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Tylosin PK/PD for A. pleuropneumoniae and P. multocida co-infection in pigs (Lee 2023)

Source: vignettes/articles/Lee_2023_tylosin.Rmd
Lee_2023_tylosin.Rmd

Model and source

  • Citation: Lee E-B, Abbas MA, Park J, Tassew DD, Park S-C. (2023). Optimizing tylosin dosage for co-infection of Actinobacillus pleuropneumoniae and Pasteurella multocida in pigs using pharmacokinetic/pharmacodynamic modeling. Frontiers in Pharmacology 14:1258403.
  • Article: https://doi.org/10.3389/fphar.2023.1258403

This vignette validates the four packaged models contributed by Lee 2023 against the published results.

Lee 2023 gave 14 piglets a single 20 mg/kg intramuscular dose of tylosin – seven clinically healthy, and seven co-infected intranasally with A. pleuropneumoniae and P. multocida 12 h before dosing. Plasma collected across the dosing interval was then used ex vivo as the growth medium for each pathogen, and the change in bacterial count over 24 h of incubation was related to the drug exposure in that plasma. The PK/PD integration is an inhibitory sigmoid Emax model on a PK/PD index (Section 2.8):

E=E0−Emax×CγCγ+EC50γE = E_0 - \frac{E_{max} \times C^{\gamma}}{C^{\gamma} + EC_{50}^{\gamma}}

where E is the log10(CFU/mL) difference between 0 and 24 h of incubation, E0 is that same 24 h change in the drug-free control, C is the PK/PD index AUC24h/MIC, and gamma is the Hill coefficient. Table 3 reports a complete, independent parameter set for each of the four pathogen x health-state combinations, so the paper contributes four models:

Model Pathogen Plasma donor
Lee_2023_tylosin_Apleuropneumoniae_healthy A. pleuropneumoniae (BA2000013) healthy pigs
Lee_2023_tylosin_Apleuropneumoniae_infected A. pleuropneumoniae (BA2000013) co-infected pigs
Lee_2023_tylosin_Pmultocida_healthy P. multocida (BA1700127) healthy pigs
Lee_2023_tylosin_Pmultocida_infected P. multocida (BA1700127) co-infected pigs

Three features of this source shape the packaged models.

  • There is no PK model to package. Lee 2023 analysed the plasma concentrations non-compartmentally in WinNonlin 8.3 (Section 2.7) and reports only NCA summaries (Table 2: Cmax, Tmax, T1/2, AUC, Vz/F, Cl/F, MRT). Drug exposure therefore enters each packaged model as an externally supplied covariate, exactly as the paper’s own PK/PD integration consumed it. Because there is no simulated concentration-time profile, there is no PKNCA section in this vignette; the validations below are the mechanistic checks appropriate to a PD-only model.
  • The exposure covariate carries the ratio, not an absolute AUC. The covariate is AUCMIC_TYLO, in units of h, and holds AUC24h/MIC directly. Lee 2023 never reports the MIC of either challenge isolate – Sections 2.4 and 3.1 say only that strains “with MIC values similar to the MIC90” were selected – so there is no sourceable MIC with which to split the ratio into numerator and denominator. See Assumptions and deviations below.
  • E is a signed change, not a reduction magnitude. In the printed equation E falls from E0 (net growth in the drug-free control, a positive number for all four fits) to E0 - Emax at saturating exposure. Table 3’s separately printed Emax - Eo row equals Emax minus E0 exactly for all four fits, which is what fixes this sign convention – the Table 3 footnote, which calls E0 “the maximal antibacterial effect”, is garbled. The convention is confirmed numerically below.

Population

Fourteen clinically healthy crossbred Duroc x (Landrace x Yorkshire) male pigs, approximately 5-6 weeks of age and weighing 9.5 +/- 1.1 kg, were randomised seven to a healthy (non-infected) group and seven to a co-infected group (Section 2.3). All 14 were confirmed negative for A. pleuropneumoniae (apxIVA) and P. multocida (kmt1) by nasal-swab PCR before the study. The infected group was inoculated intranasally with a 1 mL mixed suspension (0.5 mL per naris) of 2.0 x 10^9 CFU/mL A. pleuropneumoniae BA2000013 and 2.0 x 10^9 CFU/mL P. multocida BA1700127. Infection was confirmed by clinical signs, by fever (40.1 +/- 1.1 C versus 37.2 +/- 1.5 C, p < 0.001) and by PCR (Section 3.4).

