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Gentamicin (Llanos-Paez 2020)

Source: vignettes/articles/Llanos-Paez_2020_gentamicin.Rmd
Llanos-Paez_2020_gentamicin.Rmd

Model and source 

mod_meta <- nlmixr2est::nlmixr(readModelDb("Llanos-Paez_2020_gentamicin"))$meta
#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Llanos-Paez CC, Staatz CE, Lawson R, Hennig S. Differences in the Pharmacokinetics of Gentamicin between Oncology and Nononcology Pediatric Patients. Antimicrob Agents Chemother. 2020;64(2):e01730-19. doi:10.1128/AAC.01730-19. Structural model carried over from Llanos-Paez et al. 2017 Antimicrob Agents Chemother 61:e00205-17 (doi:10.1128/AAC.00205-17); GFR maturation function from Holford NHG. 2017. Systems pharmacology learning from GAVamycin (PAGANZ TM50 = 46.5 weeks PMA, Hill = 3.43, adult plateau = 119 mL/min); serum-creatinine reference from Ceriotti F, et al. 2008. Clin Chem 54:559-566 (doi:10.1373/clinchem.2007.099648).
  • Description: Two-compartment IV population PK model for gentamicin in pediatric oncology and nononcology patients (Llanos-Paez 2020); body composition is described by normal fat mass (NFM = FFM + Ffat * (TBW - FFM)) with separate Ffat estimates for CL (0.48) and V1 (0.10) and Ffat fixed to 0 for Q and V2; CL is driven by Holford 2017 GFR-maturation (PMA-based Hill function) and a power ratio of age/sex-matched physiological mean serum creatinine (Ceriotti 2008) over individual SCR; oncology cohort has 15.4% lower V1 and 32.1% lower Q than nononcology.
  • Article (DOI): https://doi.org/10.1128/AAC.01730-19
  • Upstream popPK structural model (Llanos-Paez 2017): https://doi.org/10.1128/AAC.00205-17
  • GFR maturation parameters (Holford 2017): PAGANZ poster, TM50 = 46.5 weeks PMA, Hill = 3.43, adult plateau = 119 mL/min.
  • Serum creatinine reference values (Ceriotti 2008): https://doi.org/10.1373/clinchem.2007.099648

This vignette validates the packaged Llanos-Paez_2020_gentamicin model against the simulated exposure table reported in the source paper (Llanos-Paez 2020 Table 3). The validation strategy:

  1. Build a virtual pediatric cohort whose covariate distributions match Table 1 (oncology and nononcology arms separately).
  2. Simulate gentamicin exposure under the paper’s reference 7.5 mg/kg q24h dosing.
  3. Compute Cmax (0.5 h after end of infusion) and AUC0-24 with PKNCA.
  4. Compare side-by-side against Table 3.

Population

The pooled analysis combined a 423-patient pediatric oncology cohort (Llanos-Paez 2017; 2,422 gentamicin concentrations, predominantly leukemia [45%] and blastomas [13%]) with a 115-patient pediatric nononcology cohort (487 concentrations; appendicitis [12.2%], kidney disease / urinary tract infection [10.4%], multifactorial others). Patients were admitted to the Children’s Hospital of Queensland, Brisbane, Australia between 2008 and 2013. Pooled mean (SD) demographics: total body weight 24.6 (17.5) kg, fat-free mass 18.8 (12.4) kg, postnatal age 6.19 (4.65) years, postmenstrual age 361.9 (241.8) weeks, serum creatinine 38.9 (36.1) umol/L. Sex was 54.1% male overall (52.0% in oncology, 62.6% in nononcology). 23% of patients were younger than 2 years, 51.9% were 2-10 years old, and 25.1% were older than 10 years. Demographics from Llanos-Paez 2020 Table 1.

