.675 

# Within-weight age ratios (55 vs 18 years).
age_ratios <- wt_age_summary |>
  select(age_band, wt_band, Cmax) |>
  pivot_wider(names_from = age_band, values_from = Cmax) |>
  mutate(Cmax_ratio_55_vs_18 = `55-year-old` / `18-year-old`)

knitr::kable(age_ratios, digits = 3,
             caption = "Simulated steady-state OC Cmax 55-year-old vs 18-year-old, by weight band. Paper reports 1.08- to 1.17-fold over the same weight range.")
Simulated steady-state OC Cmax 55-year-old vs 18-year-old, by weight band. Paper reports 1.08- to 1.17-fold over the same weight range.
wt_band 18-year-old 55-year-old Cmax_ratio_55_vs_18
50 kg 0.397 0.459 1.156
70 kg 0.331 0.365 1.102
90 kg 0.287 0.310 1.079

Stochastic VPC: 200-subject virtual cohort

A 200-subject stochastic cohort spanning the published demographic range provides a between-subject sanity check on the model. The virtual cohort distribution approximates Table 1 in spirit but is not a literal demographic resampling.

n_subj <- 200L

vpc_cov <- tibble(
  id   = seq_len(n_subj),
  AGE  = pmin(pmax(round(rnorm(n_subj, mean = 30, sd = 18)), 1L), 78L),
  WT   = pmin(pmax(round(rnorm(n_subj, mean = 64, sd = 22)), 8L), 115L),
  CRCL = pmin(pmax(round(rnorm(n_subj, mean = 95, sd = 25)), 14L), 178L)
)

vpc_doses <- vpc_cov |>
  tidyr::crossing(time = dose_times) |>
  mutate(evid = 1L, amt = 75, cmt = "depot")

vpc_obs <- vpc_cov |>
  tidyr::crossing(time = obs_times) |>
  mutate(evid = 0L, amt = 0, cmt = "Cc")

vpc_events <- bind_rows(vpc_doses, vpc_obs) |>
  arrange(id, time, desc(evid))
stopifnot(!anyDuplicated(unique(vpc_events[, c("id", "time", "evid")])))

sim_vpc <- rxode2::rxSolve(mod, events = vpc_events,
                           keep = c("AGE","WT","CRCL"), nSub = 1L) |>
  as.data.frame()
sim_vpc_ss <- sim_vpc |>
  filter(time >= 108, time <= 132) |>
  mutate(t_in_interval = time - 108) |>
  group_by(t_in_interval) |>
  summarise(Q05_oc = quantile(Cc_oc, 0.05),
            Q50_oc = quantile(Cc_oc, 0.50),
            Q95_oc = quantile(Cc_oc, 0.95),
            Q05_op = quantile(Cc,    0.05),
            Q50_op = quantile(Cc,    0.50),
            Q95_op = quantile(Cc,    0.95),
            .groups = "drop")

vpc_long <- sim_vpc_ss |>
  pivot_longer(-t_in_interval,
               names_to = c(".value","analyte"),
               names_pattern = "Q(\\d+)_(.*)") |>
  rename(Q05 = `05`, Q50 = `50`, Q95 = `95`) |>
  mutate(analyte = factor(analyte, levels = c("op","oc"),
                          labels = c("Oseltamivir (OP)","Oseltamivir carboxylate (OC)")))

ggplot(vpc_long, aes(t_in_interval, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "steelblue") +
  geom_line(colour = "steelblue4", linewidth = 0.7) +
  facet_wrap(~ analyte, scales = "free_y") +
  scale_x_continuous(name = "Time after morning dose at steady state (h)",
                     breaks = seq(0, 24, 6)) +
  scale_y_continuous(name = "Plasma concentration (mg/L)") +
  labs(title = "Stochastic VPC at steady state, 200 virtual subjects") +
  theme_minimal()
Median and 5-95 percent intervals of simulated OC plasma concentrations at steady state across the 200-subject virtual cohort (75 mg q12h).

Median and 5-95 percent intervals of simulated OC plasma concentrations at steady state across the 200-subject virtual cohort (75 mg q12h).

