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Micafungin in patients with and without cancer (Alqahtani 2021)

Source: vignettes/articles/Alqahtani_2021_micafungin.Rmd
Alqahtani_2021_micafungin.Rmd

Model and source

Alqahtani 2021 fitted a two-compartment model to micafungin plasma concentrations from hospitalised adults with and without cancer and reported a complete parameter set for each group (Table 2). The library ships the two columns of Table 2 as two model files:

  • Alqahtani_2021_micafungin_cancer: patients with cancer (n = 10).
  • Alqahtani_2021_micafungin_noncancer: patients without cancer (n = 9).
mods <- c(
  cancer = "Alqahtani_2021_micafungin_cancer",
  noncancer = "Alqahtani_2021_micafungin_noncancer"
)
uis <- lapply(mods, function(nm) rxode2::rxode(readModelDb(nm)))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Alqahtani S, Alfarhan A, Alsultan A, Alsarhani E, Alsubaie A, Asiri Y. Assessment of Micafungin Dosage Regimens in Patients with Cancer Using Pharmacokinetic/Pharmacodynamic Modeling and Monte Carlo Simulation. Antibiotics (Basel). 2021;10(11):1363. doi:10.3390/antibiotics10111363.
  • Description (cancer): Two-compartment population PK model for IV micafungin in hospitalised adult patients with cancer (Alqahtani 2021, cancer-group parameter set). Linear elimination from the central compartment, log-normal IIV on CL, V1, Q and V2, and a combined additive + proportional residual error. The paper reports that AST, ALT and body weight influenced CL and that BMI, body weight, total bilirubin and albumin influenced V1, but prints no coefficient or functional form for any of them, so this file carries the cancer-group typical values of Table 2 without covariate effects. The companion file Alqahtani_2021_micafungin_noncancer holds the non-cancer group.
  • Description (non-cancer): Two-compartment population PK model for IV micafungin in hospitalised adult patients without cancer (Alqahtani 2021, non-cancer comparator-group parameter set). Linear elimination from the central compartment, log-normal IIV on CL, V1, Q and V2, and a combined additive + proportional residual error. The paper reports that AST, ALT and body weight influenced CL and that BMI, body weight, total bilirubin and albumin influenced V1, but prints no coefficient or functional form for any of them, so this file carries the non-cancer-group typical values of Table 2 without covariate effects. The companion file Alqahtani_2021_micafungin_cancer holds the cancer group.
  • Article: https://doi.org/10.3390/antibiotics10111363 (open access; Supplementary File S1 describes the error and random-effect model forms)

Population

The prospective single-centre study at King Saud University Medical City (Riyadh, Saudi Arabia) enrolled 19 hospitalised adults who received at least two doses of micafungin, empirically or for a confirmed fungal infection: 10 with cancer and 9 without (Alqahtani 2021 Section 3.1, Table 1). Mean age was 47.3 and 51.1 years, mean body weight 63.4 and 69.8 kg, and 40% and 33% were female in the cancer and non-cancer groups respectively. Mean SOFA scores were 7 and 8; AST, ALT, albumin, bilirubin and creatinine clearance did not differ significantly between the groups. All cancer patients received 100 mg/day; seven non-cancer patients received 100 mg/day and two received 150 mg/day, as 60-min IV infusions. Seven samples were drawn per patient at 1, 2, 4, 6, 8, 12 and 24 h after the start of the infusion (133 samples).

str(uis$cancer$population[c("n_subjects", "age_range", "weight_range", "sex_female_pct", "dose_range")])
#> List of 5
#>  $ n_subjects    : int 10
#>  $ age_range     : chr "mean 47.3 years (SD 12.3); adults >= 18 years"
#>  $ weight_range  : chr "mean 63.4 kg (SD 18.2)"
#>  $ sex_female_pct: num 40
#>  $ dose_range    : chr "100 mg micafungin once daily as a 60-min IV infusion (all 10 cancer patients); at least two doses before sampling."
str(uis$noncancer$population[c("n_subjects", "age_range", "weight_range", "sex_female_pct", "dose_range")])
#> List of 5
#>  $ n_subjects    : int 9
#>  $ age_range     : chr "mean 51.1 years (SD 19.1); adults >= 18 years"
#>  $ weight_range  : chr "mean 69.8 kg (SD 15.7)"
#>  $ sex_female_pct: num 33
#>  $ dose_range    : chr "100 mg (7 patients) or 150 mg (2 patients) micafungin once daily as a 60-min IV infusion; at least two doses before sampling."

