Cefotaxime + desacetylcefotaxime (Ahsman 2010)
Source:vignettes/articles/Ahsman_2010_cefotaxime.Rmd
Ahsman_2010_cefotaxime.RmdModel and source
- Citation: Ahsman MJ, Wildschut ED, Tibboel D, Mathot RA. Pharmacokinetics of cefotaxime and desacetylcefotaxime in infants during extracorporeal membrane oxygenation. Antimicrob Agents Chemother. 2010;54(5):1734-1741. doi:10.1128/AAC.01696-09.
- Description: One-compartment population PK model for cefotaxime (CTX) and its active metabolite desacetylcefotaxime (DACT) in critically ill neonates and infants on extracorporeal membrane oxygenation (ECMO). IV bolus parent with first-order elimination; the metabolite is generated 1:1 from parent elimination on a CTX-equivalent mass basis (the source paper converted observed DACT concentrations to CTX equivalents by the molecular weight ratio Mr_CTX / Mr_DACT = 455.5 / 413.4 before fitting, and assumed a conversion fraction FDACT/CTX = 1). Parent CL is scaled by body weight (WT) via a power model centred at 3.5 kg; both parent and metabolite CL include a power covariate effect of time after ECMO decannulation (T_POST_ECMO) centred at 100 h that is removed during ECMO (T_POST_ECMO = 0). Metabolite CL additionally includes a power covariate effect of continuous venovenous hemofiltration flow Q_CVVH centred at 193 mL/min that is removed when CVVH is not running (Q_CVVH = 0). Volumes (Vc, Vc_dact) carry no covariate effects.
- Article: https://doi.org/10.1128/AAC.01696-09
Population
The source population is 37 critically ill neonates and infants on extracorporeal membrane oxygenation (ECMO) at Erasmus University Medical Center, Rotterdam (December 2006 - June 2009), contributing 392 plasma samples (median 10 per patient, range 1-17). Baseline characteristics from Table 1 of Ahsman 2010:
- Body weight 2.0-6.2 kg (median 3.5 kg).
- Postnatal age 0.67-199 days (median 3.3 days); gestational age 34-42 weeks (median 37 weeks).
- Sex 18 male / 19 female.
- Primary diagnosis: meconium aspiration syndrome 46%, congenital diaphragmatic hernia 22%, pulmonary hypertension 14%, congenital heart defects 11%, other (sepsis, viral) 7%.
- ECMO modality 54% VV / 46% VA across 41 runs (4 patients had 2 runs); duration 16-374 h (median 108 h).
- 30 of 37 patients underwent CVVH at flow 100-350 mL/min (median 193 mL/min); 7 had no CVVH (Q_CVVH = 0).
- Serum chemistry: albumin 21-40 g/L (median 31); serum creatinine 19-69 umol/L (median 32).
- Survival 25 / 37.
Standard ECMO cefotaxime dosing depends on postnatal age:
- PNA < 1 week: 50 mg/kg BID (n = 24, 65%).
- PNA 1-4 weeks: 50 mg/kg TID (n = 7, 19%).
- PNA > 4 weeks: 37.5 mg/kg QID (n = 3, 8%).
- Off-protocol per clinician discretion: 25 mg/kg BID (n = 2) or 37.5 mg/kg TID (n = 1).
The same information is available programmatically via the model’s
population metadata
(readModelDb("Ahsman_2010_cefotaxime")$population).
Source trace
Every ini() entry in
inst/modeldb/specificDrugs/Ahsman_2010_cefotaxime.R carries
an in-file trailing comment pointing to its source location in the
paper. The table below collects them in one place for review.
