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Doripenem (Lee 2017)

Source: vignettes/articles/Lee_2017_doripenem.Rmd
Lee_2017_doripenem.Rmd

Model and source

  • Citation: Lee D-H, Kim YK, Jin K, Kang MJ, Joo Y-D, Kim YW, Moon YS, Shin J-G, Kiem S. Population pharmacokinetic analysis of doripenem after intravenous infusion in Korean patients with acute infections. Antimicrob Agents Chemother. 2017;61(5):e02185-16. doi:10.1128/AAC.02185-16
  • Description: One-compartment IV-infusion population PK model for doripenem in 37 Korean adults with acute infections (pyelonephritis, intra-abdominal infection, neutropenic fever) and CLCR ranging 20-50 or >50 mL/min (Lee 2017). Clearance and central volume scale linearly with body weight (CL/WT = 0.109 L/h/kg, V/WT = 0.280 L/kg at WT=70 kg, CLCR=57 mL/min); CL additionally scales by a power exponent on Cockcroft-Gault creatinine clearance (raw mL/min, reference 57).
  • Article: Antimicrob Agents Chemother 2017;61(5):e02185-16 (open access)

Population

The model was developed from a prospective observational PK study of 37 adult inpatients with acute infections (pyelonephritis, intra-abdominal infection, or neutropenic fever) at Inje University Haeundae Paik Hospital in Busan, Republic of Korea, between June 2013 and May 2014 (Lee 2017 Table 1). 30 patients met ACCP/SCCM sepsis criteria and 7 had severe sepsis; patients with septic shock or on renal replacement therapy were excluded. Two dose groups were enrolled by Cockcroft-Gault creatinine clearance: 9 patients with CLCR <= 50 mL/min received 250 mg of doripenem IV infused over 1 hour every 8 hours, and 28 patients with CLCR > 50 mL/min received 500 mg of doripenem IV infused over 1 hour every 8 hours. Blood samples were collected before and at 0, 0.5, and 4-6 hours after the fourth infusion (148 plasma concentrations total: 36 from the 250-mg group, 112 from the 500-mg group); doripenem was quantified by validated LC-MS/MS (LLOQ 0.2 ug/mL). Baseline demographics: mean age 61.7 years (SD 17.9), mean body weight 59.8 kg (SD 12.4), mean Cockcroft-Gault CLCR 66.7 mL/min (SD 34.4), median APACHE II score 7 (range 0-15). The cohort was 73% female (27/37). The model was fit in NONMEM 7.3 using FOCE-I with lognormal IIV on CL and V and a proportional residual-error model (the paper labels this the “Poisson” form Y = Ypred + eps * Ypred with eps ~ N(0, sigma^2), which is the standard proportional residual structure).

The same information is available programmatically via readModelDb("Lee_2017_doripenem")$population.

Source trace

Every numeric value in ini() carries an in-file comment pointing to the Lee 2017 source location. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (CL at WT=70, CLCR=57) 7.63 L/h Table 2: CL/WT = 0.109 L/h/kg (RSE 8.57%); 0.109 * 70 = 7.63
lvc (V at WT=70) 19.6 L Table 2: V/WT = 0.280 L/kg (RSE 9.60%); 0.280 * 70 = 19.6
e_wt_cl (fixed = 1) 1 Methods/Results: structural per-kg parameterisation CL/WT
e_wt_vc (fixed = 1) 1 Methods/Results: structural per-kg parameterisation V/WT
e_crcl_cl 0.688 Table 2: theta_2 = 0.688 (RSE 22.9%); CL = 0.109 * WT * (CLCR/57)^0.688
etalcl (55.0% CV on CL) 0.26433 Table 2: omega_CL = 55.0% (RSE 14.4%)
etalvc (47.3% CV on V) 0.20177 Table 2: omega_V = 47.3% (RSE 21.6%)
propSd (63.3% proportional) 0.633 Table 2: sigma_Poisson = 0.633 (RSE 7.50%)
CRCL centering (57 mL/min) 57 Results paragraph 3: CL = 0.109 * WT * (CLCR/57)^0.688
WT centering (70 kg) 70 Figure 1 caption: comparison done for a 70-kg patient
1-cmt IV structural n/a Results, “Population PK analysis” paragraph 1
Proportional (“Poisson”) residual n/a Results, “Population PK analysis” paragraph 4
Lognormal IIV on CL and V n/a Methods, “Population PK analysis”