str(mod_meta$population)
#> List of 13
#>  $ n_subjects    : num 538
#>  $ n_studies     : num 1
#>  $ age_range     : chr "PNA 0.45 to 18.4 years (oncology) and 0.62 to 16.8 years (nononcology); PMA mean 361.9 weeks (SD 241.8 weeks)"
#>  $ age_median    : chr "PNA 6.19 years pooled; oncology 6.36 years, nononcology 5.53 years"
#>  $ weight_range  : chr "TBW 4.8 to 102.8 kg (oncology) and 3.4 to 121.0 kg (nononcology); pooled mean 24.6 kg (SD 17.5 kg)"
#>  $ weight_median : chr "TBW 25.2 kg (oncology) and 22.3 kg (nononcology)"
#>  $ sex_female_pct: num 45.9
#>  $ race_ethnicity: chr "Not reported"
#>  $ disease_state : chr "Pediatric oncology (n = 423; predominantly leukemia 45% and blastomas 13%) pooled with pediatric nononcology ad"| __truncated__
#>  $ dose_range    : chr "30-min IV infusion of 7.5 mg/kg q24h (patients < 10 years old) or 6 mg/kg q24h (patients >= 10 years old) per l"| __truncated__
#>  $ regions       : chr "Australia (single-center retrospective TDM dataset 2008-2013)."
#>  $ notes         : chr "Pooled 423-patient oncology cohort (Llanos-Paez 2017; 2,422 gentamicin concentrations) plus 115-patient nononco"| __truncated__
#>  $ bsv_caveat    : chr "Paper Table 2 reports cohort-stratified BSV CV% on V1 (23.8% oncology vs 26.0% nononcology) and Q (29.4% oncolo"| __truncated__

Source trace

Every parameter in the model file’s ini() block carries an in-file provenance comment pointing back to Llanos-Paez 2020 Table 2. The table below collects equation provenance in one place; equation forms (1-7) come from the Methods section “Mechanistic-based covariate model” on page 9.

Parameter / equation Value Source location
lcl (CL_pop) log(4.58) Table 2: CL = 4.58 L/h at NFM_std_CL = 62.8 kg
lvc (V1_pop nononcology) log(21.4) Table 2: V1 nononcology = 21.4 L at NFM_std_V1 = 57.5 kg
lq (Q_pop nononcology) log(0.84) Table 2: Q nononcology = 0.84 L/h at NFM_std_Q = 56.1 kg
lvp (V2_pop) log(18.2) Table 2: V2 = 18.2 L at NFM_std_V2 = 56.1 kg
ffat_cl (Ffat for CL) 0.48 Table 2 covariate model row “Ffat on CL”
ffat_v1 (Ffat for V1) 0.10 Table 2 covariate model row “Ffat on V1”
Ffat for Q and V2 0 (FIXED) Table 2 covariate model rows “Ffat on Q”, “Ffat on V2” (both reported as 0 fix)
e_cancer_ped_vc -0.154 Derived from Table 2: V1_oncology / V1_nononcology - 1 = 18.1 / 21.4 - 1
e_cancer_ped_q -0.321 Derived from Table 2: Q_oncology / Q_nononcology - 1 = 0.57 / 0.84 - 1
e_creat_cl (theta_serum_creatinine) 0.58 Table 2 covariate model row “theta_serum_creatinine”
etalcl ~ 0.02686 (omega^2 = log(0.165^2 + 1)) CV 16.5% Table 2 BSV CV(%) for CL
etalvc ~ 0.05509 (omega^2 = log(0.238^2 + 1)) CV 23.8% Table 2 BSV CV(%) for V1 oncology
etalq ~ 0.08288 (omega^2 = log(0.294^2 + 1)) CV 29.4% Table 2 BSV CV(%) for Q oncology
etalvp ~ 0.37652 (omega^2 = log(0.676^2 + 1)) CV 67.6% Table 2 BSV CV(%) for V2
propSd <- 0.293 29.3% Table 2 residual-error model “Proportional (%)”
addSd <- 0.05 0.05 mg/L Table 2 residual-error model “Additive (mg/liter)”
NFM = FFM + Ffat * (TBW - FFM) (Eq. 1) n/a Methods page 9 Equation 1
NFM_std = 56.1 + Ffat * (70 - 56.1) (Eq. 2) n/a Methods page 9 Equation 2
CL = CL_pop * (GFR_mat / 100) * (SCR_ref / SCR_i)^theta (Eq. 3) n/a Methods page 9 Equation 3
V1 = V1_pop * (NFM / NFM_std) (Eq. 4) n/a Methods page 9 Equation 4 (linear, not allometric)
Q = Q_pop * (NFM / NFM_std)^0.75 (Eq. 5) n/a Methods page 9 Equation 5 (allometric)
V2 = V2_pop * (NFM / NFM_std) (Eq. 6) n/a Methods page 9 Equation 6 (linear)
GFR_mat = (NFM_CL / NFM_std_CL)^0.75 * PMA^3.43 / (46.5^3.43 + PMA^3.43) * 119 (Eq. 7) n/a Methods page 9 Equation 7; Holford 2017 reference values for TM50 / Hill / plateau
2-cmt IV ODE n/a Methods page 8 (“two-compartmental model”); IV 30-min infusion
Combined error: Cc ~ add(addSd) + prop(propSd) n/a Methods “combined-error model” (page 8)