Twelve hours after inoculation both groups received 20 mg/kg tylosin intramuscularly, with plasma sampling at 0, 0.25, 0.5, 0.75, 1, 2, 4, 6, 8, 12 and 24 h. The ex vivo time-kill assay used plasma from n = 3 pigs per group, pre-filtered through a 0.22 um membrane and inoculated to a final density of 1 x 10^6 CFU/mL (Section 2.6). Ethics approval PTB-2022-IACUC013-A.

The susceptibility survey behind the challenge-isolate selection covered 89 A. pleuropneumoniae and 363 P. multocida pig isolates: tylosin MIC50/MIC90 were 16/16 ug/mL and 16/32 ug/mL respectively, MBC was 32 ug/mL for both, and the EUCAST ECOFFinder ECOFF was 64 ug/mL for both (Section 3.1, Table 1).

mods <- c(
  "Lee_2023_tylosin_Apleuropneumoniae_healthy",
  "Lee_2023_tylosin_Apleuropneumoniae_infected",
  "Lee_2023_tylosin_Pmultocida_healthy",
  "Lee_2023_tylosin_Pmultocida_infected"
)
pop <- readModelDb(mods[1])()$population
shown <- c("species", "n_subjects", "n_studies", "age_range", "weight_range",
           "sex_female_pct", "disease_state", "dose_range")
data.frame(
  Field = shown,
  Value = vapply(pop[shown], function(x) paste(as.character(x), collapse = "; "), character(1))
) |>
  knitr::kable(row.names = FALSE)
Field Value
species pig (crossbred Duroc x (Landrace x Yorkshire), male)
n_subjects 3
n_studies 1
age_range 5-6 weeks
weight_range 9.5 +/- 1.1 kg (mean +/- SD)
sex_female_pct 0
disease_state Clinically healthy and PCR-negative on nasal swab for A. pleuropneumoniae apxIVA and P. multocida kmt1 (Section 2.3)
dose_range 20 mg/kg tylosin (50 mg/mL injectable solution) as a single intramuscular dose (Section 2.3)

Source trace

Every value in every ini() block comes from Lee 2023 Table 3. The table below lists the source location for each parameter and each model equation.

Quantity Symbol in file Source location
Sigmoid Emax equation effect <- e0 - emax * AUCMIC_TYLO^hill / (AUCMIC_TYLO^hill + ec50^hill) Section 2.8, printed equation
Control 24 h change le0 = log(E0) Table 3, row E 0
Maximum effect span lemax = log(Emax) Table 3, row E max
Half-maximal index lec50 = log(EC50) Table 3, row EC 50
Hill coefficient lhill = log(gamma) Table 3, row gamma
Starting inoculum log10_cfu0 = fixed(6) Section 2.6, “final inoculum of 1 x 10^6 CFU/mL”
Residual SD addSd = fixed(0) Not reported; only R^2 = 0.99 (Discussion)
Exposure covariate AUCMIC_TYLO Section 2.8, C represents the AUC24h/MIC ratio
Bacterial ODE d/dt(bact) <- log(10) * (effect / 24) * bact Encoding of the 24 h difference; see below

Units

Dimensional analysis of the single ODE:

Symbol Units Note
AUCMIC_TYLO h (h*ug/mL) / (ug/mL)
ec50 h same units as the driver
hill unitless exponent
e0, emax, effect log10 CFU/mL change over a 24 h window
effect / 24 log10 CFU/mL per h rate of change of log10 density
bact CFU/mL ODE state
log(10) * (effect / 24) * bact CFU/mL per h matches d/dt(bact)

The log(10) factor converts a log10-scale rate to a natural-log-scale relative growth rate: if d(log10 N)/dt = r then d(N)/dt = ln(10) * r * N. Dividing effect by 24 spreads the paper’s 24 h difference uniformly across the window, so log10(bact) changes by exactly effect over any 24 h span – which reproduces the paper’s model at the only times bacteria were counted.

