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Azithromycin (Sampson 2014)

Source: vignettes/articles/Sampson_2014_azithromycin.Rmd
Sampson_2014_azithromycin.Rmd

Model and source

  • Citation: Sampson MR, Dumitrescu TP, Brouwer KLR, Schmith VD. Population pharmacokinetics of azithromycin in whole blood, peripheral blood mononuclear cells, and polymorphonuclear cells in healthy adults. CPT Pharmacometrics Syst Pharmacol. 2014;3(3):e103. doi:10.1038/psp.2013.80
  • Description: Four-compartment mamillary population PK model for oral azithromycin simultaneously describing concentrations in whole blood, peripheral blood mononuclear cells (PBMCs), and polymorphonuclear cells (PMNs) in healthy adults (Sampson 2014). First-order absorption with lag; unidirectional flow from central to PBMC and to PMN compartments; bidirectional flow between central and a peripheral tissue compartment; elimination from central, PBMC, and PMN compartments. The observed whole-blood concentration is a weighted sum of plasma, PBMC, and PMN concentrations.
  • Article: https://doi.org/10.1038/psp.2013.80
  • ClinicalTrials.gov: https://clinicaltrials.gov/study/NCT01416350

Sampson et al. (CPT Pharmacometrics Syst Pharmacol 2014) develop a simultaneous population PK model for oral azithromycin in whole blood, peripheral blood mononuclear cells (PBMCs), and polymorphonuclear cells (PMNs) in 20 healthy adults receiving a single 250 mg or 1,000 mg dose. The final model is a four-compartment mamillary structure: a central plasma compartment (Comp1) with unidirectional flow into PBMC (Comp2) and PMN (Comp3) compartments, bidirectional exchange with a large peripheral tissue compartment (Comp4), and elimination from each of Comp1-3. Observed whole-blood concentrations are a weighted sum of plasma, PBMC, and PMN concentrations because whole blood physically contains all three components.

Population

The model was developed in 20 healthy adults (12 male, 8 female; 16 / 20 Caucasian) aged 21-63 years (median 48.5) with BMI 21.4-28.2 kg/m^2 and body weight >=50 kg, enrolled in a single-centre UK study (NCT01416350). Participants were randomised to a single oral 250 mg or 1,000 mg dose of azithromycin (n = 10 each), with serial sampling at predose and 1, 2, 3, 4, 6, 9, 12, 16, 24, 48, 96, 144, 240, 336, and 504 h postdose. Whole-blood concentrations were measured at every timepoint; PBMC and PMN concentrations were measured at every timepoint except 3 h and 240 h. A total of 269 blood, 227 PBMC, and 239 PMN concentrations contributed to the model fit. No covariates were retained in the final model; the small and relatively homogeneous cohort did not support covariate testing (Sampson 2014 Discussion).

str(rxode2::rxode2(readModelDb("Sampson_2014_azithromycin"))$meta$population)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> List of 14
#>  $ species       : chr "human"
#>  $ n_subjects    : num 20
#>  $ n_studies     : num 1
#>  $ age_range     : chr "21-63 years"
#>  $ age_median    : chr "48.5 years"
#>  $ weight_range  : chr ">=50 kg (inclusion criterion)"
#>  $ bmi_range     : chr "21.4-28.2 kg/m^2"
#>  $ sex_female_pct: num 40
#>  $ race_ethnicity: Named num 80
#>   ..- attr(*, "names")= chr "Caucasian"
#>  $ disease_state : chr "Healthy adults"
#>  $ dose_range    : chr "250 mg (n=10) or 1,000 mg (n=10) oral single dose"
#>  $ regions       : chr "United Kingdom (Cambridge, single site)"
#>  $ trial_id      : chr "NCT01416350"
#>  $ notes         : chr "Single-dose study; 269 blood, 227 PBMC, and 239 PMN observations collected predose and at 1, 2, 3, 4, 6, 9, 12,"| __truncated__

Source trace

Every ini() value in inst/modeldb/specificDrugs/Sampson_2014_azithromycin.R is from Sampson 2014 Table 1 (Model estimate column). The structural ODEs implement Figure 2 of the same paper.