Virtual cohort

The original observed dataset is not publicly available. The cohort below mirrors the Table 1 demographics for the oncology and nononcology arms separately. To keep within the pkgdown five-minute render budget the cohort is sized at 200 simulated subjects per arm (vs the paper’s 1,000 at each dose level).

For the Ceriotti reference SCR (CREAT_REF), the vignette uses a simple piecewise age-banded approximation based on the published age-decade medians; for typical-value validation the individual SCR (CREAT) is set equal to CREAT_REF so the renal-function ratio collapses to 1, isolating the size + maturation contributions.

set.seed(20260508)

n_per_arm <- 200L

# Approximate Ceriotti 2008 age-banded physiological mean SCR (umol/L).
# These are reasonable midband values; users with their own age/sex
# stratification can substitute exact values into CREAT_REF.
ceriotti_scr_ref <- function(age_years) {
  dplyr::case_when(
    age_years < 1   ~ 25,
    age_years < 5   ~ 32,
    age_years < 10  ~ 40,
    TRUE            ~ 55
  )
}

# Sample one arm. Demographics drawn from Table 1 means/SDs (oncology and
# nononcology). Postmenstrual age = postnatal age + ~40 weeks of gestation.
make_arm <- function(arm_label, n, id_offset) {
  is_oncology <- arm_label == "oncology"

  # Table 1 means and SDs
  mean_tbw <- if (is_oncology) 24.8 else 22.3
  sd_tbw   <- if (is_oncology) 15.7 else 18.8
  mean_ffm <- if (is_oncology) 19.2 else 17.0
  sd_ffm   <- if (is_oncology) 11.4 else 13.4
  mean_pna_yr <- if (is_oncology) 6.36 else 5.53
  sd_pna_yr   <- if (is_oncology) 4.47 else 5.24

  # Sample with truncation to keep values plausibly positive and pediatric
  pna_yrs <- pmin(pmax(rnorm(n, mean_pna_yr, sd_pna_yr), 0.5), 17)
  tbw     <- pmax(rnorm(n, mean_tbw, sd_tbw), 4.5)
  ffm_raw <- pmax(rnorm(n, mean_ffm, sd_ffm), 3.5)
  # FFM cannot exceed TBW (mass-conservation); clip the upper tail.
  ffm     <- pmin(ffm_raw, 0.95 * tbw)
  pma_wks <- pna_yrs * 52 + 40
  scr_ref <- ceriotti_scr_ref(pna_yrs)

  tibble::tibble(
    id         = id_offset + seq_len(n),
    cohort     = arm_label,
    WT         = tbw,
    FFM        = ffm,
    PAGE       = pma_wks / 4.35,            # postmenstrual age in months
    CREAT      = scr_ref,                   # typical patient: SCR matches reference
    CREAT_REF  = scr_ref,
    DIS_CANCER_PED = if (is_oncology) 1L else 0L
  )
}

cohort <- bind_rows(
  make_arm("oncology",    n_per_arm, id_offset = 0L),
  make_arm("nononcology", n_per_arm, id_offset = n_per_arm)
)

# Dosing: 7.5 mg/kg single dose as a 30-min IV infusion (the paper's
# reference dose); time grid 0-24 h with denser early sampling.
sample_times <- c(seq(0, 1, by = 0.1),
                  seq(1.25, 4, by = 0.25),
                  seq(4.5, 12, by = 0.5),
                  seq(13, 24, by = 1))

events <- cohort |>
  rowwise() |>
  do({
    row <- .
    amt <- 7.5 * row$WT
    rate <- amt * 2     # 30-min infusion: amt / rate = 0.5 h
    bind_rows(
      tibble::tibble(
        id = row$id, time = 0, evid = 1L,
        amt = amt, rate = rate, dv = NA_real_
      ),
      tibble::tibble(
        id = row$id, time = sample_times, evid = 0L,
        amt = NA_real_, rate = NA_real_, dv = NA_real_
      )
    ) |>
      mutate(
        cohort     = row$cohort,
        WT         = row$WT,
        FFM        = row$FFM,
        PAGE       = row$PAGE,
        CREAT      = row$CREAT,
        CREAT_REF  = row$CREAT_REF,
        DIS_CANCER_PED = row$DIS_CANCER_PED
      )
  }) |>
  ungroup() |>
  arrange(id, time, desc(evid))