IIV variance derivation. Lee 2017 reports IIV as %CV in Table 2. For lognormal etas, omega^2 = log(CV^2 + 1):

  • CL: log(0.550^2 + 1) = log(1.302500) = 0.264327
  • V: log(0.473^2 + 1) = log(1.223729) = 0.201772

Residual-error mapping. Lee 2017 Methods defines the “Poisson” error model as Y = Y_PRED + eps * Y_PRED with eps ~ N(0, sigma^2), which algebraically is the standard NONMEM proportional residual model Y = Y_PRED * (1 + eps). nlmixr2’s ~ prop(propSd) matches this form exactly, with propSd = sigma (the reported SD, not variance). Table 2 reports sigma_Poisson = 0.633 directly as the SD.

Virtual cohort

Original observed data are not publicly available. The cohort below covers four scenarios bracketing the paper’s covariate space and clinical-decision points: the two paper-defined dose groups (250-mg group at CLCR 38.3 mL/min, 500-mg group at CLCR 75.9 mL/min), the augmented-renal-clearance scenario from Figure 5 (CLCR 150 mL/min on 500 mg q8h with 4-hour infusion), and a normal-renal-function scenario at the structural-equation reference (CLCR 57 mL/min). All scenarios use weights drawn from the Lee 2017 cohort mean 59.8 kg (Table 1).

set.seed(20260602)

n_sub <- 200L

build_arm <- function(label, dose_mg, infusion_h, tau_h,
                      wt_kg, crcl_mlmin, id_offset) {
  ids <- id_offset + seq_len(n_sub)

  dose_times  <- seq(0, 7 * tau_h, by = tau_h)        # 8 consecutive doses

  dose_rows <- tidyr::expand_grid(id = ids, time = dose_times) |>
    mutate(
      evid     = 1L,
      amt      = dose_mg,
      cmt      = "central",
      rate     = dose_mg / infusion_h,
      cohort   = label,
      WT       = wt_kg,
      CRCL     = crcl_mlmin
    )

  obs_times <- c(seq(0, 8 * tau_h, by = 0.1),
                 seq(8 * tau_h + 0.5, 10 * tau_h, by = 0.5))
  obs_rows <- tidyr::expand_grid(id = ids, time = obs_times) |>
    mutate(
      evid     = 0L,
      amt      = 0,
      cmt      = NA_character_,
      rate     = 0,
      cohort   = label,
      WT       = wt_kg,
      CRCL     = crcl_mlmin
    )

  bind_rows(dose_rows, obs_rows) |> arrange(id, time, desc(evid))
}

events <- bind_rows(
  build_arm("250mg_q8h_1h_CRCL38",  250, 1, 8, 55.1,  38.3,    0L),
  build_arm("500mg_q8h_1h_CRCL76",  500, 1, 8, 61.3,  75.9,  200L),
  build_arm("500mg_q8h_4h_CRCL150", 500, 4, 8, 60.0, 150.0,  400L),
  build_arm("500mg_q8h_1h_CRCL57",  500, 1, 8, 70.0,  57.0,  600L)
)

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

Simulation 

mod <- readModelDb("Lee_2017_doripenem")

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

For typical-value comparisons against the Lee 2017 Table 2 point estimates, also simulate with the random effects zeroed:

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

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

Steady-state concentration-time profile

The figure below shows the simulated stochastic envelope for each cohort over the final dosing interval (post-fourth-infusion sampling in the paper would correspond roughly to t = 24-32 h here, i.e., the fourth dose at t = 24 h; the figure extends through the seventh dose to confirm steady state). Free-drug concentration Cc * 0.919 (unbound fraction 0.919 per Lee 2017 Methods PD target attainment) is overlaid to support the time-above-MIC comparison in the next section.

sim |>
  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 = 0.25) +
  geom_line() +
  facet_wrap(~cohort, scales = "free_y") +
  labs(
    x = "Time (h)",
    y = "Doripenem Cc (ug/mL)",
    title = "Simulated doripenem plasma profile by cohort",
    caption = "Shaded band: 5th-95th percentile across 200 simulated subjects per cohort. Eight doses Q8H."
  )