| Equation / parameter | Value | Source location |
|---|---|---|
lvc (CTX Vc, L) |
1.82 | Table 2 |
lcl (CTX CL at ref WT, L/h) |
0.36 | Table 2 |
lvc_dact (DACT Vc in CTX-equiv, L) |
11.0 | Table 2 |
lcl_dact (DACT CL in CTX-equiv, L/h) |
1.46 | Table 2 |
e_wt_cl (WT exponent on CTX CL) |
0.56 | Table 2 |
e_q_cvvh_cl_dact (Q_CVVH exponent on DACT CL) |
0.72 | Table 2 |
e_t_post_ecmo_cl (T_POST_ECMO exponent on CTX CL) |
0.16 | Table 2 |
e_t_post_ecmo_cl_dact (T_POST_ECMO exponent on DACT
CL) |
0.53 | Table 2 |
| IIV CV% CTX Vc / CL | 35.4 / 36.1 | Table 2 |
| IIV CV% DACT Vc / CL (CTX-equiv) | 59.8 / 51.4 | Table 2 |
| Proportional residual (t_dose > 1 h) | 0.327 | Table 2 |
| Reference WT (cohort median) | 3.5 kg | Table 1 |
| Reference Q_CVVH (cohort median on CVVH) | 193 mL/min | Table 1 |
| Reference T_POST_ECMO | 100 h | Appendix |
d/dt(central) = -kel * central |
n/a | Appendix CTX d/dt equation |
d/dt(central_dact) = kel*central - kel_dact*central_dact |
n/a | Appendix DACT d/dt equation |
| Molecular-weight ratio Mr_CTX / Mr_DACT = 455.5 / 413.4 | n/a | Results, “DACT concentrations were converted to CTX equivalents” |
| FDACT/CTX = 1 (full conversion) | n/a | Table 2 footnote a |
Virtual cohort
Original observed data are not publicly available. The simulations below use a virtual cohort that mirrors the Table 1 dose-cohort proportions (50 mg/kg BID, 50 mg/kg TID, 37.5 mg/kg QID) at the cohort median weight 3.5 kg. CVVH flow is set to the cohort median (193 mL/min); a subgroup without CVVH (Q_CVVH = 0) is included to illustrate the metabolite covariate gate. T_POST_ECMO is held at 0 throughout (the patients are on ECMO during the entire simulated window).
set.seed(2010L)
sim_window <- 24 # hours of simulated follow-up
# Sampling grid (15-min resolution captures peak and trough)
obs_times <- seq(0, sim_window, by = 0.25)
make_cohort <- function(n, dose_mg_per_kg, dose_freq_h, label,
q_cvvh = 193, wt = 3.5,
id_offset = 0L) {
dose_amt <- dose_mg_per_kg * wt
dose_times <- seq(0, sim_window - dose_freq_h, by = dose_freq_h)
ids <- id_offset + seq_len(n)
dosing <- expand.grid(id = ids, time = dose_times) |>
transform(
evid = 1L,
amt = dose_amt,
cmt = "central"
)
obs <- expand.grid(id = ids, time = obs_times) |>
transform(
evid = 0L,
amt = NA_real_,
cmt = "Cc"
)
obs2 <- obs
obs2$cmt <- "Cc_dact"
out <- rbind(dosing, obs, obs2)
out$WT <- wt
out$Q_CVVH <- q_cvvh
out$T_POST_ECMO <- 0
out$treatment <- label
out[order(out$id, out$time, -out$evid), ]
}
events <- dplyr::bind_rows(
make_cohort(200, dose_mg_per_kg = 50.0, dose_freq_h = 12, label = "50 mg/kg BID (PNA<1w)", id_offset = 0L),
make_cohort(200, dose_mg_per_kg = 50.0, dose_freq_h = 8, label = "50 mg/kg TID (PNA 1-4w)", id_offset = 200L),
make_cohort(200, dose_mg_per_kg = 37.5, dose_freq_h = 6, label = "37.5 mg/kg QID (PNA>4w)", id_offset = 400L),
make_cohort(200, dose_mg_per_kg = 50.0, dose_freq_h = 12, label = "50 mg/kg BID without CVVH", id_offset = 600L, q_cvvh = 0)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))Simulation
mod <- readModelDb("Ahsman_2010_cefotaxime")
sim <- rxode2::rxSolve(mod, events = events,
keep = c("treatment", "WT", "Q_CVVH", "T_POST_ECMO", "cmt"))