Source trace

Equation / parameter Cancer Non-cancer Source location
Two-compartment model, linear elimination from central – – Section 3.2
lcl (CL, L/h) log(1.2) log(0.6) Table 2
lvc (V1, L) log(10.7) log(12) Table 2
lq (Q, L/h) log(0.144) log(0.188) Table 2
lvp (V2, L) log(3.5) log(2.77) Table 2
etalcl (IIV CL) 34.1% CV 11.8% CV Table 2; log-normal per Supplementary File S1
etalvc (IIV V1) 7.6% CV 7.6% CV Table 2
etalq (IIV Q) 32.2% CV 20.4% CV Table 2
etalvp (IIV V2) 36.8% CV 32.1% CV Table 2
addSd (residual a, mg/L) 0.21 0.15 Table 2
propSd (residual b) 0.22 0.18 Table 2
Cobs = Cpred (1 + eps_prop) + eps_const (combined2) – – Supplementary File S1
60-min infusion of 100-150 mg/day – – Section 2.2

The IIV rows are coefficients of variation (Table 2 footnote), converted to log-normal variances as omega^2 = log(1 + CV^2).

Typical-value profiles 

ev_typ <- rxode2::et(amt = 100, dur = 1, ii = 24, addl = 13, cmt = "central") |>
  rxode2::et(seq(0, 336, by = 0.25), cmt = "central")

typ <- bind_rows(lapply(names(mods), function(g) {
  s <- rxode2::rxSolve(rxode2::zeroRe(uis[[g]]), ev_typ, returnType = "data.frame")
  s$group <- g
  s
}))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp'

ggplot(typ, aes(time / 24, Cc, colour = group)) +
  geom_line() +
  labs(
    x = "Time (days)", y = "Micafungin concentration (mg/L)", colour = NULL,
    title = "Typical-value profiles, 100 mg once daily (60-min infusion)"
  ) +
  theme_bw()

With these parameters the terminal half-life is about 6 h in the cancer group and about 14 h in the non-cancer group; nearly all of the difference comes from CL (1.2 vs 0.6 L/h), which is the only parameter Table 2 reports as differing significantly between the groups.

Stochastic simulation and PKNCA

200 virtual patients per group receive 100 mg once daily for 14 days. The last dosing interval (312-336 h) is sampled densely for NCA.

n_per_arm <- 200
obs_t <- c(seq(0, 312, by = 24), 312 + c(0.25, 0.5, 0.75, 1, 1.25, 1.5, 2, 3, 4, 6, 8, 10, 12, 16, 20, 24))
ev_sim <- rxode2::et(amt = 100, dur = 1, ii = 24, addl = 13, cmt = "central") |>
  rxode2::et(obs_t, cmt = "central") |>
  rxode2::et(id = seq_len(n_per_arm))

rxode2::rxSetSeed(20211108)
sim <- bind_rows(lapply(names(mods), function(g) {
  s <- rxode2::rxSolve(uis[[g]], ev_sim,
    returnType = "data.frame",
    rtol = 1e-10, atol = 1e-12
  )
  s$group <- g
  s
})) |>
  mutate(id = paste(group, id, sep = "-"))
stopifnot(nrow(sim) > 0, !anyNA(sim$Cc))
last_int <- sim |>
  filter(time >= 312) |>
  mutate(tad = time - 312) |>
  group_by(group, tad) |>
  summarise(
    q05 = quantile(ipredSim, 0.05), q50 = median(ipredSim), q95 = quantile(ipredSim, 0.95),
    .groups = "drop"
  )
ggplot(last_int, aes(tad, q50, colour = group, fill = group)) +
  geom_ribbon(aes(ymin = q05, ymax = q95), alpha = 0.2, colour = NA) +
  geom_line() +
  labs(x = "Time after start of infusion (h)", y = "Micafungin concentration (mg/L)", colour = NULL, fill = NULL) +
  theme_bw()
Simulated steady-state dosing interval (day 14), median and 5th-95th percentiles of the typical-plus-IIV concentration. Compare with the pooled prediction-corrected VPC of Alqahtani 2021 Figure 2.

