Skip to contents

Tenofovir / emtricitabine PKPD with dNTP pool (Chen 2016)

Source: vignettes/articles/Chen_2016_tenofovir_emtricitabine.Rmd
Chen_2016_tenofovir_emtricitabine.Rmd
library(nlmixr2lib)
library(rxode2)
#> rxode2 5.1.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter

Chen 2016 linked plasma + intracellular + dNTP-pool PKPD model

Chen et al. (2016, PLOS ONE) developed a linked population pharmaco- kinetic / pharmacodynamic model for the nucleoside-analog antiretrovirals tenofovir (TFV, given as the prodrug tenofovir disoproxil fumarate, TDF) and emtricitabine (FTC). The model describes:

  • TFV and FTC plasma PK with classical two-compartment first-order absorption models;
  • intracellular formation of the active anabolites tenofovir diphosphate (TFV-DP) and emtricitabine triphosphate (FTC-TP) via a hybrid first-order + saturation link from the corresponding plasma parent, with a two-compartment “recycle” elimination structure for the anabolites;
  • inhibition of the zero-order production of four endogenous deoxynucleoside triphosphates – dATP, dGTP, dCTP, and TTP – via Emax indirect-response models. TFV-DP inhibits the deoxypurines (dATP, dGTP) and FTC-TP inhibits the deoxypyrimidines (dCTP, TTP). The dGTP response includes an additional 1/(1 + t^gamma) time-waning factor.

The model was fit to first-dose-to-steady-state data from 40 adults receiving daily co-formulated TDF/FTC for 30 (HIV-negative) or 60 (HIV-positive) days, with peripheral blood mononuclear cell (PBMC) samples drawn at densely-spaced time points on days 1, 3, 7, 20, and 30, plus single washout samples at days 35, 45, and 60.

The packaged model Chen_2016_tenofovir_emtricitabine combines all eight observation variables (plasma TFV, plasma FTC, intracellular TFV-DP, intracellular FTC-TP, and the four dNTPs) in a single linked-PKPD function so that downstream simulations – in particular the analog:dNTP molar-ratio simulations used in the paper’s IPERGAY on-demand PrEP application – have access to every state directly.

  • Citation: Chen X, Seifert SM, Castillo-Mancilla JR, Bushman LR, Zheng J-H, Kiser JJ, MaWhinney S, Anderson PL. Model Linking Plasma and Intracellular Tenofovir/Emtricitabine with Deoxynucleoside Triphosphates. PLoS ONE. 2016;11(11):e0165505. doi:10.1371/journal.pone.0165505
  • Article: https://doi.org/10.1371/journal.pone.0165505
  • Supplement (S1 File: differential equations, NONMEM code; S2 File: study protocol): bundled with the open-access PLOS ONE article at the same DOI.

Population

Per Chen 2016 Results “Study demographics” (page 6): 21 HIV-negative adults and 19 HIV-positive adults were enrolled at the University of Colorado Anschutz Medical Campus (Cell-PrEP study; NCT01040091). The cohort had median (range) age 31 (20-52) years, weight 81.1 (56.5-127) kg, body-mass index 26.6 (19.9-37.7) kg/m^2, and estimated GFR 93.3 (66.0-131) mL/min/1.73m^2. Of the 40 subjects, 13 were female (32.5%); race / ethnicity was 47.5% White, 40% Black or African American, and 12.5% Hispanic. HIV-negative subjects received daily oral TDF 300 mg (equivalent to TFV 136 mg) + FTC 200 mg for 30 days with washout samples at days 35, 45, and 60. HIV-positive subjects received the same TDF/FTC regimen + efavirenz 600 mg PO QD for 60 days. 34 of 40 subjects completed all visits.

The same metadata is available programmatically:

readModelDb("Chen_2016_tenofovir_emtricitabine")$meta$population

Source trace

Per-parameter origins are recorded as in-file comments in inst/modeldb/specificDrugs/Chen_2016_tenofovir_emtricitabine.R; the table below collects them.