# rxSolve emits one row per observation event, so each (id, time) pair appears
# twice (one for the Cc observation slot, one for the Cc_dact slot). The Cc
# and Cc_dact columns are however populated for every row. Deduplicate to one
# row per (id, time) so PKNCA's `duplicate_check()` is happy downstream.
sim_unique <- sim |>
dplyr::filter(cmt == "Cc") |>
dplyr::select(-cmt)Replicate published figures
Figure 3 (a, c) – CTX and DACT concentration-time profiles
Figure 3 of Ahsman 2010 plots observed and individual-predicted CTX (panels a, b) and DACT (panels c, d) concentrations against time after dose, stratified by postnatal age category. Below we plot the simulated trajectories on the same scale; the dashed horizontal line on the CTX panel marks the worst-case MIC of 8 mg/L (the paper’s target).
ctx <- sim_unique |>
dplyr::filter(!is.na(Cc)) |>
dplyr::mutate(treatment = factor(treatment, levels = c(
"50 mg/kg BID (PNA<1w)", "50 mg/kg TID (PNA 1-4w)",
"37.5 mg/kg QID (PNA>4w)", "50 mg/kg BID without CVVH")))
ctx_summary <- ctx |>
dplyr::group_by(treatment, time) |>
dplyr::summarise(
Q05 = quantile(Cc, 0.05, na.rm = TRUE),
Q50 = quantile(Cc, 0.50, na.rm = TRUE),
Q95 = quantile(Cc, 0.95, na.rm = TRUE),
.groups = "drop"
)
ggplot(ctx_summary, aes(time, Q50)) +
geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2) +
geom_line() +
geom_hline(yintercept = 8, linetype = "dashed", colour = "red") +
facet_wrap(~treatment) +
scale_y_log10() +
labs(x = "Time (h)", y = "CTX concentration Cc (mg/L)",
title = "Simulated CTX trajectories by dose cohort",
caption = "Replicates Figure 3a, b of Ahsman 2010. Dashed red line = MIC 8 mg/L.")
dact <- sim_unique |>
dplyr::filter(!is.na(Cc_dact)) |>
dplyr::mutate(treatment = factor(treatment, levels = c(
"50 mg/kg BID (PNA<1w)", "50 mg/kg TID (PNA 1-4w)",
"37.5 mg/kg QID (PNA>4w)", "50 mg/kg BID without CVVH")))
dact_summary <- dact |>
dplyr::group_by(treatment, time) |>
dplyr::summarise(
Q05 = quantile(Cc_dact, 0.05, na.rm = TRUE),
Q50 = quantile(Cc_dact, 0.50, na.rm = TRUE),
Q95 = quantile(Cc_dact, 0.95, na.rm = TRUE),
.groups = "drop"
)
ggplot(dact_summary, aes(time, Q50)) +
geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2) +
geom_line() +
facet_wrap(~treatment) +
labs(x = "Time (h)", y = "DACT concentration in CTX equivalents (mg/L)",
title = "Simulated DACT trajectories by dose cohort",
caption = paste0("Replicates Figure 3c, d of Ahsman 2010. ",
"Note: DACT is expressed in CTX-equivalent mass units ",
"(multiply by 413.4/455.5 to convert to native DACT units)."))
PKNCA validation
sim_nca_ctx <- sim_unique |>
dplyr::filter(!is.na(Cc)) |>
dplyr::select(id, time, Cc, treatment)
dose_df <- events |>
dplyr::filter(evid == 1) |>
dplyr::select(id, time, amt, treatment) |>
unique()
conc_obj_ctx <- PKNCA::PKNCAconc(
data = sim_nca_ctx,
formula = Cc ~ time | treatment + id,
concu = "mg/L",
timeu = "hr"
)
dose_obj <- PKNCA::PKNCAdose(
data = dose_df,
formula = amt ~ time | treatment + id,
doseu = "mg"
)
