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Ciprofloxacin (Thuo 2011)

Source: vignettes/articles/Thuo_2011_ciprofloxacin.Rmd
Thuo_2011_ciprofloxacin.Rmd

Model and source

  • Citation: Thuo N, Ungphakorn W, Karisa J, Muchohi S, Muturi A, Kokwaro G, Thomson AH, Maitland K. Dosing regimens of oral ciprofloxacin for children with severe malnutrition: a population pharmacokinetic study with Monte Carlo simulation. J Antimicrob Chemother. 2011 Oct;66(10):2336-45. doi:10.1093/jac/dkr314
  • Description: One-compartment population PK model with first-order absorption and absorption lag for oral ciprofloxacin in Kenyan children with severe malnutrition (Thuo 2011). Apparent CL and apparent Vc are allometrically scaled to body weight (exponents 0.75 and 1) and modified by linear deviations from a serum sodium reference of 136 mmol/L; apparent CL is further reduced by 28.3% in the paper-defined high-mortality-risk stratum.
  • Article: https://doi.org/10.1093/jac/dkr314

Population

Thuo 2011 is a single-site population PK study of oral ciprofloxacin in 52 Kenyan children (8 to 102 months, weight 4.1 to 14.5 kg) hospitalised at Kilifi District Hospital between July 2008 and February 2009 with severe malnutrition. Severe malnutrition was defined as weight-for-height z-score <= -3, mid-upper arm circumference < 11 cm, or bilateral pedal oedema (kwashiorkor). The cohort was 56% male, 46% had oedematous malnutrition, and 15% were HIV-antibody-positive. Three mortality-risk strata were enrolled per the Berkley 2003 paediatric severe-malnutrition risk score: 42% low risk, 27% intermediate risk, and 31% high risk (depressed conscious state, bradycardia, shock, or hypoglycaemia). All children received empirical parenteral ampicillin and gentamicin plus WHO-standard nutritional rehabilitation; oral ciprofloxacin was added at 10 mg/kg every 12 h for 48 h (four doses), with tablets reformulated into an aqueous suspension by the study pharmacist. See Thuo 2011 Table 1 for the full baseline demographic and laboratory distributions.

The same information is available programmatically via rxode2::rxode(readModelDb("Thuo_2011_ciprofloxacin"))$population.

Source trace

The per-parameter origin is recorded as a trailing in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Thuo_2011_ciprofloxacin.R. The table below collects them in one place.

Equation / parameter Value Source location (Thuo 2011)
Structural model: one-compartment, first-order absorption with lag n/a Methods “Pharmacokinetic analysis”; Results paragraph 2 of “Pharmacokinetic data analysis”
Apparent CL allometric form: CL = theta1 * (WT/70)^0.75 * [1 + theta2*(Na - 136)] * [1 + theta3*highrisk] n/a Methods “Pharmacokinetic analysis”; Results structural-model statement
Apparent Vc allometric form: V = theta4 * (WT/70) * [1 + theta5*(Na - 136)] n/a Methods “Pharmacokinetic analysis”; Results structural-model statement
lka = log(2.97) 2.97 /h Table 2 theta6
lcl = log(42.7) 42.7 L/h/70 kg Table 2 theta1
lvc = log(372) 372 L/70 kg Table 2 theta4
lalag = log(0.742) 0.742 h Table 2 theta7
allo_cl = fixed(0.75) 0.75 Methods “Pharmacokinetic analysis” (fixed allometric exponent on CL)
allo_vc = fixed(1) 1 Methods “Pharmacokinetic analysis” (fixed allometric exponent on V)
e_sod_cl 0.0368 /(mmol/L) Table 2 theta2
e_sod_vc 0.0291 /(mmol/L) Table 2 theta5
e_mortrisk_high_cl -0.283 (fractional) Table 2 theta3
etalcl 0.13554 (var) Table 2 BSV CL = 38.1% CV; log(1 + 0.381^2)
etalvc 0.16966 (var) Table 2 BSV V = 43.0% CV; log(1 + 0.430^2)
etalka 0.71304 (var) Table 2 BSV ka = 102% CV; log(1 + 1.02^2)
propSd 0.186 Table 2 proportional residual error 18.6 %CV
addSd 0.0273 mg/L Table 2 additive residual error 0.0273 (SD)