PKNCA validation

NCA is run separately for OP and OC on the typical-value Figure 4A panels (one PKNCA block per analyte; treatment-grouping variable is the covariate scenario label so per-group AUC and Cmax line up with the paper’s commentary).

nca_grid <- sim_crcl |>
  filter(time >= 108, time <= 132) |>
  mutate(time = time - 108)

conc_oc  <- nca_grid |> select(id, time, Cc_oc, group) |>
  rename(Cc = Cc_oc)
dose_oc  <- nca_grid |>
  group_by(id, group) |>
  slice_min(time, n = 1, with_ties = FALSE) |>
  ungroup() |>
  mutate(amt = 75, time = 0) |>
  select(id, time, amt, group)

conc_obj_oc <- PKNCA::PKNCAconc(conc_oc, Cc ~ time | group + id)
dose_obj_oc <- PKNCA::PKNCAdose(dose_oc, amt ~ time | group + id)

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

nca_data_oc <- PKNCA::PKNCAdata(conc_obj_oc, dose_obj_oc, intervals = intervals_oc)
nca_res_oc  <- PKNCA::pk.nca(nca_data_oc)

nca_table_oc <- as.data.frame(nca_res_oc$result) |>
  select(group, PPTESTCD, PPORRES) |>
  pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

knitr::kable(nca_table_oc, digits = 3,
             caption = "Simulated OC NCA parameters across the steady-state 12-hour interval (cmax in mg/L, tmax in h, auclast in mg*h/L, half-life in h).")
Simulated OC NCA parameters across the steady-state 12-hour interval (cmax in mg/L, tmax in h, auclast in mg*h/L, half-life in h).
group auclast cmax tmax tlast lambda.z r.squared adj.r.squared lambda.z.time.first lambda.z.time.last lambda.z.n.points clast.pred half.life span.ratio
CRCL 120 4.554 0.348 3.5 24 0.070 1 1 21.5 24 6 0.068 9.848 0.254
CRCL 30 10.197 0.603 3.5 24 0.047 1 1 5.5 24 38 0.241 14.635 1.264
CRCL 50 7.612 0.489 3.5 24 0.057 1 1 15.0 24 19 0.155 12.064 0.746
CRCL 80 5.785 0.406 3.5 24 0.066 1 1 19.5 24 10 0.101 10.580 0.425 
conc_op  <- nca_grid |> select(id, time, Cc, group)
conc_obj_op <- PKNCA::PKNCAconc(conc_op, Cc ~ time | group + id)
dose_obj_op <- PKNCA::PKNCAdose(dose_oc, amt ~ time | group + id)

intervals_op <- data.frame(
  start = 0, end = 12,
  cmax = TRUE, tmax = TRUE, auclast = TRUE, half.life = TRUE
)

nca_data_op <- PKNCA::PKNCAdata(conc_obj_op, dose_obj_op, intervals = intervals_op)
nca_res_op  <- PKNCA::pk.nca(nca_data_op)

nca_table_op <- as.data.frame(nca_res_op$result) |>
  select(group, PPTESTCD, PPORRES) |>
  pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

knitr::kable(nca_table_op, digits = 3,
             caption = "Simulated OP NCA parameters across the steady-state 12-hour dosing interval.")
Simulated OP NCA parameters across the steady-state 12-hour dosing interval.
group auclast cmax tmax tlast lambda.z r.squared adj.r.squared lambda.z.time.first lambda.z.time.last lambda.z.n.points clast.pred half.life span.ratio
CRCL 120 0.141 0.047 1 12 0.044 1 0.999 11 12 3 0.002 15.84 0.063
CRCL 30 0.141 0.047 1 12 0.044 1 0.999 11 12 3 0.002 15.84 0.063
CRCL 50 0.141 0.047 1 12 0.044 1 0.999 11 12 3 0.002 15.84 0.063
CRCL 80 0.141 0.047 1 12 0.044 1 0.999 11 12 3 0.002 15.84 0.063

Comparison against published values

The paper does not report NCA parameters in a table; instead it reports covariate-effect ratios in the Discussion (page 3474). The relevant benchmarks and the simulated values:

Comparison Paper value Simulated value
OC AUC at SS, CRCL 30 vs 120 (40 y, 70 kg) ~2-fold 2.24-fold
OC AUC at SS, CRCL 50 vs 120 (40 y, 70 kg) not quantified in text 1.67-fold
OC Cmax at SS, WT 90 vs 50 kg (18 y, CRCL 120) 1.38-fold 0.72-fold
OC Cmax at SS, 55 y vs 18 y, range across weights 1.08-1.17-fold 1.08-1.16-fold

The CRCL 50 mL/min/1.73 m^2 scenario (referenced in the paper Discussion page 3474 as having “0.51- to 0.71-fold decrease in CLm/F” relative to CRCL 120, equivalent to a 1.41- to 1.96-fold increase in OC AUC) is also covered by the simulated AUC table above.

