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Gentamicin (Llanos 2017)

Source: vignettes/articles/Llanos_2017_gentamicin.Rmd
Llanos_2017_gentamicin.Rmd
library(nlmixr2lib)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter
library(rxode2)
#> rxode2 5.0.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)

Model and source

  • Citation: Llanos-Paez CC, Staatz CE, Lawson R, Hennig S. A Population Pharmacokinetic Model of Gentamicin in Pediatric Oncology Patients To Facilitate Personalized Dosing. Antimicrob Agents Chemother. 2017;61(8):e00205-17.
  • Article: https://doi.org/10.1128/AAC.00205-17
  • Model identifier: Llanos_2017_gentamicin

Population

Llanos-Paez 2017 developed the model from 2,422 gentamicin concentration-time observations collected in 423 pediatric oncology patients with febrile or fever-only neutropenia at The Lady Cilento Children’s Hospital, Brisbane, Australia, between 2008 and 2013 (Table 1 of the paper). Patients had a median postnatal age of 5.18 years (range 0.2 to 18.2 years), a median total body weight of 19.4 kg (4.8 to 102.8 kg), a median fat-free mass of 15.7 kg (3.4 to 72.6 kg), and 48% were female. Gentamicin was administered as a 30-min IV infusion once daily at 7.5 mg/kg in patients younger than 10 years and at 6 mg/kg in patients aged 10 years or older, per local hospital guidelines. Twenty- four percent of patients had received nephrotoxic chemotherapy (cisplatin or carboplatin) in the 6 months before gentamicin therapy. The model was externally evaluated on a separate cohort of 52 pediatric oncology patients (174 concentrations) collected in 2014 to 2015.

The same metadata is available programmatically via the model’s population field (readModelDb("Llanos_2017_gentamicin")$population).

Source trace

Each ini() entry in inst/modeldb/specificDrugs/Llanos_2017_gentamicin.R carries an in-file comment pointing to its source location. The table below collects them in one place for review.

Equation / parameter Value Source location
Two-compartment IV with first-order elimination structural Table 2 (Final model) and Methods Eq. 3-4
lcl (CL, L/h per 70 kg) log(5.77) Table 2, Final model column
lvc (V1, L per 70 kg) log(21.6) Table 2, Final model column
lvp (V2, L per 70 kg) log(13.8) Table 2, Final model column
lq (Q, L/h per 70 kg) log(0.62) Table 2, Final model column
e_creat_cl (theta_Scr) 0.55 Table 2, “Covariate model theta_Scr” row
e_ffm_cl_q (FFM allometric exponent on CL via GFRmat and on Q) 0.75 Methods Eq. 4 (also appears in Table 2 footer Q term and Eq. 3 GFRmat term)
e_ffm_vc_vp (FFM linear exponent on V1, V2) 1 Table 2 footer (V1 and V2 multipliers (FFM/70) with no exponent)
pma_hill (Hill coefficient) 3.33 Methods Eq. 3 (Rhodin et al. 2009)
pma_tm50 (PMA at half-maximal GFR maturation, weeks) 55.4 Methods Eq. 3 (Rhodin et al. 2009)
gfr_max (asymptotic mature GFR, mL/min) 112 Methods Eq. 3 (Rhodin et al. 2009)
gfr_ref (CL covariate normalizer, mL/min) 100 Table 2 footer CL equation
BSV CL (CV%) 16.0 Table 2, Final model BSV column
BSV V1 (CV%) 21.5 Table 2, Final model BSV column
BSV V2 (CV%) 62.4 Table 2, Final model BSV column
Correlation(CL, V1) 0.692 Table 2, “Correlation (%) between CL and V1” row
propSd (proportional residual error, fraction) 0.275 Table 2, “Proportional (%)” row, Final model
addSd (additive residual error, mg/L) 0.04 Table 2, “Additive (mg/liter)” row, Final model

Virtual cohort

The original individual-level data are not publicly available. The simulations below use a virtual cohort whose covariate distributions approximate the published trial demographics from Table 1 of Llanos-Paez 2017. Three age strata reproduce the paper’s Table 1 stratification (< 2 y, 2-10 y, > 10 y).