Parameter table (paper versus file) 

pars_of <- function(nm) {
  th <- rxode2::rxode(readModelDb(nm))$theta
  c(e0 = exp(th[["le0"]]), emax = exp(th[["lemax"]]),
    ec50 = exp(th[["lec50"]]), hill = exp(th[["lhill"]]),
    log10_cfu0 = th[["log10_cfu0"]])
}
fits <- data.frame(
  model    = mods,
  pathogen = c("A. pleuropneumoniae", "A. pleuropneumoniae", "P. multocida", "P. multocida"),
  donor    = c("Healthy", "Infected", "Healthy", "Infected"),
  stringsAsFactors = FALSE
)
fits <- cbind(fits, do.call(rbind, lapply(mods, pars_of)))

# Lee 2023 Table 3, transcribed independently of the model files.
paper <- data.frame(
  pathogen  = c("A. pleuropneumoniae", "A. pleuropneumoniae", "P. multocida", "P. multocida"),
  donor     = c("Healthy", "Infected", "Healthy", "Infected"),
  p_emax    = c(7.19, 7.34, 6.98, 7.04),
  p_ec50    = c(1.21, 1.33, 1.17, 1.06),
  p_e0      = c(2.84, 2.76, 3.49, 3.41),
  p_hill    = c(2.76, 1.86, 4.78, 2.90),
  p_diff    = c(4.35, 4.58, 3.49, 3.63),   # Table 3 row "E max - E o"
  p_static  = c(0.98, 1.03, 1.10, 1.12),   # Table 3, bacteriostatic (E = 0)
  p_cidal   = c(1.97, 2.54, 1.99, 2.36),   # Table 3, bactericidal (E = -3)
  stringsAsFactors = FALSE
)
chk <- dplyr::left_join(fits, paper, by = c("pathogen", "donor"))

chk |>
  transmute(
    Pathogen = pathogen, Donor = donor,
    `Emax (paper)` = p_emax, `Emax (file)` = round(emax, 4),
    `EC50 (paper)` = p_ec50, `EC50 (file)` = round(ec50, 4),
    `E0 (paper)`   = p_e0,   `E0 (file)`   = round(e0, 4),
    `gamma (paper)` = p_hill, `gamma (file)` = round(hill, 4)
  ) |>
  knitr::kable()
Pathogen Donor Emax (paper) Emax (file) EC50 (paper) EC50 (file) E0 (paper) E0 (file) gamma (paper) gamma (file)
A. pleuropneumoniae Healthy 7.19 7.19 1.21 1.21 2.84 2.84 2.76 2.76
A. pleuropneumoniae Infected 7.34 7.34 1.33 1.33 2.76 2.76 1.86 1.86
P. multocida Healthy 6.98 6.98 1.17 1.17 3.49 3.49 4.78 4.78
P. multocida Infected 7.04 7.04 1.06 1.06 3.41 3.41 2.90 2.90 

stopifnot(
  all.equal(chk$emax, chk$p_emax, tolerance = 1e-8),
  all.equal(chk$ec50, chk$p_ec50, tolerance = 1e-8),
  all.equal(chk$e0,   chk$p_e0,   tolerance = 1e-8),
  all.equal(chk$hill, chk$p_hill, tolerance = 1e-8),
  all(chk$log10_cfu0 == 6)
)

Study exposures (model input)

Lee 2023 Table 3 reports the observed AUC/MIC as 1.29 +/- 0.39 h in healthy pigs and 1.01 +/- 0.26 h in infected pigs (the paper prints the same values for both pathogens; see Errata below). Those observed exposures straddle the bacteriostatic threshold and fall short of the bactericidal one, which is the paper’s central finding: the licensed 20 mg/kg dose does not reach the bactericidal target, so a higher dose is required.