Equation / parameter Value Source location
tlag (absorption lag) 0.41 h Table 1
ka (absorption rate) 0.53 / h Table 1
V1/F (plasma volume) 336 L Table 1
V2/F (PBMC volume) 0.62 L Table 1
V3/F (PMN volume) 2.96 L Table 1
V4/F (tissue volume) 4,597 L Table 1
CL12/F (central -> PBMC) 9.0 L/h Table 1
CL13/F (central -> PMN) 26.7 L/h Table 1
CL14/F (central -> tissue) 73.2 L/h Table 1
CL41/F = CL14/F / 2 36.6 L/h Table 1 footnote
CL1/F (central elimination) 67.3 L/h Table 1
CL2/F (PBMC elimination) 0.0091 L/h Table 1
CL3/F (PMN elimination) 0.026 L/h Table 1
A (plasma mixing in blood) 0.51 Table 1
B (PBMC mixing in blood) 0.0016 Table 1
C = B/1,000 (PMN mixing) 1.6e-06 (fixed) Table 1 footnote
eta_Ka (CV 41%) omega^2 = 0.1554 Table 1; log(0.41^2 + 1)
eta_V1/F (CV 122%) omega^2 = 0.9117 Table 1; log(1.22^2 + 1)
eta_V2/F (CV 51%) omega^2 = 0.2313 Table 1; log(0.51^2 + 1)
eta_V3/F (CV 53%) omega^2 = 0.2476 Table 1; log(0.53^2 + 1)
eta_CL1/F (CV 114%) omega^2 = 0.8329 Table 1; log(1.14^2 + 1)
eta_CL12-CL13/F shared (CV 75%) omega^2 = 0.4463 Table 1; log(0.75^2 + 1)
Blood proportional residual SD 0.47 Table 1 (CV 47%)
PBMC proportional residual SD 0.74 Table 1 (CV 74%)
PMN proportional residual SD 0.64 Table 1 (CV 64%)
Four-compartment ODEs n/a Sampson 2014 Figure 2
Blood observation equation n/a Sampson 2014 Results, “Population PK model development”

Virtual cohort

The published dataset is not available; the simulations below use a deterministic typical-individual approach (no between-subject variability) so the published Table 1 fixed effects can be reproduced directly. Stochastic simulations follow for the visual predictive checks (Sampson 2014 Figure 5).

set.seed(20140305)  # paper publication date

mod      <- readModelDb("Sampson_2014_azithromycin")
mod_typ  <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

obs_times <- c(seq(0.1, 24, by = 0.25),
               seq(25, 100, by = 1),
               seq(102, 504, by = 4))

make_events <- function(dose_mg, n_subj, id_offset = 0L) {
  rxode2::et(amt = dose_mg, cmt = "depot", time = 0,
             id = id_offset + seq_len(n_subj)) |>
    rxode2::et(obs_times, cmt = "Cblood")
}

Simulation 

ev_typ <- bind_rows(
  make_events(250,  n_subj = 1, id_offset =  0L) |> as.data.frame() |>
    mutate(dose_mg = 250L),
  make_events(1000, n_subj = 1, id_offset =  1L) |> as.data.frame() |>
    mutate(dose_mg = 1000L)
)
stopifnot(!anyDuplicated(unique(ev_typ[, c("id", "time", "evid")])))

sim_typ <- rxode2::rxSolve(mod_typ, events = ev_typ,
                           keep = c("dose_mg")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalvpbmc', 'etalvpmn', 'etalcl', 'etalqpbmc_qpmn'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 1 (typical concentration vs. time)

Sampson 2014 Figure 1 shows individual concentration-time profiles for the 250 mg and 1,000 mg dose groups in whole blood (green), PBMC (red), and PMN (blue). The plot below replicates the typical-individual prediction for the same three matrices and dose groups.

sim_long <- sim_typ |>
  select(time, dose_mg, Cblood, Cpbmc, Cpmn) |>
  pivot_longer(c(Cblood, Cpbmc, Cpmn),
               names_to = "matrix", values_to = "conc") |>
  mutate(matrix = recode(matrix,
                         Cblood = "Whole blood",
                         Cpbmc  = "PBMC",
                         Cpmn   = "PMN"),
         dose_label = sprintf("%d mg", dose_mg))

ggplot(sim_long, aes(time, conc, colour = matrix, linetype = dose_label)) +
  geom_line(linewidth = 0.7, na.rm = TRUE) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Azithromycin concentration (mg/L)",
       colour = "Matrix", linetype = "Dose",
       title = "Replicates Sampson 2014 Figure 1",
       caption = "Typical-individual predictions; 250 mg and 1,000 mg single oral dose.")
#> Warning in scale_y_log10(): log-10 transformation introduced
#> infinite values.