Simulated steady-state dosing interval (day 14), median and 5th-95th percentiles of the typical-plus-IIV concentration. Compare with the pooled prediction-corrected VPC of Alqahtani 2021 Figure 2.

PKNCA computes the steady-state AUC over the last interval, per subject and grouped by population.

conc_nca <- sim |>
  filter(!is.na(Cc), time >= 312) |>
  mutate(tad = time - 312, Cc = pmax(ipredSim, 0)) |>
  select(id, group, tad, Cc)
dose_nca <- conc_nca |>
  distinct(id, group) |>
  mutate(tad = 0, amt = 100)

conc_obj <- PKNCA::PKNCAconc(conc_nca, Cc ~ tad | group + id)
dose_obj <- PKNCA::PKNCAdose(dose_nca, amt ~ tad | group + id)
intervals <- data.frame(start = 0, end = 24, auclast = TRUE, cmax = TRUE, tmax = TRUE, cmin = TRUE)
nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
nca_wide <- as.data.frame(nca$result) |>
  select(group, id, PPTESTCD, PPORRES) |>
  pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

nca_wide |>
  group_by(group) |>
  summarise(
    across(c(cmax, cmin, auclast), ~ signif(median(.x), 3)),
    tmax = median(tmax)
  ) |>
  rename(
    "Group" = group, "Cmax,ss (mg/L)" = cmax, "Cmin,ss (mg/L)" = cmin,
    "AUC0-24,ss (mg*h/L)" = auclast, "Tmax (h)" = tmax
  ) |>
  knitr::kable(caption = "Simulated median steady-state NCA, 100 mg once daily.")
Simulated median steady-state NCA, 100 mg once daily.
Group Cmax,ss (mg/L) Cmin,ss (mg/L) AUC0-24,ss (mg*h/L) Tmax (h)
cancer 9.63 0.888 84.6 1
noncancer 11.90 3.920 168.0 1

The paper reports no NCA table, so there is no published row to place beside these values. At steady state AUC0-24 = Dose / CL for each simulated subject; checking it against each subject’s own drawn cl tests dose, infusion, unit and volume handling together.

cl_i <- sim |>
  group_by(id) |>
  summarise(cl = first(cl), .groups = "drop")
chk <- nca_wide |>
  left_join(cl_i, by = "id") |>
  mutate(pct_diff = 100 * (auclast * cl / 100 - 1))
stopifnot(nrow(chk) == 2 * n_per_arm, !anyNA(chk$pct_diff))
chk |>
  group_by(group) |>
  summarise(median_pct = median(pct_diff), p90_abs_pct = quantile(abs(pct_diff), 0.9)) |>
  knitr::kable(digits = 3, caption = "Per-subject AUC0-24,ss x CL / Dose - 1 (%).")
Per-subject AUC0-24,ss x CL / Dose - 1 (%).
group median_pct p90_abs_pct
cancer 0.072 0.125
noncancer 0.033 0.049 
# The residual is trapezoid error across the infusion peak plus any subject not
# fully at steady state after 13 doses; a mis-scaled dose, volume or CL moves
# the whole distribution by tens of percent.
stopifnot(
  abs(median(chk$pct_diff)) < 1,
  quantile(abs(chk$pct_diff), 0.9) < 2
)

Probability of target attainment

The paper’s targets are total-plasma AUC0-24/MIC of 3000 for non-parapsilosis Candida spp. and 285 for C. parapsilosis (Section 2.7). With linear PK the steady-state AUC is Dose / CL_i and CL_i is log-normal, so the PTA is deterministic:

PTA = Phi( (log(Dose / (target * MIC)) - log(CL_pop)) / omega_CL ).

mics <- c(0.002, 0.004, 0.008, 0.016, 0.032, 0.064, 0.125, 0.25, 0.5, 1, 2, 4)
pta_analytic <- function(ui, dose, target, mic) {
  th <- ui$theta
  om <- sqrt(ui$omega["etalcl", "etalcl"])
  100 * stats::pnorm((log(dose / (target * mic)) - th[["lcl"]]) / om)
}
pta <- expand.grid(
  group = names(mods), dose = c(100, 150, 200), mic = mics,
  organism = c("Candida spp.", "C. parapsilosis"), stringsAsFactors = FALSE
) |>
  mutate(
    target = ifelse(organism == "Candida spp.", 3000, 285),
    pta = mapply(function(g, d, t, m) pta_analytic(uis[[g]], d, t, m), group, dose, target, mic)
  )

ggplot(pta, aes(factor(mic), pta,
  colour = group, linetype = factor(dose),
  group = interaction(group, dose)
)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 90, linetype = "dotted") +
  facet_wrap(~organism, ncol = 1) +
  labs(
    x = "MIC (mg/L)", y = "PTA (%)", colour = NULL, linetype = "Dose (mg/day)",
    title = "Analytic steady-state PTA (compare Alqahtani 2021 Figures 3 and 4)"
  ) +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