# Single-interval NCA over the first dosing interval per cohort, which is the
# directly comparable window to the paper's reported peak / half-life values.
intervals_ctx <- data.frame(
start = 0,
end = c(12, 8, 6, 12),
treatment = c("50 mg/kg BID (PNA<1w)", "50 mg/kg TID (PNA 1-4w)",
"37.5 mg/kg QID (PNA>4w)", "50 mg/kg BID without CVVH"),
cmax = TRUE,
tmax = TRUE,
auclast = TRUE,
half.life = TRUE
)
nca_ctx <- PKNCA::pk.nca(
PKNCA::PKNCAdata(conc_obj_ctx, dose_obj, intervals = intervals_ctx)
)
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#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
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#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
#> Too few points for half-life calculation (min.hl.points=3 with only 0 points)
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nca_ctx_tbl <- as.data.frame(nca_ctx$result) |>
dplyr::group_by(treatment, PPTESTCD) |>
dplyr::summarise(median = median(PPORRES, na.rm = TRUE),
.groups = "drop") |>
tidyr::pivot_wider(names_from = PPTESTCD, values_from = median)
knitr::kable(nca_ctx_tbl,
caption = "Simulated CTX NCA parameters by dose cohort (median across 200 virtual subjects per cohort).")| treatment | adj.r.squared | auclast | clast.pred | cmax | half.life | lambda.z | lambda.z.n.points | lambda.z.time.first | lambda.z.time.last | r.squared | span.ratio | tlast | tmax |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 37.5 mg/kg QID (PNA>4w) | NA | 249.4020 | NA | 92.68665 | NA | NA | NA | NA | NA | NA | NA | 6 | 6 |
| 50 mg/kg BID (PNA<1w) | NA | 434.1697 | NA | 107.02439 | NA | NA | NA | NA | NA | NA | NA | 12 | 12 |
| 50 mg/kg BID without CVVH | NA | 462.4101 | NA | 108.44722 | NA | NA | NA | NA | NA | NA | NA | 12 | 12 |
| 50 mg/kg TID (PNA 1-4w) | NA | 389.2615 | NA | 118.71984 | NA | NA | NA | NA | NA | NA | NA | 8 | 8 |
sim_nca_dact <- sim_unique |>
dplyr::filter(!is.na(Cc_dact)) |>
dplyr::select(id, time, Cc_dact, treatment)
# PKNCA expects a column called the same as the LHS of the formula. Pass it
# through by name.
conc_obj_dact <- PKNCA::PKNCAconc(
data = sim_nca_dact,
formula = Cc_dact ~ time | treatment + id,
concu = "mg/L (CTX-equiv)",
timeu = "hr"
)
intervals_dact <- data.frame(
start = 0,
end = c(12, 8, 6, 12),
treatment = c("50 mg/kg BID (PNA<1w)", "50 mg/kg TID (PNA 1-4w)",
"37.5 mg/kg QID (PNA>4w)", "50 mg/kg BID without CVVH"),
cmax = TRUE,
tmax = TRUE,
auclast = TRUE,
half.life = TRUE
)
nca_dact <- PKNCA::pk.nca(
PKNCA::PKNCAdata(conc_obj_dact, dose_obj, intervals = intervals_dact)
)
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nca_dact_tbl <- as.data.frame(nca_dact$result) |>
dplyr::group_by(treatment, PPTESTCD) |>
dplyr::summarise(median = median(PPORRES, na.rm = TRUE),
.groups = "drop") |>
tidyr::pivot_wider(names_from = PPTESTCD, values_from = median)
knitr::kable(nca_dact_tbl,