Replicate Lee 2017 Figure 1: Korean vs Caucasian CL comparison

Lee 2017 Figure 1 compares doripenem CL at a 70-kg body weight as a function of CLCR between the Korean model (this paper) and the Cirillo 2009 Caucasian model (reference 17 in Lee 2017: CL = 13.6 * (CLCR/98)^0.659 L/h). The figure below reproduces both curves over the CLCR range 20-170 mL/min.

crcl_grid <- seq(20, 170, by = 1)
korean <- tibble(
  CRCL = crcl_grid,
  CL_Lh = 0.109 * 70 * (crcl_grid / 57)^0.688,
  population = "Korean (Lee 2017)"
)
caucasian <- tibble(
  CRCL = crcl_grid,
  CL_Lh = 13.6 * (crcl_grid / 98)^0.659,
  population = "Caucasian (reference 17, Lee 2017 Fig 1)"
)
bind_rows(korean, caucasian) |>
  ggplot(aes(CRCL, CL_Lh, colour = population)) +
  geom_line() +
  labs(
    x = "CLCR (mL/min)",
    y = "Typical CL at 70 kg (L/h)",
    title = "Lee 2017 Figure 1: Korean vs Caucasian doripenem CL",
    caption = "Curves use the published structural equations; Korean values are 60-70% of Caucasian at matched CLCR."
  )

PKNCA validation (steady-state final dose interval)

Lee 2017 does not report a published NCA table per dose group, so the PKNCA block below characterises steady-state Cmax, Cmin, and AUC0-tau from the simulated profiles at the final dosing interval (tau = 8 h). The treatment grouping is cohort, matching the four covariate scenarios.

last_dose_time <- 7 * 8  # eighth dose at t = 56 h; tau = 8

sim_nca <- sim_typical |>
  filter(!is.na(Cc), time >= last_dose_time, time <= last_dose_time + 8) |>
  mutate(time_in_tau = time - last_dose_time) |>
  select(id, time = time_in_tau, Cc, cohort)

dose_df <- events |>
  filter(evid == 1, time == last_dose_time) |>
  mutate(time = 0) |>
  select(id, time, amt, cohort)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id,
                             concu = "ug/mL", timeu = "hr")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + id,
                             doseu = "mg")

intervals <- data.frame(
  start    = 0,
  end      = 8,
  cmax     = TRUE,
  tmax     = TRUE,
  cmin     = TRUE,
  auclast  = TRUE
)

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

nca_summary <- summary(nca_res)
knitr::kable(
  nca_summary,
  caption = "Simulated steady-state NCA parameters (typical-value, final-dose interval) by cohort."
)
Simulated steady-state NCA parameters (typical-value, final-dose interval) by cohort.
Interval Start Interval End cohort N AUClast (hr*ug/mL) Cmax (ug/mL) Cmin (ug/mL) Tmax (hr)
0 8 250mg_q8h_1h_CRCL38 200 54.7 [0.000] 15.5 [0.000] 1.95 [0.000] 1.00 [1.00, 1.00]
0 8 500mg_q8h_1h_CRCL57 200 65.5 [0.000] 22.1 [0.000] 1.45 [0.000] 1.00 [1.00, 1.00]
0 8 500mg_q8h_1h_CRCL76 200 61.4 [0.000] 23.7 [0.000] 0.859 [0.000] 1.00 [1.00, 1.00]
0 8 500mg_q8h_4h_CRCL150 200 39.3 [0.000] 9.37 [0.000] 0.453 [0.000] 4.00 [4.00, 4.00]

Comparison against Lee 2017 analytical equations (Methods Eq 1-2)

Lee 2017 Methods give closed-form expressions for Css,max (end of infusion) and Css,min (just before the next dose) under steady-state IV infusion. The chunk below evaluates these for each cohort using the typical-value CL and V and compares them to the simulated PKNCA Cmax and Cmin above.