Equation / parameter Value Source location
TFV plasma 2-cmt ODEs (depot, central, peripheral1) n/a S1 File Eqs A-C; Methods “Population pharmacokinetics modeling of plasma TFV/FTC”
TFV Ka 80.1 /day Table 1A
TFV CL/F 1410 L/day Table 1A
TFV Vc/F 390 L Table 1A
TFV Q/F 5390 L/day Table 1A
TFV Vp/F 877 L Table 1A
FTC plasma 2-cmt ODEs (depot_ftc, central_ftc, peripheral1_ftc) n/a S1 File Eqs A-C
FTC Ka 55.7 /day Table 1B
FTC CL/F 482 L/day Table 1B
FTC Vc/F 99.4 L (female reference) Table 1B
FTC Q/F 141 L/day Table 1B
FTC Vp/F 166 L Table 1B
Sex on FTC Vc/F tvVc/F = 99.4 + 24.3 * SEX (male = 1, female = 0) Table 1B; Results “Population pharmacokinetics modeling of plasma TFV/FTC”
Hybrid first-order + saturation link for TFV-DP / FTC-TP formation n/a Eqs 1-3; Methods “Population pharmacokinetics modeling of TFV-DP/FTC-TP”
TFV-DP Kf 1.4 /day Table 1A
TFV-DP SC50 6.55 (ng/mL of plasma TFV) Table 1A
TFV-DP Kel 0.228 /day Table 1A
TFV-DP recycle ratio R 5.82% Table 1A
FTC-TP Kf 41.6 /day (HIV-negative reference) Table 1B
FTC-TP SC50 3320 (ng/mL of plasma FTC) Table 1B
FTC-TP Kel 1.6 /day Table 1B
FTC-TP recycle ratio R 16.0% Table 1B
HIV on FTC-TP Kf tvKf = 41.6 + 31.3 * HIV (positive = 1) Table 1B
Indirect-response Emax dNTP model with Kout = 1/day fixed, Emax = 1 fixed n/a Eq 4; Methods “Population pharmacodynamics modeling of dATP/dGTP and dCTP/TTP”
dATP R0 155 fmol/10^6 PBMC Table 1A
dATP EC50 (TFV-DP) 1020 fmol/10^6 PBMC Table 1A
dGTP R0 245 fmol/10^6 PBMC Table 1A
dGTP EC50 (TFV-DP) 54.6 fmol/10^6 PBMC Table 1A
dGTP time-waning gamma 0.928 (unitless; effect attenuated by 1/(1 + t^gamma)) Table 1A; S1 File Eq D
dCTP R0 771 fmol/10^6 PBMC Table 1B
dCTP EC50 (FTC-TP) 44400 fmol/10^6 PBMC Table 1B
TTP R0 335 fmol/10^6 PBMC Table 1B
TTP EC50 (FTC-TP) 18800 fmol/10^6 PBMC Table 1B
dATP baseline estimation: method 3 (weighted population + observed individual baseline) n/a Eq 5; Methods; Dansirikul et al. ref [45]
TFV plasma terminal half-life 17.3 h (95% CI 15.7-19.1) Results “Population pharmacokinetics modeling of plasma TFV/FTC”
FTC plasma terminal half-life 26.8 h (95% CI 25.6-28.1) Results
TFV-DP alpha / beta half-lives 73.4 h / 55.6 days Results
FTC-TP alpha / beta half-lives 8.8 h / 76.8 h Results
Operational multi-dose half-life t1/2,op TFV-DP 6.7 days; FTC-TP 33 h Results; Discussion
Dosing regimen used in the trial TDF 300 mg + FTC 200 mg PO QD x 30 (HIV-) or 60 (HIV+) days Methods “Study design”

Covariate column naming

Source column Canonical column
SEX (male = 1, female = 0; FTC Vc/F covariate) SEXF (canonical; female = 1). Values inverted: SEXF = 1 - source_SEX. The model applies the additive +24.3 L shift via (1 - SEXF) so males get the +24.3 L bump and females stay at 99.4 L.
HIV (positive = 1, negative = 0; FTC-TP Kf covariate) HIV_POS (canonical; same orientation, positive = 1). No transformation.