Virtual cohort

We approximate the Thuo 2011 cohort (n = 52) with 52 simulated subjects. Weights are drawn from a log-normal distribution centred on the cohort median 6.9 kg and truncated at the reported range 4.1 to 14.5 kg. Serum sodium is drawn from a truncated normal centred on the cohort median 136 mmol/L (range 120 to 160 mmol/L). The high-risk indicator is a Bernoulli draw with probability 0.31 to match the paper’s 31% high-risk prevalence.

set.seed(20110707)

n_subj <- 52

draw_truncated <- function(n, mu, sd, lo, hi) {
  out <- numeric(0)
  while (length(out) < n) {
    candidate <- rnorm(n, mu, sd)
    candidate <- candidate[candidate >= lo & candidate <= hi]
    out <- c(out, candidate)
  }
  out[seq_len(n)]
}

cohort <- tibble::tibble(
  id  = seq_len(n_subj),
  WT  = pmin(pmax(exp(rnorm(n_subj, log(6.9), 0.18)), 4.1), 14.5),
  SOD = draw_truncated(n_subj, mu = 136, sd = 6.5, lo = 120, hi = 160),
  MORTRISK_HIGH = rbinom(n_subj, 1, 0.31)
) %>%
  mutate(
    risk_label = if_else(MORTRISK_HIGH == 1L, "high", "low/intermediate")
  )

knitr::kable(
  cohort %>% summarise(
    WT_median            = median(WT),
    WT_range_lo          = min(WT),
    WT_range_hi          = max(WT),
    SOD_median           = median(SOD),
    SOD_range_lo         = min(SOD),
    SOD_range_hi         = max(SOD),
    pct_high_risk        = round(100 * mean(MORTRISK_HIGH), 1)
  ),
  caption = "Simulated virtual cohort summary; cf. Thuo 2011 Table 1 (WT median 6.9 kg range 4.1-14.5; sodium median 136 range 120-160; 31% high-risk)."
)
Simulated virtual cohort summary; cf. Thuo 2011 Table 1 (WT median 6.9 kg range 4.1-14.5; sodium median 136 range 120-160; 31% high-risk).
WT_median WT_range_lo WT_range_hi SOD_median SOD_range_lo SOD_range_hi pct_high_risk
6.839969 4.737971 11.1795 135.0618 125.4365 150.3607 23.1

Build event table

Each simulated child receives 10 mg/kg oral ciprofloxacin every 12 h for 48 h (four doses at t = 0, 12, 24, 36 h), matching the Thuo 2011 dosing protocol. The paper reports steady-state-style AUC over the first 24 h of dosing (AUC0-24 = daily dose / individual CL); we follow the same convention by computing AUC over a single 24 h dosing window after the third dose so the cohort is at approximate steady state.

n_doses        <- 4
tau            <- 12
ss_window_lo   <- 24
ss_window_hi   <- ss_window_lo + 24
dose_time_grid <- (seq_len(n_doses) - 1) * tau

obs_grid <- sort(unique(c(
  ss_window_lo + c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 8, 10, 12),
  ss_window_lo + 12 + c(0.25, 0.5, 1, 2, 4, 8, 12)
)))

events <- cohort %>%
  rowwise() %>%
  do({
    row <- .
    doses <- tibble(
      id            = row$id,
      time          = dose_time_grid,
      amt           = round(10 * row$WT, 2),
      evid          = 1L,
      cmt           = "depot",
      WT            = row$WT,
      SOD           = row$SOD,
      MORTRISK_HIGH = row$MORTRISK_HIGH,
      risk_label    = row$risk_label
    )
    obs <- tibble(
      id            = row$id,
      time          = obs_grid,
      amt           = 0,
      evid          = 0L,
      cmt           = "central",
      WT            = row$WT,
      SOD           = row$SOD,
      MORTRISK_HIGH = row$MORTRISK_HIGH,
      risk_label    = row$risk_label
    )
    bind_rows(doses, obs)
  }) %>%
  ungroup() %>%
  arrange(id, time, desc(evid))