Validation 1: the Emax - Eo identity

Table 3 prints Emax - Eo as its own row. Under the packaged parameterisation that row must equal Emax minus E0 exactly, because the model’s asymptotic effect at saturating exposure is E0 - Emax. This is an exact, closed-form gate on the sign convention.

chk <- chk |> mutate(calc_diff = emax - e0)

chk |>
  transmute(Pathogen = pathogen, Donor = donor,
            `Emax - Eo (paper)` = p_diff,
            `Emax - Eo (model)` = round(calc_diff, 6),
            `Difference` = round(calc_diff - p_diff, 12)) |>
  knitr::kable()
Pathogen Donor Emax - Eo (paper) Emax - Eo (model) Difference
A. pleuropneumoniae Healthy 4.35 4.35 0
A. pleuropneumoniae Infected 4.58 4.58 0
P. multocida Healthy 3.49 3.49 0
P. multocida Infected 3.63 3.63 0 

# Exact to the precision Table 3 is printed at, for all four fits.
stopifnot(max(abs(chk$calc_diff - chk$p_diff)) < 5e-15)

All four reproduce exactly. Had E0 and Emax been swapped, or had the equation been the additive form used by the sibling model Chen_2023_tilmicosin (E = E0 + (Emax - E0) * ...), this identity would not hold.

Validation 2: PK/PD index thresholds

Table 3 also reports, independently of the four fitted parameters, the AUC24h/MIC required for bacteriostatic activity (E = 0) and bactericidal activity (E = -3). Inverting the sigmoid Emax equation gives a closed form,

C=EC50(f1−f)1/γ,f=E0−EEmaxC = EC_{50} \left( \frac{f}{1-f} \right)^{1/\gamma}, \qquad f = \frac{E_0 - E}{E_{max}}

which must reproduce the published thresholds. This is the strongest available check: it uses four fitted numbers to predict two numbers the authors printed separately.

threshold_for <- function(E, e0, emax, ec50, hill) {
  f <- (e0 - E) / emax
  ec50 * (f / (1 - f))^(1 / hill)
}
chk <- chk |>
  mutate(
    calc_static = threshold_for(0,  e0, emax, ec50, hill),
    calc_cidal  = threshold_for(-3, e0, emax, ec50, hill)
  )

thr_tab <- chk |>
  transmute(
    Pathogen = pathogen, Donor = donor,
    `Bacteriostatic (paper)` = p_static,
    `Bacteriostatic (model)` = round(calc_static, 3),
    `Bacteriostatic % diff`  = round(100 * (calc_static - p_static) / p_static, 1),
    `Bactericidal (paper)`   = p_cidal,
    `Bactericidal (model)`   = round(calc_cidal, 3),
    `Bactericidal % diff`    = round(100 * (calc_cidal - p_cidal) / p_cidal, 1)
  )
knitr::kable(thr_tab)
Pathogen Donor Bacteriostatic (paper) Bacteriostatic (model) Bacteriostatic % diff Bactericidal (paper) Bactericidal (model) Bactericidal % diff
A. pleuropneumoniae Healthy 0.98 1.037 5.8 1.97 2.057 4.4
A. pleuropneumoniae Infected 1.03 1.013 -1.7 2.54 2.666 5.0
P. multocida Healthy 1.10 1.170 6.4 1.99 2.009 0.9
P. multocida Infected 1.12 1.037 -7.4 2.36 2.359 0.0 

# All eight thresholds agree with the published values to within 8%.
stopifnot(
  max(abs(100 * (chk$calc_static - chk$p_static) / chk$p_static)) < 8,
  max(abs(100 * (chk$calc_cidal  - chk$p_cidal)  / chk$p_cidal))  < 8
)

All eight agree, within -7.4% to +6.4%. The residual differences are consistent with Table 3 reporting the mean of per-animal fitted parameters (each printed with an SD across n = 3 animals) while the thresholds were read off the pooled mean curve in Figure 5 – averaging the parameters and averaging the curve are not the same operation for a nonlinear model. No parameter was tuned to close these gaps.