Virtual cohort

The virtual cohort below approximates the trial demographics from Chen 2016 Results “Study demographics” page 6. Body weight is sampled log-normal around the reported median (81.1 kg). Sex is sampled as Bernoulli(0.325) for SEXF = 1 to match the 13/40 female fraction. HIV serostatus is sampled as Bernoulli(0.475) for HIV_POS = 1 (19/40 HIV-positive). The cohort is sized at 200 subjects to make per-time- point quantiles smooth without inflating the runtime.

set.seed(2016)
n_subj <- 200L

cohort <- tibble(
  ID      = seq_len(n_subj),
  WT      = pmin(pmax(rlnorm(n_subj, log(81.1), 0.18), 50), 130),
  SEXF    = as.integer(rbinom(n_subj, 1, 0.325)),
  HIV_POS = as.integer(rbinom(n_subj, 1, 0.475))
)
summary(cohort)
#>        ID               WT              SEXF          HIV_POS     
#>  Min.   :  1.00   Min.   : 50.00   Min.   :0.000   Min.   :0.000  
#>  1st Qu.: 50.75   1st Qu.: 71.66   1st Qu.:0.000   1st Qu.:0.000  
#>  Median :100.50   Median : 80.93   Median :0.000   Median :1.000  
#>  Mean   :100.50   Mean   : 82.79   Mean   :0.335   Mean   :0.525  
#>  3rd Qu.:150.25   3rd Qu.: 91.96   3rd Qu.:1.000   3rd Qu.:1.000  
#>  Max.   :200.00   Max.   :130.00   Max.   :1.000   Max.   :1.000

Dosing dataset

The trial’s daily oral TDF 300 mg / FTC 200 mg regimen is encoded as two separate dose events per day: one into the depot compartment (TFV 136 mg, the prodrug-equivalent amount of TFV per TDF tablet) and one into the depot_ftc compartment (FTC 200 mg). Both compartments must be dosed simultaneously to drive the linked PKPD model. The simulation horizon spans 30 days of daily dosing followed by a 30-day washout (matching the HIV-negative arm of the Cell-PrEP study).

dose_times <- seq(0, 29)               # daily dosing on days 0..29
obs_times  <- sort(unique(c(
  seq(0, 1,  by = 0.05),               # densely sampled across day 1
  seq(1, 7,  by = 0.25),               # quarter-day through day 7
  seq(7, 30, by = 0.5),                # half-day through day 30
  seq(30, 60, by = 1)                  # daily washout
)))

# Two dose events per administration (one to depot, one to depot_ftc).
# Observation rows use cmt = "Cc" -- rxSolve returns every defined
# output variable for each observation row regardless of which output
# name is in cmt, but specifying an existing output keeps the event
# table valid.
make_events <- function(pop_df, dose_times, obs_times) {
  dose_tfv <- pop_df %>%
    crossing(TIME = dose_times) %>%
    mutate(AMT = 136,          # mg TFV equivalent per TDF 300 mg tablet
           EVID = 1L, CMT = "depot",     DV = NA_real_)
  dose_ftc <- pop_df %>%
    crossing(TIME = dose_times) %>%
    mutate(AMT = 200,          # mg FTC per tablet
           EVID = 1L, CMT = "depot_ftc", DV = NA_real_)
  obs <- pop_df %>%
    crossing(TIME = obs_times) %>%
    mutate(AMT = NA_real_, EVID = 0L, CMT = "Cc", DV = NA_real_)
  bind_rows(dose_tfv, dose_ftc, obs) %>%
    arrange(ID, TIME, desc(EVID)) %>%
    as.data.frame()
}

events <- make_events(cohort, dose_times, obs_times)
stopifnot(!anyDuplicated(unique(events[, c("ID", "TIME", "EVID", "CMT")])))

Simulate the trial-like 30-day regimen + 30-day washout 

mod <- readModelDb("Chen_2016_tenofovir_emtricitabine")
sim <- rxSolve(mod, events, returnType = "data.frame",
               keep = c("WT", "SEXF", "HIV_POS"))
#> ℹ parameter labels from comments will be replaced by 'label()'

The output sim has columns for Cc (TFV plasma, ng/mL), Cc_ftc (FTC plasma, ng/mL), Cc_tfvdp (intracellular TFV-DP, fmol per 10^6 PBMC), Cc_ftctp (intracellular FTC-TP, fmol per 10^6 PBMC), plus the four dNTP state values datp, dgtp, dctp, ttp (fmol per 10^6 PBMC). The model performs the internal mg/L -> ng/mL conversion so that Cc and Cc_ftc match the paper’s native ng/mL plasma units directly.