Simulate (typical-value, no IIV)

We zero out between-subject variability so the simulated cohort demonstrates the structural-model behaviour given the cohort weight, sodium, and risk-stratum distributions. The published Table 3 summarises individual posthoc estimates (Bayes), so the cohort-median typical-value prediction is the right anchor for a structural-model sanity check.

mod <- readModelDb("Thuo_2011_ciprofloxacin")
mod_typ <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

sim <- rxode2::rxSolve(
  mod_typ,
  events = events,
  keep   = c("WT", "SOD", "MORTRISK_HIGH", "risk_label")
) %>%
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka'
#> Warning: multi-subject simulation without without 'omega'

Replicate Figure 1: concentration-time profiles 

sim_plot <- sim %>%
  filter(!is.na(Cc), time <= 24)

ggplot(sim_plot, aes(x = time, y = Cc, group = id, colour = risk_label)) +
  geom_line(alpha = 0.5) +
  scale_colour_manual(
    values = c("high" = "#d95f02", "low/intermediate" = "#1b9e77"),
    name   = "Mortality risk"
  ) +
  labs(
    x       = "Time after first dose (h)",
    y       = "Ciprofloxacin plasma concentration (mg/L)",
    title   = "Simulated ciprofloxacin profiles after oral 10 mg/kg",
    subtitle = "52 virtual children; typical-value (zero-IIV) simulation",
    caption = "Replicates Thuo 2011 Figure 1 (individual concentration-time profiles after the first dose)."
  ) +
  theme_bw()
#> `geom_line()`: Each group consists of only one observation.
#> ℹ Do you need to adjust the group aesthetic?

PKNCA validation

PKNCA computes Cmax, Tmax, AUC0-tau (12 h), and AUC0-24 across a single 24 h window starting at t = 24 h (after two prior doses to approximate steady state). The treatment-grouping variable is the high-risk stratum so results roll up per stratum as in Thuo 2011 Table 3.

sim_ss <- sim %>%
  filter(time >= ss_window_lo, time <= ss_window_hi) %>%
  mutate(time_in_window = time - ss_window_lo)

sim_nca <- sim_ss %>%
  filter(!is.na(Cc)) %>%
  transmute(id, risk_label, time = time_in_window, Cc)

dose_nca <- events %>%
  filter(evid == 1, time == ss_window_lo) %>%
  transmute(id, risk_label, time = 0, amt)

conc_obj <- PKNCA::PKNCAconc(
  data    = sim_nca,
  formula = Cc ~ time | risk_label + id,
  concu   = "mg/L",
  timeu   = "h"
)

dose_obj <- PKNCA::PKNCAdose(
  data    = dose_nca,
  formula = amt ~ time | risk_label + id,
  doseu   = "mg"
)

intervals <- data.frame(
  start    = c(0, 0),
  end      = c(12, 24),
  cmax     = c(TRUE,  FALSE),
  tmax     = c(TRUE,  FALSE),
  auclast  = c(TRUE,  TRUE),
  cav      = c(TRUE,  FALSE),
  half.life = c(TRUE, FALSE)
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)

knitr::kable(
  summary(nca_res),
  caption = "Simulated NCA parameters by mortality-risk stratum after the third dose; ciprofloxacin 10 mg/kg q12h."
)
Simulated NCA parameters by mortality-risk stratum after the third dose; ciprofloxacin 10 mg/kg q12h.
Interval Start Interval End risk_label N AUClast (h*mg/L) Cmax (mg/L) Tmax (h) Cav (mg/L) Half-life (h)
0 12 high 12 13.5 [20.4] 2.04 [18.5] 2.00 [2.00, 2.00] 1.12 [20.4] 4.82 [0.244]
0 24 high 12 27.0 [20.5] . . . .
0 12 low/intermediate 40 9.20 [23.1] 1.69 [19.6] 1.50 [1.50, 2.00] 0.766 [23.1] 3.40 [0.224]
0 24 low/intermediate 40 18.4 [23.1] . . . .