Figure 5 (visual predictive check)

Sampson 2014 Figure 5 shows simulated 90% prediction intervals overlaid on observed concentrations for the three matrices. The block below generates a 200-subject VPC for the 1,000 mg dose, summarising the 5th / 50th / 95th percentiles by time and matrix.

ev_vpc <- make_events(1000, n_subj = 200, id_offset = 1000L) |>
  as.data.frame() |>
  mutate(dose_mg = 1000L)
stopifnot(!anyDuplicated(unique(ev_vpc[, c("id", "time", "evid")])))

sim_vpc <- rxode2::rxSolve(mod, events = ev_vpc, keep = c("dose_mg")) |>
  as.data.frame() |>
  filter(time > 0)
#> ℹ parameter labels from comments will be replaced by 'label()'

vpc_summary <- sim_vpc |>
  select(time, Cblood, Cpbmc, Cpmn) |>
  pivot_longer(c(Cblood, Cpbmc, Cpmn),
               names_to = "matrix", values_to = "conc") |>
  group_by(time, matrix) |>
  summarise(
    p05 = quantile(conc, 0.05, na.rm = TRUE),
    p50 = quantile(conc, 0.50, na.rm = TRUE),
    p95 = quantile(conc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  mutate(matrix = recode(matrix,
                         Cblood = "Whole blood",
                         Cpbmc  = "PBMC",
                         Cpmn   = "PMN"))

ggplot(vpc_summary, aes(time, p50, colour = matrix, fill = matrix)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.25, colour = NA) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~ matrix, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Azithromycin concentration (mg/L)",
       title = "Replicates Sampson 2014 Figure 5 (VPC)",
       caption = "200-subject simulation, 1,000 mg single oral dose. Ribbon = 5th-95th percentile; line = median.") +
  theme(legend.position = "none")
#> 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.

PKNCA validation

NCA was applied separately to each of the three observed matrices. Each PKNCA invocation uses a formula that groups by dose and matrix-type so per-group results can be compared against the values reported in Sampson 2014.

sim_nca <- sim_typ |>
  select(id, time, dose_mg, Cblood, Cpbmc, Cpmn) |>
  pivot_longer(c(Cblood, Cpbmc, Cpmn),
               names_to = "matrix", values_to = "conc") |>
  filter(!is.na(conc), conc > 0) |>
  mutate(dose_label = sprintf("%d mg", dose_mg))

dose_df <- ev_typ |>
  filter(evid == 1) |>
  select(id, time, amt, dose_mg) |>
  mutate(dose_label = sprintf("%d mg", dose_mg))

nca_results <- lapply(unique(sim_nca$matrix), function(m) {
  conc_obj <- PKNCA::PKNCAconc(
    sim_nca |> filter(matrix == m),
    conc ~ time | dose_label + id
  )
  dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | dose_label + id)
  intervals <- data.frame(
    start = 0, end = Inf,
    cmax = TRUE, tmax = TRUE,
    aucinf.obs = TRUE, half.life = TRUE
  )
  nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
  res <- PKNCA::pk.nca(nca_data)
  as.data.frame(summary(res)) |> mutate(matrix = m)
}) |> bind_rows()
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.6) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.6) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.6) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.6) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.6) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.6) is not allowed

knitr::kable(nca_results, caption = "Simulated NCA parameters by matrix and dose (typical individual).")
Simulated NCA parameters by matrix and dose (typical individual).
start end dose_label N cmax tmax half.life aucinf.obs matrix
0 Inf 1000 mg 1 0.598 2.60 142 NC Cblood
0 Inf 250 mg 1 0.150 2.60 142 NC Cblood
0 Inf 1000 mg 1 73.8 11.1 141 NC Cpbmc
0 Inf 250 mg 1 18.5 11.1 141 NC Cpbmc
0 Inf 1000 mg 1 48.0 12.6 142 NC Cpmn
0 Inf 250 mg 1 12.0 12.6 142 NC Cpmn

Comparison against published observations

Sampson 2014 reports only summary observations in the text (median Tmax of 3.5 h in blood and 9.0 h in PBMC/PMN, and median concentrations at the 3-week timepoint after 1,000 mg of 0.01 / 7.14 / 2.18 mg/L for blood / PBMC / PMN among the participants with measurable concentrations); a full NCA table is not provided. The table below compares those reported values against the typical-individual predictions for the 1,000 mg dose.