Plasma TFV and FTC concentration-time profiles

Replicates the shape of Chen 2016 Figure 3A and 3B upper-left panels (plasma TFV and plasma FTC visual predictive checks across day 1 and days 30-60, including the washout).

plasma_long <- sim %>%
  transmute(id, time, WT, SEXF, HIV_POS,
            `TFV plasma`  = Cc,
            `FTC plasma`  = Cc_ftc) %>%
  pivot_longer(c(`TFV plasma`, `FTC plasma`),
               names_to = "analyte", values_to = "conc_ngmL")

plasma_summary <- plasma_long %>%
  filter(time > 0, !is.na(conc_ngmL)) %>%
  group_by(analyte, time) %>%
  summarise(
    median = median(conc_ngmL, na.rm = TRUE),
    lo     = quantile(conc_ngmL, 0.05, na.rm = TRUE),
    hi     = quantile(conc_ngmL, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(plasma_summary, aes(time, median, colour = analyte, fill = analyte)) +
  geom_ribbon(aes(ymin = pmax(lo, 1e-3), ymax = hi),
              alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.9) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Concentration (ng/mL)",
       title = "TFV and FTC plasma PK -- 30-day daily TDF/FTC + 30-day washout",
       subtitle = "Median and 90% prediction interval (N = 200 virtual subjects)",
       caption = "Replicates the shape of Chen 2016 Figure 3A/3B upper-left panels.") +
  theme_bw()

Intracellular TFV-DP and FTC-TP

Replicates the shape of Chen 2016 Figure 3A and 3B upper-right panels. Concentrations are in fmol per 10^6 PBMC.

ic_long <- sim %>%
  transmute(id, time,
            `TFV-DP IC` = Cc_tfvdp,
            `FTC-TP IC` = Cc_ftctp) %>%
  pivot_longer(c(`TFV-DP IC`, `FTC-TP IC`),
               names_to = "analyte", values_to = "conc_fmol")

ic_summary <- ic_long %>%
  filter(time > 0) %>%
  group_by(analyte, time) %>%
  summarise(
    median = median(conc_fmol, na.rm = TRUE),
    lo     = quantile(conc_fmol, 0.05, na.rm = TRUE),
    hi     = quantile(conc_fmol, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(ic_summary, aes(time, median, colour = analyte, fill = analyte)) +
  geom_ribbon(aes(ymin = pmax(lo, 1e-3), ymax = hi),
              alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.9) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Concentration (fmol per 10^6 PBMC)",
       title = "Intracellular TFV-DP and FTC-TP",
       subtitle = "Median and 90% prediction interval (N = 200)",
       caption = "Replicates the shape of Chen 2016 Figure 3A/3B upper-right panels.") +
  theme_bw()

dNTP pool changes during treatment

Replicates the shape of Chen 2016 Figure 3A and 3B lower panels (the indirect-response time courses of dATP, dGTP, dCTP, TTP across the 30-day treatment and 30-day washout). The paper reports model-predicted median (5%, 95% percentile) reductions of 11% (0.45%, 53%) in dATP, 14% (2.6%, 35%) in dCTP, 24% (4.5%, 62%) in TTP, and a transient 13% (6.9%, 21%) dGTP nadir around day 2.5 followed by return to baseline.

dntp_long <- sim %>%
  transmute(id, time,
            dATP = datp,
            dGTP = dgtp,
            dCTP = dctp,
            TTP  = ttp) %>%
  pivot_longer(c(dATP, dGTP, dCTP, TTP),
               names_to = "analyte", values_to = "conc_fmol")

dntp_summary <- dntp_long %>%
  filter(time > 0) %>%
  group_by(analyte, time) %>%
  summarise(
    median = median(conc_fmol, na.rm = TRUE),
    lo     = quantile(conc_fmol, 0.05, na.rm = TRUE),
    hi     = quantile(conc_fmol, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(dntp_summary, aes(time, median, colour = analyte, fill = analyte)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.15, colour = NA) +
  geom_line(linewidth = 0.9) +
  facet_wrap(~ analyte, scales = "free_y") +
  labs(x = "Time (days)", y = "Concentration (fmol per 10^6 PBMC)",
       title = "Endogenous dNTP responses to 30-day TDF/FTC + 30-day washout",
       subtitle = "Median and 90% prediction interval (N = 200)",
       caption = "Replicates the shape of Chen 2016 Figure 3A/3B lower panels.") +
  theme_bw() +
  theme(legend.position = "none")

Typical-subject reproduction of published values

Simulate a typical HIV-negative female subject (the paper’s reference covariate combination for FTC Vc/F and for the TFV plasma model) with between-subject variability zeroed. Compare the simulated steady-state concentrations to those expected from the published parameters.