Comparison against published NCA

Thuo 2011 Table 3 reports posthoc individual estimates of Cmax, Tmax, half-life, and AUC0-24. Below we compare the model-predicted (typical- value) NCA medians against the paper’s model-predicted (posthoc) medians.

nca_df <- as.data.frame(nca_res$result)

cmax_med <- nca_df %>%
  filter(PPTESTCD == "cmax", end == 12) %>%
  pull(PPORRES) %>%
  median(na.rm = TRUE)

tmax_med <- nca_df %>%
  filter(PPTESTCD == "tmax", end == 12) %>%
  pull(PPORRES) %>%
  median(na.rm = TRUE)

thalf_med <- nca_df %>%
  filter(PPTESTCD == "half.life", end == 12) %>%
  pull(PPORRES) %>%
  median(na.rm = TRUE)

auc24_med <- nca_df %>%
  filter(PPTESTCD == "auclast", end == 24) %>%
  pull(PPORRES) %>%
  median(na.rm = TRUE)

published <- tibble::tribble(
  ~metric,         ~units,    ~published_model_median, ~simulated_typical_median,
  "Cmax",          "mg/L",    1.50,                     round(cmax_med, 2),
  "Tmax",          "h",       1.79,                     round(tmax_med, 2),
  "Half-life",     "h",       3.78,                     round(thalf_med, 2),
  "AUC0-24",       "mg.h/L",  22.4,                     round(auc24_med, 2)
)

knitr::kable(
  published,
  caption = paste0(
    "Comparison of simulated typical-value cohort-median NCA against ",
    "Thuo 2011 Table 3 model-predicted (posthoc Bayes) medians."
  )
)
Comparison of simulated typical-value cohort-median NCA against Thuo 2011 Table 3 model-predicted (posthoc Bayes) medians.
metric units published_model_median simulated_typical_median
Cmax mg/L 1.50 1.76
Tmax h 1.79 1.50
Half-life h 3.78 3.45
AUC0-24 mg.h/L 22.40 19.67

Replicate Table 3 risk-stratum AUC contrast

Thuo 2011 reports a clear AUC contrast between low/intermediate-risk children (median AUC0-24 = 20.5 mgh/L) and high-risk children (median AUC0-24 = 29.7 mgh/L), attributable to the -28.3% effect of high risk on apparent oral clearance.

risk_stratum_summary <- nca_df %>%
  filter(PPTESTCD == "auclast", end == 24) %>%
  group_by(risk_label) %>%
  summarise(
    n           = sum(!is.na(PPORRES)),
    auc24_median = median(PPORRES, na.rm = TRUE),
    auc24_p25   = quantile(PPORRES, 0.25, na.rm = TRUE),
    auc24_p75   = quantile(PPORRES, 0.75, na.rm = TRUE),
    .groups     = "drop"
  )

published_risk <- tibble::tribble(
  ~risk_label,        ~published_median_auc24,
  "low/intermediate", 20.5,
  "high",             29.7
)

risk_stratum_summary %>%
  left_join(published_risk, by = "risk_label") %>%
  knitr::kable(
    digits  = 2,
    caption = paste0(
      "Simulated AUC0-24 (mg*h/L) by risk stratum vs Thuo 2011 Table 3 ",
      "published median posthoc estimate."
    )
  )
Simulated AUC0-24 (mg*h/L) by risk stratum vs Thuo 2011 Table 3 published median posthoc estimate.
risk_label n auc24_median auc24_p25 auc24_p75 published_median_auc24
high 12 26.66 25.02 29.92 29.7
low/intermediate 40 17.82 15.28 20.92 20.5