set.seed(2017L)

ceriotti_creat_ref <- function(pna_yr, sexF) {
  pna <- pmax(0, pna_yr)
  vapply(seq_along(pna), function(i) {
    a <- pna[i]; f <- sexF[i]
    if (a <  1) 24.5
    else if (a <  3) 29.9
    else if (a <  5) 34.3
    else if (a <  7) 38.8
    else if (a <  9) 42.4
    else if (a < 11) 45.9
    else if (a < 13) 49.5
    else if (a < 15) ifelse(f == 1, 51.3, 53.1)
    else if (a < 17) ifelse(f == 1, 53.1, 63.7)
    else             ifelse(f == 1, 56.7, 74.3)
  }, numeric(1))
}

janmahasatian_ffm <- function(WT, HT_cm, sexF) {
  HT_m  <- HT_cm / 100
  BMI   <- WT / (HT_m^2)
  whs_m <- 9270 * WT / (6680 + 216 * BMI)
  whs_f <- 9270 * WT / (8780 + 244 * BMI)
  ifelse(sexF == 1, whs_f, whs_m)
}

approx_height_cm <- function(pna_yr, sexF) {
  age <- pmax(0.083, pna_yr)
  pmin(180, 50 + 75 * (1 - exp(-0.30 * age)))
}

make_cohort <- function(n, age_lo, age_hi, dose_mg_per_kg, id_offset = 0L,
                        obs_h = c(0, 0.5, 1, 1.5, 2, 4, 6, 8, 10, 12, 16, 20, 24)) {
  PNA   <- runif(n, age_lo, age_hi)
  SEXF  <- rbinom(n, 1, 0.48)
  WT    <- pmax(2, 3.5 + 2.0 * PNA + 0.10 * PNA^2 + rnorm(n, 0, 1.5))
  HT    <- approx_height_cm(PNA, SEXF) + rnorm(n, 0, 5)
  FFM   <- janmahasatian_ffm(WT, HT, SEXF)
  PAGE  <- (40 / 4.35) + PNA * 12
  CREAT_REF <- ceriotti_creat_ref(PNA, SEXF)
  CREAT     <- pmax(15, CREAT_REF * exp(rnorm(n, 0, 0.20)))
  AMT       <- WT * dose_mg_per_kg

  pop <- data.frame(
    id = id_offset + seq_len(n),
    PNA, SEXF, WT, HT, FFM, PAGE, CREAT, CREAT_REF, AMT,
    cohort = sprintf("%g-%g y, %g mg/kg", age_lo, age_hi, dose_mg_per_kg)
  )

  d_dose <- pop |>
    mutate(time = 0, evid = 1, cmt = "central", dv = NA, dur = 0.5)
  d_obs <- pop[rep(seq_len(n), each = length(obs_h)), ] |>
    mutate(time = rep(obs_h, times = n), evid = 0, cmt = "central",
           dv = NA, dur = NA, AMT = 0)

  bind_rows(d_dose, d_obs) |>
    arrange(id, time, desc(evid)) |>
    select(id, time, amt = AMT, evid, cmt, dur, dv,
           FFM, PAGE, CREAT, CREAT_REF, WT, PNA, SEXF, cohort)
}

events <- bind_rows(
  make_cohort(150, 0.2,  2.0, 7.5, id_offset =   0L),
  make_cohort(200, 2.0, 10.0, 7.5, id_offset = 150L),
  make_cohort(150, 10.0, 18.2, 6.0, id_offset = 350L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Llanos_2017_gentamicin")
sim <- rxode2::rxSolve(mod, events = events, keep = c("cohort", "WT", "PNA")) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

For the typical-value replications used in the figures below, set the random effects to zero with zeroRe():

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typ <- rxode2::rxSolve(mod_typical, events = events,
                           keep = c("cohort", "WT", "PNA")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp'
#> Warning: multi-subject simulation without without 'omega'

Replicate published behavior

Llanos-Paez 2017 publishes a prediction-corrected VPC and goodness-of-fit plots (Figure 1) and an external-evaluation comparison against three prior pediatric models (Figure 2). The original concentration data are not publicly available, so the panels below are simulated VPC-style prediction intervals from the packaged model rather than overlays on the trial dataset.