Assumptions and deviations

  • Inter-individual variability omega^2 conversion. Kamal 2013 Table 2 reports the diagonal IIV terms as lognormal % CV (e.g. “42.1 % CV” for CLp/F) and the two off-diagonal covariances (CLp/F-CLm/F, Vp/F-Vcm/F) as numerical values with associated r^2. The variances on the eta scale are computed in the model file via the canonical conversion omega^2 = log(CV^2 + 1). The off-diagonal covariances are carried verbatim from Table 2 (0.0987 and 0.218). The paper’s reported r^2 values (0.372 and 0.274) are computed using the small-omega approximation r ~= omega_xy / (CV_x * CV_y) rather than the strict log-scale correlation; under the strict conversion the implied correlations are slightly higher (~0.66 and ~0.62 respectively). The chosen encoding preserves both the lognormal-correct diagonal variances and the literal numerical covariance values from Table 2; the resulting variance-covariance matrix is positive-definite for both 2x2 blocks.
  • Vcm/F age dependence is additive, not multiplicative. The Table 2 equation is Vcm/F = 238*(WT/70)^0.830 - 2.25*(AGE - 21). The age effect is subtracted from the WT-scaled volume rather than applied as a percentage. Outside the fitted age x weight range the additive form can yield a negative typical Vcm/F (e.g. a 30 kg 90-year-old); simulations with covariate combinations far outside the original dataset (paediatric weight + geriatric age) should be sanity-checked. Within the cohort range (1-78 y, 8-115 kg) the equation stays positive.
  • CLp/F is treated as the OP -> OC conversion clearance with 100 % metabolism. The paper assumes complete conversion of oseltamivir to OC because the prodrug is a high-extraction drug with < 5 % excreted unchanged in urine (Kamal 2013 Discussion page 3473). The implementation routes the entire OP central- compartment elimination flux into the OC central compartment; mass balance is satisfied in mass units. The molecular-weight ratio between OP (312.4 g/mol) and OC (284.4 g/mol) is absorbed into the “apparent” parameter scaling and is not applied as an explicit MW correction; this matches the original NONMEM ADVAN13 implementation.
  • Residual-error notation. Kamal 2013 Table 2 labels the residual rows “sigma^2 CCV” and “sigma^2 ADD” but the numerical values are reported as SDs (% CV for the proportional CCV term; ng/mL for the additive ADD term). The values 40.5 %, 14.0 %, and 17.9 ng/mL are encoded as propSd, propSd_oc, and addSd_oc respectively on the linear concentration scale (mg/L for the OC additive SD), and the cross-check at the bounds reproduces the paper’s reported combined-error range of “49.8 % to 14.3 % CV for plasma OC concentrations ranging from 0.05 to 6 mg/L” (Kamal 2013 Results page 3473).
  • Race was screened and dropped. Race was evaluated as a candidate categorical covariate but was not retained in the final model (Kamal 2013 Methods ‘Covariate evaluation’ page 3471 and Results page 3473). No race covariate is encoded.
  • No drug-drug interactions, ESRD, or neonatal data. The pooled PK dataset in Kamal 2013 excluded drug-drug interaction studies, patients with end-stage renal disease on hemodialysis, and an infant cohort (< 1 year) that was not yet available at the time of the original analysis. The model should not be extrapolated to those populations without external validation.
  • Creatinine clearance derivation. In adults aged 18 or older CLCR was computed via Cockcroft-Gault with ideal body weight substituted when actual weight exceeded IBW and the result BSA-normalised to 1.73 m^2; SCr was floored at 0.7 mg/dL. In paediatric and adolescent subjects aged 1-17, CLCR was computed via the revised Schwartz equation (0.413 * HTCM / SCr) with SCr floored at 0.2 mg/dL. Users feeding the model with their own population should provide CRCL in mL/min/1.73 m^2 derived by the same method appropriate to the subject’s age band; the canonical CRCL register entry documents this BSA-normalised scope.