Replicate Figure 5: sigmoid Emax curves

Figure 5 plots logE (CFU/mL) against the ex vivo AUC24h/MIC ratio for each of the four fits, with dotted lines at bacteriostatic (E = 0) and bactericidal (E = -3) activity. The panels below are generated from the packaged parameters using the same algebra the model() block evaluates.

effect_of <- function(ce, e0, emax, ec50, hill) {
  e0 - emax * ce^hill / (ce^hill + ec50^hill)
}
grid <- seq(0, 6, length.out = 401)
curves <- do.call(rbind, lapply(seq_len(nrow(chk)), function(i) {
  r <- chk[i, ]
  data.frame(
    panel    = paste0(r$pathogen, " -- ", r$donor),
    aucmic_h = grid,
    effect   = effect_of(grid, r$e0, r$emax, r$ec50, r$hill)
  )
}))

ggplot(curves, aes(aucmic_h, effect)) +
  geom_hline(yintercept = c(0, -3), linetype = "dotted", colour = "grey40") +
  geom_line(linewidth = 0.8, colour = "steelblue") +
  facet_wrap(~panel, ncol = 2) +
  labs(
    x = "Ex vivo AUC24h/MIC (h)",
    y = "E, change in log10 CFU/mL over 24 h",
    title = "Replicates Figure 5 of Lee 2023",
    subtitle = "Dotted lines: bacteriostatic (E = 0) and bactericidal (E = -3) activity"
  ) +
  theme_bw()

Each curve starts at E0 (net growth of the drug-free control) and falls to E0 - Emax at saturating exposure, crossing the two dotted thresholds at the AUC24h/MIC values validated in the previous section.

Time-kill trajectories from the ODE

The algebraic checks above exercise the ini() values and the sigmoid equation. This section exercises the ODE encoding: solving each model over 24 h at a fixed AUCMIC_TYLO must move log10(bact) from 6 to 6 + effect.

solve_at <- function(nm, aucmic, t_end = 24, by_h = 0.25) {
  mod <- rxode2::rxode(readModelDb(nm))
  ev  <- data.frame(id = 1L, time = seq(0, t_end, by = by_h),
                    AUCMIC_TYLO = aucmic, amt = 0, evid = 0)
  out <- as.data.frame(rxode2::rxSolve(mod, events = ev, keep = "AUCMIC_TYLO"))
  out$model <- nm
  out
}

scenarios <- do.call(rbind, lapply(seq_len(nrow(chk)), function(i) {
  r <- chk[i, ]
  levels_ <- c(`Control (0)` = 0,
               `Bacteriostatic target` = r$p_static,
               `Bactericidal target` = r$p_cidal,
               `2x bactericidal` = 2 * r$p_cidal)
  do.call(rbind, lapply(names(levels_), function(lb) {
    s <- solve_at(r$model, unname(levels_[[lb]]))
    s$panel <- paste0(r$pathogen, " -- ", r$donor)
    s$scenario <- factor(lb, levels = names(levels_))
    s
  }))
}))

ggplot(scenarios, aes(time, Cc, colour = scenario)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~panel, ncol = 2) +
  labs(x = "Ex vivo incubation time (h)", y = "log10 CFU/mL",
       colour = "AUC24h/MIC",
       title = "Ex vivo 24 h time-kill trajectories at the paper's own targets",
       subtitle = "Starting inoculum 1 x 10^6 CFU/mL (Lee 2023 Section 2.6)") +
  theme_bw() +
  theme(legend.position = "bottom")

At the bacteriostatic target the 24 h trajectory returns to its starting density; at the bactericidal target it falls by three logs. Those are the defining properties of the two thresholds, recovered here from the ODE rather than from the algebra.

Validation 3: encoding checks

These checks read the ODE state bact rather than the observation Cc, because Cc <- log10(bact + 1) carries a deliberate 1-CFU/mL floor that displaces the log10 by up to ~0.01 once the density falls into the tens of CFU/mL. The floor is a numerical guard on the observation, not part of the paper’s model, so the state is what the encoding must be exact against.

end_change <- function(nm, aucmic) {
  s <- solve_at(nm, aucmic, t_end = 24, by_h = 24)
  log10(s$bact[s$time == 24]) - log10(s$bact[s$time == 0])
}

# Check 1 -- 24 h exactness. The ODE must move log10(bact) by exactly the
# algebraic `effect` over 24 h, for an arbitrary exposure.
probe <- 1.75
c1 <- vapply(seq_len(nrow(chk)), function(i) {
  r <- chk[i, ]
  end_change(r$model, probe) - effect_of(probe, r$e0, r$emax, r$ec50, r$hill)
}, numeric(1))
stopifnot(max(abs(c1)) < 1e-5)