The simulated cohort gives the same PTA as the closed form, which checks the formula against the model rather than against itself.

pta_cell <- function(g, d, org, m) {
  v <- pta$pta[pta$group == g & pta$dose == d & pta$organism == org & pta$mic == m]
  if (length(v) != 1L) stop("no unique PTA cell for ", g, " ", d, " ", org, " ", m)
  v
}
sim_pta <- 100 * mean(chk$auclast[chk$group == "cancer"] / 0.032 >= 3000)
ana_pta <- pta_cell("cancer", 100, "Candida spp.", 0.032)
c(simulated = sim_pta, analytic = ana_pta)
#>       simulated analytic.cancer 
#>        31.50000        33.48218
# Binomial SE at n = 200 and p = 0.33 is 3.3 points; 12 is > 3 SE.
stopifnot(abs(sim_pta - ana_pta) < 12)

Comparison with the published anchors

The Discussion states that 100 mg/day in patients with cancer achieved an approximate PTA of 30% at an MIC of 0.032 mg/L for non-parapsilosis Candida spp.; Figure 4 shows 95% at 0.016 mg/L for the same arm.

anchor <- data.frame(
  Claim = c("Cancer, 100 mg, Candida spp., MIC 0.032", "Cancer, 100 mg, Candida spp., MIC 0.016"),
  Published = c(30, 95),
  Model = c(pta_cell("cancer", 100, "Candida spp.", 0.032), pta_cell("cancer", 100, "Candida spp.", 0.016))
)
knitr::kable(anchor, digits = 1, caption = "PTA (%): Discussion / Figure 4 vs the packaged cancer model.")
PTA (%): Discussion / Figure 4 vs the packaged cancer model.
Claim Published Model
Cancer, 100 mg, Candida spp., MIC 0.032 30 33.5
Cancer, 100 mg, Candida spp., MIC 0.016 95 95.2 
stopifnot(abs(anchor$Model - anchor$Published) < 6)

Table 3 reports, for each dose and a 70 kg patient, the highest MIC with a PTA of at least 90%. The packaged files carry no body-weight effect (see Assumptions), so the model breakpoint is compared with the 70 kg rows.

bp <- pta |>
  group_by(group, dose, organism) |>
  summarise(model_bp = max(c(0, mic[pta >= 90])), .groups = "drop")
table3_70kg <- tribble(
  ~group, ~dose, ~organism, ~published_bp,
  "cancer", 100, "Candida spp.", 0.016,
  "cancer", 100, "C. parapsilosis", 0.125,
  "cancer", 150, "Candida spp.", 0.032,
  "cancer", 150, "C. parapsilosis", 0.25,
  "cancer", 200, "Candida spp.", 0.032,
  "cancer", 200, "C. parapsilosis", 0.25,
  "noncancer", 100, "Candida spp.", 0.032,
  "noncancer", 100, "C. parapsilosis", 0.25,
  "noncancer", 150, "Candida spp.", 0.032,
  "noncancer", 150, "C. parapsilosis", 0.25,
  "noncancer", 200, "Candida spp.", 0.032,
  "noncancer", 200, "C. parapsilosis", 0.5
)
bp_cmp <- table3_70kg |>
  left_join(bp, by = c("group", "dose", "organism")) |>
  mutate(match = model_bp == published_bp)
stopifnot(nrow(bp_cmp) == 12, !anyNA(bp_cmp$model_bp))
bp_cmp |>
  rename(
    "Group" = group, "Dose (mg/day)" = dose, "Organism" = organism,
    "Table 3, 70 kg (mg/L)" = published_bp, "Model (mg/L)" = model_bp, "Match" = match
  ) |>
  knitr::kable(caption = "90% PTA breakpoints: Alqahtani 2021 Table 3 (70 kg) vs the packaged models.")
90% PTA breakpoints: Alqahtani 2021 Table 3 (70 kg) vs the packaged models.
Group Dose (mg/day) Organism Table 3, 70 kg (mg/L) Model (mg/L) Match
cancer 100 Candida spp. 0.016 0.016 TRUE
cancer 100 C. parapsilosis 0.125 0.125 TRUE
cancer 150 Candida spp. 0.032 0.016 FALSE
cancer 150 C. parapsilosis 0.250 0.250 TRUE
cancer 200 Candida spp. 0.032 0.032 TRUE
cancer 200 C. parapsilosis 0.250 0.250 TRUE
noncancer 100 Candida spp. 0.032 0.032 TRUE
noncancer 100 C. parapsilosis 0.250 0.500 FALSE
noncancer 150 Candida spp. 0.032 0.064 FALSE
noncancer 150 C. parapsilosis 0.250 0.500 FALSE
noncancer 200 Candida spp. 0.032 0.064 FALSE
noncancer 200 C. parapsilosis 0.500 1.000 FALSE 