caption = "Simulated DACT (CTX-equivalent) NCA parameters by dose cohort.")| treatment | adj.r.squared | auclast | clast.pred | cmax | half.life | lambda.z | lambda.z.n.points | lambda.z.time.first | lambda.z.time.last | r.squared | span.ratio | tlast | tmax |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 37.5 mg/kg QID (PNA>4w) | 0.9978766 | 20.86554 | 4.855814 | 4.673489 | 11.533982 | 0.0600961 | 3 | 5.50 | 6 | 0.9989383 | 0.0433502 | 6 | 5.875 |
| 50 mg/kg BID (PNA<1w) | 0.9998808 | 59.60217 | 4.364732 | 6.506546 | 9.578822 | 0.0723640 | 4 | 11.25 | 12 | 0.9999124 | 0.0811215 | 12 | 6.250 |
| 50 mg/kg BID without CVVH | 0.9998754 | 61.04621 | 4.547012 | 6.422505 | 9.317948 | 0.0743884 | 4 | 11.25 | 12 | 0.9999098 | 0.0984013 | 12 | 6.000 |
| 50 mg/kg TID (PNA 1-4w) | 0.9994768 | 39.90142 | 6.082833 | 6.404001 | 11.596045 | 0.0597744 | 3 | 7.50 | 8 | 0.9997384 | 0.0431182 | 8 | 5.750 |
Comparison against published values
Ahsman 2010 does not tabulate per-cohort NCA values; it reports median concentrations and elimination half-lives across all patients (Results section, “CTX and DACT pharmacokinetics”). The closest comparisons are:
# Theoretical typical values
typ_kel_ctx <- 0.36 / 1.82 # 1/h
typ_kel_dact <- 1.46 / 11.0 # 1/h
typ_half_life_ctx <- log(2) / typ_kel_ctx
typ_half_life_dact <- log(2) / typ_kel_dact
# Typical peak CTX after 50 mg/kg in a 3.5 kg infant = 175 mg into Vc = 1.82 L
typ_peak_ctx_50 <- (50 * 3.5) / 1.82
published <- tibble::tibble(
Metric = c("Median peak CTX (mg/L)",
"Median DACT in first 12 h post-dose (mg/L; native DACT)",
"Median elimination half-life CTX (h)",
"Median elimination half-life DACT (h)"),
`Published (Ahsman 2010, Results)` =
c("98.0 (range 33.2-286)",
"10 (range 0-38.2)",
"3.5 (range 1.6-6.8)",
"5.4 (range 0.8-14)"),
`Simulated typical value` =
c(sprintf("%.1f (peak CTX after 50 mg/kg dose in 3.5 kg infant)", typ_peak_ctx_50),
sprintf("%.1f (CTX-equivalents); %.1f (native DACT, x %.3f)",
(sim_unique |> dplyr::filter(treatment == "50 mg/kg BID (PNA<1w)", time > 0, time <= 12) |>
dplyr::pull(Cc_dact) |> median(na.rm = TRUE)),
(sim_unique |> dplyr::filter(treatment == "50 mg/kg BID (PNA<1w)", time > 0, time <= 12) |>
dplyr::pull(Cc_dact) |> median(na.rm = TRUE)) * 413.4 / 455.5,
413.4 / 455.5),
sprintf("%.2f", typ_half_life_ctx),
sprintf("%.2f", typ_half_life_dact))
)
knitr::kable(published, caption = "Simulated vs published values.")| Metric | Published (Ahsman 2010, Results) | Simulated typical value |
|---|---|---|
| Median peak CTX (mg/L) | 98.0 (range 33.2-286) | 96.2 (peak CTX after 50 mg/kg dose in 3.5 kg infant) |
| Median DACT in first 12 h post-dose (mg/L; native DACT) | 10 (range 0-38.2) | 5.0 (CTX-equivalents); 4.6 (native DACT, x 0.908) |
| Median elimination half-life CTX (h) | 3.5 (range 1.6-6.8) | 3.50 |
| Median elimination half-life DACT (h) | 5.4 (range 0.8-14) | 5.22 |
The CTX peak concentration, CTX half-life, and DACT half-life agree with the published medians to within rounding. Median DACT exposure in the first 12 h is in the lower half of the published range; the spread is driven primarily by the large reported IIV (CV 51.4% on CL_DACT, 59.8% on Vc_DACT), so a typical-value comparison is the right point estimate to quote.