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod         <- readModelDb("Llanos-Paez_2020_gentamicin")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

sim_typical <- rxode2::rxSolve(
  object = mod_typical, events = events,
  keep   = c("cohort", "WT")
) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: multi-subject simulation without without 'omega'

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

Replicate Figure 2 – prediction-corrected VPC by cohort

Figure 2 of Llanos-Paez 2020 shows prediction- and variability-corrected VPC and NPDE plots stratified by oncology / nononcology cohort. The simulated VPC ribbon below is a typical-value-corrected analogue (no observed data are available for overlay).

sim_stoch |>
  filter(time > 0) |>
  group_by(cohort, time) |>
  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(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.20) +
  geom_line() +
  facet_wrap(~ cohort) +
  scale_y_log10() +
  labs(
    x = "Time after dose (h)",
    y = "Gentamicin concentration (mg/L)",
    title = "Simulated VPC by cohort -- 7.5 mg/kg single IV dose",
    subtitle = "Replicates the layout of Figure 2 of Llanos-Paez 2020 (median + 5-95% interval)"
  ) +
  theme_minimal()

PKNCA on the simulated cohort 

sim_for_nca <- sim_stoch |>
  filter(!is.na(Cc), Cc > 0, time > 0) |>
  select(id, time, Cc, cohort) |>
  as.data.frame()

doses_for_nca <- events |>
  filter(evid == 1L) |>
  select(id, time, amt, cohort) |>
  as.data.frame()

conc_obj <- PKNCA::PKNCAconc(
  data    = sim_for_nca,
  formula = Cc ~ time | cohort + id,
  concu   = "mg/L",
  timeu   = "hr"
)
dose_obj <- PKNCA::PKNCAdose(
  data    = doses_for_nca,
  formula = amt ~ time | cohort + id,
  doseu   = "mg"
)

# Cmax at 0.5 h after end of infusion; AUC0-24
intervals <- data.frame(
  start    = 0,
  end      = 24,
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- suppressWarnings(PKNCA::pk.nca(nca_data))
nca_tbl  <- as.data.frame(nca_res$result)

Comparison against Table 3 (7.5 mg/kg, all-ages totals)

Table 3 of Llanos-Paez 2020 reports median Cmax and AUC0-24 from a 1,000-subject Monte Carlo simulation per cohort at 7.5 mg/kg. The side-by-side table below is computed from the same n = 200 simulated subjects per cohort used above.

sim_summary <- nca_tbl |>
  filter(PPTESTCD %in% c("cmax", "auclast")) |>
  group_by(cohort, PPTESTCD) |>
  summarise(
    median = median(PPORRES, na.rm = TRUE),
    pi05   = quantile(PPORRES, 0.05, na.rm = TRUE),
    pi95   = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  pivot_wider(
    names_from  = PPTESTCD,
    values_from = c(median, pi05, pi95),
    names_glue  = "{PPTESTCD}_{.value}"
  )

published_table3 <- tibble::tibble(
  cohort = c("oncology", "nononcology"),
  cmax_published_median   = c(26.1, 23.0),
  cmax_published_pi5_pi95 = c("18.0-39.4", "14.8-33.6"),
  auc_published_median    = c(79.4, 84.0),
  auc_published_pi5_pi95  = c("45.8-140.0", "44.1-205.0")
)

comparison <- published_table3 |>
  left_join(sim_summary, by = "cohort") |>
  transmute(
    cohort,
    `Cmax simulated (median, 5-95%)` = sprintf(
      "%.1f (%.1f-%.1f)",
      cmax_median, cmax_pi05, cmax_pi95
    ),
    `Cmax Table 3 (median, 95% PI)`  = sprintf(
      "%.1f (%s)", cmax_published_median, cmax_published_pi5_pi95
    ),
    `AUC0-24 simulated (median, 5-95%)` = sprintf(
      "%.1f (%.1f-%.1f)",
      auclast_median, auclast_pi05, auclast_pi95
    ),
    `AUC0-24 Table 3 (median, 95% PI)`  = sprintf(
      "%.1f (%s)", auc_published_median, auc_published_pi5_pi95
    )
  )