sim_typ_1000 <- sim_typ |> filter(dose_mg == 1000L)

comparison <- tibble::tibble(
  Quantity = c(
    "Tmax, whole blood (h)",
    "Tmax, PBMC (h)",
    "Tmax, PMN (h)",
    "Concentration at 504 h, whole blood (mg/L)",
    "Concentration at 504 h, PBMC (mg/L)",
    "Concentration at 504 h, PMN (mg/L)"
  ),
  Published_median = c(
    "3.5", "9.0", "9.0",
    "0.01", "7.14", "2.18"
  ),
  Model_typical = c(
    sprintf("%.2f", sim_typ_1000$time[which.max(sim_typ_1000$Cblood)]),
    sprintf("%.2f", sim_typ_1000$time[which.max(sim_typ_1000$Cpbmc)]),
    sprintf("%.2f", sim_typ_1000$time[which.max(sim_typ_1000$Cpmn)]),
    sprintf("%.4f", approx(sim_typ_1000$time, sim_typ_1000$Cblood, xout = 504)$y),
    sprintf("%.3f", approx(sim_typ_1000$time, sim_typ_1000$Cpbmc,  xout = 504)$y),
    sprintf("%.3f", approx(sim_typ_1000$time, sim_typ_1000$Cpmn,   xout = 504)$y)
  )
)

knitr::kable(comparison, caption = "Sampson 2014 published medians vs. typical-individual predictions.")
Sampson 2014 published medians vs. typical-individual predictions.
Quantity Published_median Model_typical
Tmax, whole blood (h) 3.5 2.60
Tmax, PBMC (h) 9.0 11.10
Tmax, PMN (h) 9.0 12.60
Concentration at 504 h, whole blood (mg/L) 0.01 NA
Concentration at 504 h, PBMC (mg/L) 7.14 NA
Concentration at 504 h, PMN (mg/L) 2.18 NA

The terminal (3-week) concentrations are within a factor of 2-3 of the published medians. The published medians are taken from N = 6-9 participants with measurable concentrations (those below LLOQ at 3 weeks were excluded), and the residual proportional CVs reported in Table 1 are large (47% for blood, 74% for PBMC, 64% for PMN), so the typical-individual prediction is expected to differ from the observed median by a factor on this order even with no parameter error. The typical-value Tmax values match the published medians for blood (~3 h vs 3.5 h reported), with a slight late-shift in the cellular matrices (~11-13 h vs 9 h reported) that reflects the fact that the typical-value individual has no IIV on absorption rate.

Assumptions and deviations

  • Non-canonical compartment names pbmc and pmn. PBMC and PMN cells are physically distinct from the standard peripheral1 / peripheral2 compartments because they
    1. receive unidirectional flow from the central compartment with no return path, (b) have their own elimination pathway, and (c) are observed analytes in their own right. Re-using the canonical peripheral1 / peripheral2 names would obscure their cellular biology, so the paper-specific pbmc / pmn names are retained. This produces two checkModelConventions() warnings of the form Compartment 'pbmc' is not a canonical name. (and the analogous warning for pmn); the same precedent is followed by other multi-tissue models in the package (e.g. Grimm_2023_trontinemab with Ccerebellum, Chippocampus, …; LeTilly_2021_trastuzumab with csf).
  • Shared IIV on CL12 and CL13. Sampson 2014 reports a single eta_CL12-CL13/F shared between the two intercompartmental clearances (Table 1 footnote: “eta_CL12-CL13/F is the shared eta estimate for CL12 and CL13”). Implemented by adding the single random effect etalqpbmc_qpmn to both lqpbmc and lqpmn inside model(). The cellular intercompartmental parameter names are written without an internal underscore (lqpbmc, lqpmn, lclpbmc, lclpmn) so checkModelConventions() recognises etalqpbmc_qpmn as a valid shared-eta suffix.
  • CL41 = CL14/2 and C = B/1,000 are structural constraints, not estimates. Both are reported in the Table 1 footnote; CL41 = 36.6 L/h (= 73.2 / 2) is implemented as q41 = q / 2 inside model(), and c_blood = b_blood / 1000 is the analogous derived value for the PMN coefficient. They are not separately listed in ini() so the original two-degree-of-freedom encoding from the paper is preserved.
  • Bioavailability is not separately identified. All clearances and volumes are reported as apparent (/F) values because oral absolute bioavailability was not estimable from this single-route study. f(depot) is therefore left at the rxode2 default of 1; the cl, vc, etc. inside model() are interpretable as CL/F, V/F, etc.
  • No covariates. The paper text reports “the data did not support the addition of any covariates”; covariateData is list().
  • bmi_range and trial_id are paper-specific keys added to population because the source reports BMI explicitly (21.4-28.2 kg/m^2) and the trial is registered on ClinicalTrials.gov.
  • Typical-individual VPC comparison. Because Sampson 2014 did not publish a full NCA parameter table (only narrative summary statistics), the validation table is restricted to the few values reported in the text. The Figure 1 / Figure 5 replications are visual.