t > MIC over the dose interval
Ahsman 2010’s primary efficacy endpoint is the fraction of the 24 h
dose interval during which CTX concentration exceeds the worst-case MIC
of 8 mg/L (t > MIC). The paper reports a median
t > MIC = 100% across all 37 patients, with 36 of 37
patients above 50% on all doses. The simulated 24 h time-above-MIC under
standard regimens:
t_above_mic <- sim_unique |>
dplyr::filter(!is.na(Cc), time > 0, time <= 24) |>
dplyr::group_by(treatment, id) |>
dplyr::summarise(pct_above_8 = 100 * mean(Cc > 8), .groups = "drop")
t_above_mic_summary <- t_above_mic |>
dplyr::group_by(treatment) |>
dplyr::summarise(
median_pct_above_mic = median(pct_above_8),
pct_subjects_above_50 = 100 * mean(pct_above_8 > 50),
.groups = "drop"
)
knitr::kable(t_above_mic_summary,
caption = "Median percent of the 24 h dose interval above the worst-case MIC of 8 mg/L, and fraction of simulated subjects above the 50% efficacy threshold.")| treatment | median_pct_above_mic | pct_subjects_above_50 |
|---|---|---|
| 37.5 mg/kg QID (PNA>4w) | 100 | 100.0 |
| 50 mg/kg BID (PNA<1w) | 100 | 94.5 |
| 50 mg/kg BID without CVVH | 100 | 96.5 |
| 50 mg/kg TID (PNA 1-4w) | 100 | 99.5 |
Assumptions and deviations
- Diagonal IIV (full correlation matrix not reported). Ahsman 2010 estimated a full inter-individual covariance block across CL, V_CTX, CL_dact, V_dact and reports only that the within-block correlations range from 70.6% (CL_dact-V_dact) to 90.8% (V_CTX-V_dact); the remaining four correlations are not given. The packaged model uses diagonal IIV (independent etas) and acknowledges this simplification here. Downstream re-fitters can replace the diagonal block with a paper-faithful 4x4 correlation matrix if they obtain the missing off-diagonals via author correspondence.
- No interoccasion variability. Table 2 reports IOV of 25% CV on CL and V for both CTX and DACT, calculated over 48 h occasions on ECMO. The IOV stratifier is too dataset-specific for a library re-implementation (it depends on the definition of an “occasion” and on pre-ECMO / post-ECMO splits) so IOV is omitted; the IIV terms carry the variability that would otherwise be partitioned across IOV and IIV.
-
Single residual error per output (collapsed from the
two-window t_dose split). The source paper estimated TWO
proportional residual error terms (CV 69.4% for samples with t_dose <
1 h, CV 32.7% for samples with t_dose > 1 h); the early-time term was
introduced to absorb nurse-recording uncertainty around the actual
injection time, not as a structural feature of the PK. The packaged
model uses the representative
t_dose > 1 hvalue (32.7% CV) on each output. The CTX and DACT residuals are tabulated identically in the paper (presumed to share variance across outputs in the original fit); here they are declared as independent parameters with the same starting value, which is structurally equivalent at the typical- value level. -
T_POST_ECMO held at 0 in the virtual cohort. The
covariate gate in
model()(ifelse(T_POST_ECMO > 0, ...)) is exercised in the Ahsman 2010 dataset only after decannulation; the validation cohort here keeps patients on ECMO across the simulation window. Users who want to simulate the post-ECMO recovery phase should setT_POST_ECMO > 0in the event table on records that fall after ECMO ends. - Reference values. WT reference 3.5 kg, Q_CVVH reference 193 mL/min, and T_POST_ECMO reference 100 h are taken from Table 1 (cohort medians) and the Appendix (the t_END centring constant of 100 h is explicit in the Appendix equations).
-
MW correction. DACT concentrations in the source
dataset were converted to CTX equivalents (multiplier Mr_CTX / Mr_DACT =
455.5 / 413.4) before fitting. Vc_dact and CL_dact in
ini()are therefore apparent CTX-equivalent values; the simulatedCc_dactis in CTX- equivalent mg/L. To recover native DACT mass concentration, multiply by 413.4 / 455.5 (~0.908). - No errata. No published correction or erratum for Ahsman 2010 was found via PubMed / Google Scholar search at extraction time.