# Check 2 -- drug-free control. AUCMIC_TYLO = 0 must give a 24 h change of
# exactly E0 (net growth), so the sigmoid term vanishes as documented.
c2 <- vapply(seq_len(nrow(chk)), function(i) {
  end_change(chk$model[i], 0) - chk$e0[i]
}, numeric(1))
stopifnot(max(abs(c2)) < 1e-5)

# Check 3 -- saturation. As the index grows without bound the 24 h change must
# approach E0 - Emax, i.e. the negated `Emax - Eo` row of Table 3.
c3 <- vapply(seq_len(nrow(chk)), function(i) {
  end_change(chk$model[i], 1e4) - (chk$e0[i] - chk$emax[i])
}, numeric(1))
stopifnot(max(abs(c3)) < 1e-5)

data.frame(
  Check = c("24 h change equals algebraic E (AUC/MIC = 1.75)",
            "Drug-free control 24 h change equals E0",
            "Saturating exposure 24 h change equals E0 - Emax"),
  `Max absolute deviation (log10 CFU/mL)` =
    signif(c(max(abs(c1)), max(abs(c2)), max(abs(c3))), 3),
  check.names = FALSE
) |>
  knitr::kable()
Check Max absolute deviation (log10 CFU/mL)
24 h change equals algebraic E (AUC/MIC = 1.75) 8.0e-07
Drug-free control 24 h change equals E0 3.4e-06
Saturating exposure 24 h change equals E0 - Emax 1.2e-06

Check 3 is the ODE-level counterpart of Validation 1: it confirms that the Emax - Eo row of Table 3 is recovered as the model’s asymptotic 24 h kill, with the sign the printed equation implies.

The dose equation is not reproducible from the paper

Section 2.10 gives the optimal-dose calculation as

Dose=(AUC24h/MIC)×MIC×ClF×fu\text{Dose} = \frac{(AUC_{24h}/MIC) \times MIC \times Cl}{F \times f_u}

and Table 4 reports the resulting doses (for example 19.64 and 21.01 mg/kg for bactericidal activity against A. pleuropneumoniae in healthy pigs, at 50% and 90% target attainment). This vignette does not reproduce Table 4, because two of the four inputs are unavailable:

  • MIC – the challenge isolates’ MICs are not reported (see below), and the Monte Carlo simulation drew from the full isolate MIC distribution, which is published only as the Figure 1A/1B histograms.
  • f_u – the free fraction of tylosin in pig plasma is never given a value anywhere in the paper.

Substituting the reported healthy-pig Cl/F of 1416.19 mL/h/kg and the 1.97 h bactericidal target into the equation and solving against the 19.64 mg/kg Table 4 entry implies MIC / f_u = 7.04 ug/mL, which is not separable without one of the two. No value was invented to close this gap; the dose equation is documented here for completeness and is outside the packaged models’ scope, which is the sigmoid Emax layer.