Assumptions and deviations

  • Cohort-level simulation rather than per-subject posthoc reproduction. Thuo 2011 Table 3 reports individual posthoc (empirical-Bayes) estimates for each of the 52 enrolled children; the validation vignette simulates a 52-subject virtual cohort drawn from the published cohort marginals (weight median 6.9 kg, sodium median 136 mmol/L, 31% high-risk) rather than reproducing the individual subjects. Typical-value simulation (zero IIV) means the cohort-median should anchor to the population typical-value prediction; the published Table 3 medians reflect both the structural model and the posthoc shrinkage of individual eta estimates toward zero, so the two medians are not identical but should be close (within 10 to 20%).

  • Steady-state AUC convention. The paper defines AUC0-24 at steady state as daily_dose / individual_CL (Methods “Pharmacokinetic analysis”), i.e. an algebraic expression rather than an integrated NCA over a specific dosing interval. The vignette computes AUC0-24 by trapezoidal integration over the 24 h window starting at t = 24 h after dosing q12h, which is the closest in-silico approximation to the paper’s algebraic definition once the depot compartment has approximately reached steady state.

  • Half-life interpretation. The model’s terminal half-life depends on the apparent oral elimination rate constant kel = CL / Vc. For the typical 7 kg child at SOD = 136, low/intermediate risk: CL = 7.59 L/h, Vc = 37.2 L, kel = 0.204 /h, t1/2 = 3.40 h. This is shorter than the published median Bayes posthoc half-life (3.78 h) because the latter reflects the cohort distribution of Vc (median 4.49 L/kg = 31.4 L for a 7 kg child) which is slightly smaller than the structural Vc/F prediction at the reference of 372 L for a 70 kg adult (= 37.2 L for a 7 kg child at allometric exponent 1).

  • Body weight range and the high-WT tail. The cohort weight range (4.1-14.5 kg) is narrow enough that the (WT/70)^0.75 vs (WT/70) allometric distinction between CL and Vc has only a modest effect on predicted exposure. The published AUC0-24 range is 7.9 to 61.3 mg*h/L; in a typical-value simulation (zero IIV) the cohort spread reflects only the weight and sodium variation, so the simulated AUC0-24 range will be narrower than the published Bayes posthoc range. This is expected and is not a sign of model mis-specification.

  • No covariance retained. The paper investigated covariance between the BSV terms but Table 2 reports only diagonal BSV values, suggesting the inter-parameter covariance did not improve the fit and was not retained in the final model. The model file therefore encodes diagonal IIV without correlation between etalcl, etalvc, and etalka.

  • Bicarbonate / ka effect not retained. The paper notes that bicarbonate concentration produced a statistically significant reduction in OFV when added as a factor on ka, but did not reduce BSV in ka and was therefore excluded from the final model (Results paragraph 4). The vignette and model file follow the paper’s final model and omit this effect.

  • Mortality-risk stratum is paper-defined. The Berkley 2003 criteria used by Thuo 2011 to define the three risk strata are documented in the model file’s covariateData[[MORTRISK_HIGH]]$notes. Users simulating a different population should redefine the binary indicator to match either the Berkley 2003 criteria or another paper-specific risk score; do not silently reuse MORTRISK_HIGH across populations with different scoring rules.

Reference

  • Thuo N, Ungphakorn W, Karisa J, Muchohi S, Muturi A, Kokwaro G, Thomson AH, Maitland K. Dosing regimens of oral ciprofloxacin for children with severe malnutrition: a population pharmacokinetic study with Monte Carlo simulation. J Antimicrob Chemother. 2011 Oct;66(10):2336-45. doi:10.1093/jac/dkr314