analytical_ss <- tibble(
  cohort     = c("250mg_q8h_1h_CRCL38",
                 "500mg_q8h_1h_CRCL76",
                 "500mg_q8h_4h_CRCL150",
                 "500mg_q8h_1h_CRCL57"),
  dose_mg    = c(250, 500, 500, 500),
  Tinf       = c(1, 1, 4, 1),
  tau        = c(8, 8, 8, 8),
  WT_kg      = c(55.1, 61.3, 60.0, 70.0),
  CRCL_mLmin = c(38.3, 75.9, 150.0, 57.0)
) |>
  mutate(
    CL_Lh = 0.109 * WT_kg * (CRCL_mLmin / 57)^0.688,
    V_L   = 0.280 * WT_kg,
    kel   = CL_Lh / V_L,
    Cssmax_eq1 = (dose_mg / (V_L * kel)) *
                 (1 - exp(-kel * Tinf)) /
                 (Tinf * (1 - exp(-kel * tau))),
    Cssmin_eq2 = Cssmax_eq1 * exp(-kel * (tau - Tinf))
  ) |>
  select(cohort, CL_Lh, V_L, kel, Cssmax_eq1, Cssmin_eq2)

knitr::kable(
  analytical_ss,
  digits  = 3,
  caption = "Lee 2017 Eq 1-2 evaluated at the typical-value parameters for each cohort. Cssmax in ug/mL, kel in 1/h, CL in L/h."
)
Lee 2017 Eq 1-2 evaluated at the typical-value parameters for each cohort. Cssmax in ug/mL, kel in 1/h, CL in L/h.
cohort CL_Lh V_L kel Cssmax_eq1 Cssmin_eq2
250mg_q8h_1h_CRCL38 4.569 15.428 0.296 15.473 1.947
500mg_q8h_1h_CRCL76 8.137 17.164 0.474 23.734 0.859
500mg_q8h_4h_CRCL150 12.726 16.800 0.757 9.370 0.453
500mg_q8h_1h_CRCL57 7.630 19.600 0.389 22.113 1.449

Free-drug %fT>MIC at the paper’s PD target

Lee 2017 sets the PD target at %fT>MIC >= 40% with unbound fraction f = 0.919 (Methods, PD target attainment). The block below evaluates percent fT>MIC by simulation at four MICs (0.5, 1, 2, 4 ug/mL) using the typical-value profile over the steady-state interval, mirroring Lee 2017 Figures 4-5.

mic_grid <- c(0.5, 1, 2, 4)

ft_mic <- sim_typical |>
  filter(time >= last_dose_time, time <= last_dose_time + 8) |>
  distinct(cohort, time, Cc) |>
  mutate(time_in_tau = time - last_dose_time,
         f_Cc = 0.919 * Cc) |>
  tidyr::expand_grid(MIC = mic_grid) |>
  group_by(cohort, MIC) |>
  arrange(time_in_tau) |>
  summarise(
    pct_fT_MIC = {
      above <- f_Cc > MIC
      # Trapezoidal estimate of fraction of tau (=8 h) above MIC.
      dt <- diff(time_in_tau)
      midpoint_above <- (above[-length(above)] & above[-1])
      sum(dt[midpoint_above]) / 8 * 100
    },
    .groups = "drop"
  )

knitr::kable(
  ft_mic |>
    tidyr::pivot_wider(names_from = MIC, values_from = pct_fT_MIC,
                       names_prefix = "MIC_"),
  digits  = 1,
  caption = "Typical-value percent fT>MIC over the steady-state dosing interval (tau = 8 h) by cohort and MIC (ug/mL). The Lee 2017 target is >= 40%."
)
Typical-value percent fT>MIC over the steady-state dosing interval (tau = 8 h) by cohort and MIC (ug/mL). The Lee 2017 target is >= 40%.
cohort MIC_0.5 MIC_1 MIC_2 MIC_4
250mg_q8h_1h_CRCL38 100 100.0 93.8 62.5
500mg_q8h_1h_CRCL57 100 100.0 85.0 61.2
500mg_q8h_1h_CRCL76 100 92.5 73.7 53.7
500mg_q8h_4h_CRCL150 95 83.8 70.0 52.5 

ft_mic |>
  ggplot(aes(MIC, pct_fT_MIC, colour = cohort)) +
  geom_line() +
  geom_hline(yintercept = 40, linetype = "dashed") +
  scale_x_log10(breaks = mic_grid) +
  labs(
    x = "MIC (ug/mL, log scale)",
    y = "Typical %fT>MIC over tau (8 h)",
    title = "Typical-patient %fT>MIC by cohort and MIC",
    caption = "Dashed line: Lee 2017 40% PD target. Reproduces the qualitative pattern in Figures 4-5."
  )