VPC-style prediction intervals by age stratum 

vpc <- sim |>
  group_by(cohort, time) |>
  summarise(
    P05 = quantile(Cc, 0.05, na.rm = TRUE),
    P50 = quantile(Cc, 0.50, na.rm = TRUE),
    P95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc, aes(time, P50)) +
  geom_ribbon(aes(ymin = P05, ymax = P95), alpha = 0.25, fill = "steelblue") +
  geom_line(color = "steelblue") +
  facet_wrap(~ cohort) +
  scale_y_log10() +
  labs(
    x = "Time after start of infusion (h)",
    y = "Gentamicin concentration (mg/L)",
    title = "Simulated prediction intervals by age / dose stratum",
    caption = "VPC-style 5/50/95th percentiles from the packaged Llanos 2017 model."
  ) +
  theme_bw()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.

Typical-value clearance vs body size

The paper’s Discussion (page 4) reports a typical CL of 5.77 L/h for an adult-equivalent reference (FFM = 70 kg, PMA mature, CREAT at the age/sex reference). The next plot reproduces the typical CL surface across the pediatric weight range.

cl_typ <- sim_typ |>
  group_by(id, cohort) |>
  summarise(WT = first(WT), PNA = first(PNA), CL = first(cl),
            .groups = "drop")

ggplot(cl_typ, aes(WT, CL, color = cohort)) +
  geom_point(alpha = 0.6) +
  geom_smooth(se = FALSE, method = "loess", linewidth = 0.5) +
  labs(
    x = "Total body weight (kg)",
    y = "Typical clearance (L/h)",
    title = "Typical CL vs body weight by age stratum",
    caption = "Typical-value (zeroRe) CL across the simulated cohort."
  ) +
  theme_bw()
#> `geom_smooth()` using formula = 'y ~ x'

Scr effect on CL (replicates Discussion claim)

Llanos-Paez 2017 Discussion (page 8) states that “a 2-fold increase in Scr in patients with an Scr of >30 micromol/L led to a 32% decrease in gentamicin CL.” This is 1 - 0.5^0.55 = 0.317, i.e. 31.7%.

scr_grid <- expand.grid(
  CREAT = seq(20, 200, by = 5),
  CREAT_REF = c(40, 70)
) |>
  mutate(rel_cl = (CREAT_REF / CREAT)^0.55)

ggplot(scr_grid, aes(CREAT, rel_cl, color = factor(CREAT_REF))) +
  geom_line() +
  scale_x_log10() +
  scale_y_log10() +
  labs(
    x = "Observed serum creatinine (CREAT, micromol/L)",
    y = "Relative CL (vs CREAT = CREAT_REF)",
    color = "CREAT_REF (micromol/L)",
    title = "Inverse-power Scr standardization effect on CL"
  ) +
  theme_bw()

PKNCA validation

PKNCA computes Cmax and AUC0-24 per simulated subject; results are summarized by age / dose stratum and compared against the targets the paper cites.

sim_nca <- sim |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, cohort)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id)

dose_df <- events |>
  filter(evid == 1) |>
  select(id, time, amt, cohort)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + id)

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

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- suppressWarnings(PKNCA::pk.nca(nca_data))
#>  ■■■■■■■■■                         27% |  ETA:  8s
#>  ■■■■■■■■■■■■■■■■■■                56% |  ETA:  4s
#>  ■■■■■■■■■■■■■■■■■■■■■■■■■■        84% |  ETA:  2s

nca_df <- as.data.frame(nca_res$result) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "auclast", "half.life"))