Assumptions and deviations

  • The exposure covariate carries the AUC24h/MIC ratio directly. The canonical covariate AUCMIC_TYLO (units h) was founded for this extraction rather than reusing the AUC_<DRUG> family plus a model mic parameter, as the sibling model Chen_2023_tilmicosin does. The reason is that Lee 2023 reports no MIC for either challenge isolate, and the collection MIC90s are contradicted by the paper’s own Table 3 (see Errata). Carrying the ratio introduces no inferred value and matches the printed equation literally. A user who knows their isolate’s MIC can form the ratio themselves. This choice was ratified by the maintainer before the models were written.
  • The 24 h difference is spread uniformly across the window. Lee 2023 fitted only the 0-to-24 h log10 difference and counted bacteria at 1, 2, 4, 8, 12 and 24 h. The packaged ODE makes log10(bact) change linearly in time at rate effect / 24, which matches the paper’s model exactly at the 24 h endpoint it was fitted to, and is a smooth interpolation in between. The paper published no within-window kinetic model, so the shape between 0 and 24 h is an encoding choice, not a fitted result. Validation 3 check 1 confirms the endpoint is exact.
  • No between-subject variability. The +/- values in Table 3 are standard deviations of point estimates across the n = 3 animals whose plasma was used, not estimated variance components, so no eta parameters are present. The models are for typical-value simulation.
  • addSd is fixed at 0. Lee 2023 reports only the coefficient of determination of the sigmoid fit (R^2 = 0.99, Discussion) and no residual standard deviation on log10 CFU/mL.
  • log10_cfu0 is fixed at 6. Section 2.6 gives the ex vivo final inoculum as 1 x 10^6 CFU/mL. This is an experimental design input, not an estimated parameter.
  • A 1-CFU/mL floor is applied to the observation. Cc <- log10(bact + 1) keeps the log10 finite if the density is driven below 1 CFU/mL, matching the Wen_2016_enrofloxacin_* and Chen_2023_tilmicosin convention. At the exposures Lee 2023 studied the floor is never approached.
  • Table 3 SD for one parameter differs between text and table. Section 3.5 gives the healthy-pig A. pleuropneumoniae Emax as 7.19 +/- 0.27 while Table 3 gives 7.19 +/- 0.72. The point estimate, which is what the model encodes, is identical; only the SD, which the model does not use, differs.
  • The MCS-derived dose predictions and PK/PD cutoff are not packaged. Table 4 and the 2 ug/mL COPD are outputs of a 10,000-iteration Oracle Crystal Ball simulation over inputs the paper does not publish; see the section above.

Errata and internal inconsistencies in the source

None of these affect the packaged models, all of which live entirely in the ratio units the sigmoid Emax layer is expressed in. They are recorded because they are the reason the exposure covariate carries a ratio.

  1. The challenge isolates’ MICs are never reported. Sections 2.4 and 3.1 state only that strains “with MIC values similar to the MIC90” were selected (BA2000013, BA1700127). The collection MIC90s are 16 ug/mL (A. pleuropneumoniae) and 32 ug/mL (P. multocida).
  2. T > MIC is impossible under those MIC90s. Table 3 reports T > MIC = 13.08 +/- 6.15 h for A. pleuropneumoniae in healthy pigs, but Table 2 gives Cmax = 5.79 ug/mL. A plasma concentration that never reaches 16 ug/mL cannot exceed it for 13 h; the true value would be 0 h.
  3. The AUC/MIC and Cmax/MIC rows are identical for both pathogens. Table 3 prints 1.29 +/- 0.39 (healthy) and 1.01 +/- 0.26 (infected) for both, and 0.30 / 0.28 for Cmax/MIC for both, which cannot hold if the two isolates’ MICs differ as their MIC90s do.
  4. Those two rows imply mutually inconsistent MICs. AUC/MIC = 1.29 with AUC = 13.33 h*ug/mL implies MIC = 10.3 ug/mL, while Cmax/MIC = 0.30 with Cmax = 5.79 ug/mL implies MIC = 19.3 ug/mL.
  5. The Table 3 footnote swaps two definitions. It reads “Emax is the maximum difference in bacterial counts; … E0 is the maximal antibacterial effect”, which contradicts both the Section 2.8 text (“E0 represents … the change in bacterial count in the control samples after 24 h”) and the arithmetic of the Emax - Eo row. Validation 1 settles it.
  6. Table 4 is garbled in the published typesetting. Rows and columns are misaligned in the PDF (the P. multocida infected bactericidal row is missing its values, and one Healthy label appears without numbers). The dose values quoted in the Results and Discussion text – 10.45-11.75 and 11.94-15.37 mg/kg bacteriostatic, 21.01-21.21 and 25.17-27.79 mg/kg bactericidal – are internally consistent and are the ones cited above.
  7. Table 2 volume comparison is stated backwards. The Discussion says “The higher apparent volume of distribution in infected pigs (4,045.83 +/- 305.73 mL/kg) compared with healthy pigs (5,019.45 +/- 2,147.48 mL/kg)”; Table 2 assigns 4,045.83 to healthy and 5,019.45 to infected. The direction of the claim (higher in infected) matches Table 2; the parenthetical labels are swapped.