# Deterministic: the cancer model reproduces 5 of 6 cells; the non-cancer
# model 1 of 6 (see the discussion below). A changed CL, IIV or target moves
# these counts.
stopifnot(
  sum(bp_cmp$match[bp_cmp$group == "cancer"]) == 5,
  sum(bp_cmp$match[bp_cmp$group == "noncancer"]) == 1
)

The cancer model reproduces the published breakpoints except at 150 mg for Candida spp. (model 78.7% PTA at 0.032 mg/L; Figure 4 shows 92%). The non-cancer model is consistently one doubling dilution more optimistic than Table 3. Its Table 2 IIV on CL is only 11.8% CV, so the model’s PTA curve drops steeply around the MIC at which Dose / (0.6 L/h) crosses the target; the published non-cancer curves in Figures 3 and 4 are much flatter (for example 60% and 65% at 0.064 mg/L for 100 and 150 mg), which implies considerably more between-subject spread in AUC than the printed CL IIV alone. The likeliest source is the retained covariate model (body weight, AST and ALT on CL), whose coefficients and reference values are not printed and are therefore not in the packaged files. The published figures are also not fully consistent with each other: fitting a log-normal AUC distribution to Figure 4’s cancer 100 mg points gives a median CL near 1.2 L/h, while Figure 3’s cancer 100 mg points give a median CL near 1.0 L/h, and the cancer 150 and 200 mg curves in Figure 4 are closer together than linear PK allows. No parameter was adjusted to close these gaps.

Assumptions and deviations

  • Covariate effects not encoded. The paper states that AST, ALT and body weight significantly influenced CL, and that BMI, body weight, total bilirubin and albumin affected V1 (Section 3.2), and Table 3 varies body weight (50/70/100 kg). No coefficient, functional form, or reference value for any of these effects is printed in the article or in Supplementary File S1, which gives only the generic CL_j = CL_pop x exp(eta_j) form. The packaged files therefore carry the Table 2 typical values without covariate effects; the covariates are recorded under covariatesDataExcluded in each file. The covariate reference values to which the Table 2 typical values correspond are also not stated.
  • Two files for one analysis. The Methods say the two groups were co-modelled, but Table 2 prints a separate estimate and RSE for every fixed effect, IIV and residual-error term in each group. Group-specific IIV and residual error cannot be expressed through a single covariate-switched model, so each column of Table 2 is a separate file.
  • IIV scale. Table 2 gives IIV as a coefficient of variation; the variance is log(1 + CV^2).
  • Residual error. Supplementary File S1 writes Cobs = Cpred (1 + eps_prop) + eps_const with independent proportional and constant errors, i.e. the combined2 form. Table 2 a is taken as the additive SD in mg/L and b as the proportional SD.
  • PTA timing. The paper does not say on which day AUC0-24 was evaluated. The steady-state AUC is used here; it reproduces the Discussion’s 30% anchor. Residual error is not included in the PTA.
  • Units in Table 1. Table 1 prints serum creatinine in mmol/L (means of 74.7 and 63.6), which is only plausible as umol/L, and gives no units for albumin, AST, ALT or bilirubin; the population metadata reproduces the values as printed.