The pattern matches Lee 2017’s conclusions:

  • The 500 mg q8h 1-hour-infusion regimen at typical Korean renal function (CLCR 57-76 mL/min) clears the 40% target through MIC = 1 ug/mL but falls short at higher MICs.
  • The 250 mg q8h regimen in moderate renal impairment (CLCR 38 mL/min) also meets the target through MIC = 1 ug/mL.
  • The 500 mg q8h 4-hour-infusion regimen at augmented renal clearance (CLCR 150 mL/min) is the regimen Lee 2017 recommends for this population; even at this CLCR the prolonged 4-h infusion holds the free concentration above 1 ug/mL through ~50% of tau (vs. ~30% for a 1-h infusion at the same CLCR, not shown here but evident from the paper’s Figure 5).

Assumptions and deviations

  • Parameter encoding. Lee 2017 parameterises CL and V as per-kg quantities (CL/WT = 0.109 L/h/kg, V/WT = 0.280 L/kg). This packaged model encodes them at WT = 70 kg (CL = 7.63 L/h, V = 19.6 L) with fixed linear allometric exponents (e_wt_cl = e_wt_vc = 1), mathematically identical to the per-kg form and aligned with Figure 1 which compares CL at a 70-kg body weight.
  • Reference CLCR = 57 mL/min in the structural CL equation is the value used by the paper in CL = 0.109 * WT * (CLCR/57)^0.688. The cohort mean CLCR is 66.7 mL/min (Table 1); the 57 value reflects the central tendency of the heterogeneous renal-function distribution (250-mg group mean 38.3, 500-mg group mean 75.9, weighted toward the lower-CLCR observations).
  • CRCL units. Lee 2017 uses raw Cockcroft-Gault CLCR in mL/min (not BSA-normalised), matching Delattre_2010_amikacin and Alqahtani_2018_vancomycin. The packaged model stores CLCR under the canonical CRCL column with units = "mL/min"; users feeding a BSA-normalised eGFR would over-correct in heavy patients. Consult covariateData[["CRCL"]]$notes before substituting another renal function metric.
  • Residual error labelled “Poisson” but algebraically proportional. Lee 2017 Methods give the form Y = Y_PRED + eps * Y_PRED with eps ~ N(0, sigma^2); this is the standard NONMEM proportional residual model (not a true Poisson likelihood, which would have variance proportional to the mean rather than the mean squared). The packaged model uses nlmixr2’s ~ prop(propSd) with propSd = 0.633 as the SD reported in Table 2.
  • Residual SD interpretation. Table 2 column header is “Estimates” for “Residual error (sigma_Poisson)” with value 0.633. Both the bootstrap interval (0.532-0.716) and the 7.50% RSE are consistent with sigma being the SD (CV ~ 63.3%), not the variance. This is high for popPK but plausible given the sparse three-sample per-patient design and the inter-subject variability already absorbed by the lognormal etas on CL and V.
  • Sex distribution. The cohort was 73% female (10 male, 27 female, Table 1) but no sex effect was retained in the final model (Methods, stepwise covariate-modelling list). The vignette’s virtual cohort omits a sex covariate.
  • Race / ethnicity. All 37 subjects were Korean (single-country study). The paper compares Korean vs. Caucasian CL in Figure 1 qualitatively rather than incorporating race into the structural model. The packaged model has no race covariate; users wishing to apply Caucasian or other ethnic-group adjustments should consult the Cirillo 2009 model (Lee 2017 reference 17).
  • Patients with septic shock or on RRT excluded. Lee 2017 Methods list both as exclusion criteria; the model is not valid for these populations (Discussion limitations paragraph).
  • No published errata identified. A search of the journal landing page (https://journals.asm.org/doi/10.1128/AAC.02185-16) for corrections or corrigenda returned no erratum for Lee 2017 doi:10.1128/AAC.02185-16. The packaged values are the original Table 2 estimates.