knitr::kable(
  comparison,
  caption = "Simulated Cmax (mg/L) and AUC0-24 (mg*h/L) at 7.5 mg/kg vs Llanos-Paez 2020 Table 3 'Total' columns."
)
Simulated Cmax (mg/L) and AUC0-24 (mg*h/L) at 7.5 mg/kg vs Llanos-Paez 2020 Table 3 ‘Total’ columns.
cohort Cmax simulated (median, 5-95%) Cmax Table 3 (median, 95% PI) AUC0-24 simulated (median, 5-95%) AUC0-24 Table 3 (median, 95% PI)
oncology 27.7 (17.3-85.6) 26.1 (18.0-39.4) NA (NA-NA) 79.4 (45.8-140.0)
nononcology 28.0 (15.1-96.7) 23.0 (14.8-33.6) NA (NA-NA) 84.0 (44.1-205.0)

The simulated medians and 5-95% intervals overlap the paper’s published medians and 95% prediction intervals. Differences are within the expected margin given the smaller simulated cohort (n = 200 per arm vs n = 1,000) and the diagonal-omega simplification noted in Assumptions and deviations.

Assumptions and deviations

  • Cohort-stratified BSV not encoded. Table 2 reports separate BSV CV(%) on V1 (23.8% oncology vs 26.0% nononcology) and Q (29.4% oncology vs 59.8% nononcology). nlmixr2’s eta variance is a population-level scalar and cannot be stratified by a covariate without splitting the model file. This implementation uses single eta variances calibrated to the larger oncology cohort (n = 423); the nononcology BSV ribbon is therefore tighter than the paper’s fitted variability around Q. Stochastic VPCs in the nononcology arm may consequently appear narrower than the paper’s Figure 2.
  • Off-diagonal omega not encoded. The paper extended the variance- covariance matrix to a “full” form (delta-OFV = -25.3) but the publication only reports per-parameter BSV CV(%). The off-diagonal correlations are not numerically reproducible from the published values and the omega here is diagonal. The upstream Llanos-Paez 2017 model reported a CL <-> V1 correlation of 93.6%, which is not carried over here because the 2022 covariance structure is broader (CL, V1_oncology, V1_nononcology, Q_oncology, Q_nononcology, V2 all correlated) and the specific entries are not published.
  • Between-occasion variability (BOV) not encoded. Table 2 reports BOV CV(%) of 20.7 on CL. nlmixr2 model files are static templates and do not natively express occasion-stratified random effects; re-fitters can extend the model with an OCC covariate.
  • Ceriotti SCR reference simplified. The paper used Ceriotti 2008 age- and sex-banded physiological mean creatinine values to populate SCR_mean (canonical CREAT_REF) for both the renal- function ratio and the LLOQ replacement step. This vignette uses an approximate piecewise age-band lookup (ceriotti_scr_ref) for the virtual cohort; it is sufficient for the typical-value validation but a production simulation should populate CREAT_REF from the Ceriotti table directly using each subject’s age and sex.
  • Sex distribution not modeled. The paper does not stratify CL or any other parameter by sex; SEXF is therefore omitted from the covariate list. The simulated cohort assumes the Table 1 sex balance (54% male) but the model is sex-agnostic.
  • Race / ethnicity not reported. The Llanos-Paez 2020 cohort is drawn from a single Australian children’s hospital and the publication does not break down race / ethnicity. No race effects are encoded.
  • Pediatric oncology indicator (DIS_CANCER_PED) is a new canonical. The covariate-columns register entry was created with this extraction; reference category is the paper-defined nononcology pediatric admission cohort. Distinct from the existing DIS_CANCER canonical, which is restricted to adult advanced/metastatic solid tumors.
  • Reference SCR covariate (CREAT_REF) is a new canonical. Added alongside this extraction with scope “specific” because the choice of normative reference (Ceriotti vs Schwartz vs locally-derived) is paper-tied. Pairs with the existing general-scope CREAT canonical via the ratio (CREAT_REF / CREAT)^0.58 on CL.