nca_summary <- nca_df |>
  group_by(cohort, PPTESTCD) |>
  summarise(median = median(PPORRES, na.rm = TRUE),
            P05 = quantile(PPORRES, 0.05, na.rm = TRUE),
            P95 = quantile(PPORRES, 0.95, na.rm = TRUE),
            .groups = "drop") |>
  pivot_wider(names_from = PPTESTCD,
              values_from = c(median, P05, P95))

knitr::kable(nca_summary,
             digits = 2,
             caption = "Simulated NCA by age / dose stratum (median and 5/95th percentiles).")
Simulated NCA by age / dose stratum (median and 5/95th percentiles).
cohort median_auclast median_cmax median_half.life median_tmax P05_auclast P05_cmax P05_half.life P05_tmax P95_auclast P95_cmax P95_half.life P95_tmax
0.2-2 y, 7.5 mg/kg 56.09 23.83 8.89 0.5 35.39 16.64 4.36 0.5 93.06 37.44 18.40 0.5
10-18.2 y, 6 mg/kg 88.28 30.93 8.23 0.5 58.15 20.45 2.73 0.5 129.65 46.70 15.35 0.5
2-10 y, 7.5 mg/kg 67.74 26.57 9.02 0.5 42.84 17.65 3.15 0.5 100.36 38.71 18.95 0.5

Comparison against published targets

Llanos-Paez 2017 does not report a non-compartmental Cmax / AUC table. The Discussion (page 8) cites the standard once-daily aminoglycoside exposure targets of AUC24/MIC of 80-100 and Cmax/MIC > 10. With a typical Gram-negative gentamicin MIC of 1-2 mg/L:

Quantity Target Simulated median (2-10 y, 7.5 mg/kg)
Cmax > 10-20 mg/L shown above
AUC24 80-100 mg*h/L shown above

The paper notes (Discussion page 8) that “an initial dose of 8.0 mg/kg would be required for a typical patient in this study to achieve this target.” The 7.5 mg/kg simulated dose is therefore expected to land slightly below the AUC target on the median.

Assumptions and deviations

  • Between-occasion variability (BOV) is omitted from the packaged model. Llanos-Paez 2017 Table 2 reports BOV on CL of 20.7% CV (additive on top of BSV CL of 16.0% CV). nlmixr2lib models do not carry an OCC index, so BOV is not encoded here; the BSV terms are preserved verbatim. For deterministic typical-value simulation (zeroRe) this is exact; for stochastic VPCs the simulated between- individual spread on CL is narrower than the published model by approximately sqrt(0.16^2 + 0.207^2) - 0.16 = 0.10 (a 10 percentage- point CV under-coverage on CL). Document this deviation in the PR.
  • Postmenstrual age unit conversion. The Llanos 2017 paper uses PMA in weeks in its Rhodin et al. 2009 maturation function. The canonical PAGE covariate in nlmixr2lib is in months; the model converts as pma_wk = PAGE * 4.35 before evaluating the Hill expression.
  • Ceriotti 2008 reference creatinine. The age- and sex-expected mean serum creatinine CREAT_REF is computed externally per Ceriotti et al. 2008 (Clin Chem 54:559-566). This vignette uses a piecewise mid-point approximation of the Ceriotti reference table inside ceriotti_creat_ref(); downstream users are free to substitute any age/sex reference table they prefer.
  • Janmahasatian fat-free mass. FFM is computed externally per Janmahasatian et al. 2005 (Clin Pharmacokinet 44:1051-1065). The vignette’s janmahasatian_ffm() helper implements that formula.
  • Virtual cohort weight and height. Total body weight in the cohort is generated from a smooth pediatric growth approximation rather than WHO LMS curves; this is sufficient to populate the FFM and dose computations for the validation simulations and does not influence the model parameters.
  • Cohort race / ethnicity. Llanos-Paez 2017 does not report the cohort race / ethnicity distribution; race is not a covariate in the final model so this has no impact on the simulation.
  • LLOQ handling at simulation time. Llanos-Paez 2017 imputed below-LLOQ observations to LLOQ/2 during model fitting (Methods, page 10). Simulations from the packaged model produce continuous predictions and do not re-apply this imputation; observers comparing simulated and published curves at very low concentrations should factor this in.