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

typ <- tibble(ID = 1L, WT = 81.1, SEXF = 1L, HIV_POS = 0L)

# Steady-state run: 60 days of daily dosing to make sure TFV-DP / FTC-TP
# reach their pseudo-steady-state plateaus.
typ_dose_times <- seq(0, 59)
typ_events <- make_events(typ, typ_dose_times, sort(unique(c(
  seq(0, 1, by = 0.05),
  seq(1, 7, by = 0.5),
  seq(7, 60, by = 1)
))))

sim_typ <- rxSolve(mod_typ, typ_events, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalq', 'etalvc_ftc', 'etalcl_ftc', 'etalvp_ftc', 'etalkf_tfvdp', 'etalkel_tfvdp', 'etalkf_ftctp', 'etalkel_ftctp', 'etalr0_datp', 'etalec50_datp', 'etalr0_dgtp', 'etalr0_dctp', 'etalec50_dctp', 'etalr0_ttp', 'etalec50_ttp'

ss <- sim_typ %>%
  filter(time >= 30) %>%       # treat day 30+ as pseudo-steady-state
  summarise(
    TFV_Cmax_ngmL   = max(Cc,     na.rm = TRUE),
    FTC_Cmax_ngmL   = max(Cc_ftc, na.rm = TRUE),
    TFVDP_ss_median = median(Cc_tfvdp[time >= 50], na.rm = TRUE),
    FTCTP_ss_median = median(Cc_ftctp[time >= 50], na.rm = TRUE),
    dATP_nadir      = min(datp, na.rm = TRUE),
    dCTP_nadir      = min(dctp, na.rm = TRUE)
  )

knitr::kable(ss, digits = 2,
             caption = "Typical 81.1 kg HIV-negative female subject -- steady-state extracts (concentrations in ng/mL for plasma, fmol per 10^6 PBMC for intracellular).")
Typical 81.1 kg HIV-negative female subject – steady-state extracts (concentrations in ng/mL for plasma, fmol per 10^6 PBMC for intracellular).
TFV_Cmax_ngmL FTC_Cmax_ngmL TFVDP_ss_median FTCTP_ss_median dATP_nadir dCTP_nadir
50.4 87.25 88.48 4295.98 142.39 684.99

Plasma PKNCA for the first-dose interval

Run PKNCA on the simulated day-1 plasma TFV and plasma FTC profiles (0-24 h after the first dose). The paper does not publish first-dose NCA values directly, but the alpha / terminal half-lives in Table 1A / 1B can be cross-checked against PKNCA’s half.life estimate over the appropriate window. Sampling here uses the full 24-hour first-dose interval.

# Single observation grid for the first 24 h
day1_obs_times <- c(0.05, 0.1, 0.25, 0.5, 1, 2, 4, 6, 8, 12, 18, 24) / 24

day1_events <- make_events(cohort, dose_times = 0, obs_times = day1_obs_times)
sim_day1 <- rxSolve(mod, day1_events, returnType = "data.frame",
                    keep = c("WT", "SEXF", "HIV_POS"))
#> ℹ parameter labels from comments will be replaced by 'label()'

# TFV plasma NCA
nca_tfv <- sim_day1 %>%
  filter(time > 0, Cc > 0) %>%
  transmute(ID = id, time_h = time * 24, conc_ngmL = Cc,
            cohort = "HIV_pop")

conc_obj_tfv <- PKNCAconc(nca_tfv,
                          conc_ngmL ~ time_h | cohort + ID,
                          concu = "ng/mL", timeu = "h")
dose_obj_tfv <- PKNCAdose(
  cohort %>% mutate(time_h = 0, AMT_TFV_mg = 136, cohort = "HIV_pop"),
  AMT_TFV_mg ~ time_h | cohort + ID,
  doseu = "mg"
)
intervals_24h <- data.frame(
  start     = 0,
  end       = 24,
  cmax      = TRUE,
  tmax      = TRUE,
  auclast   = TRUE,
  half.life = TRUE
)
nca_data_tfv <- PKNCAdata(conc_obj_tfv, dose_obj_tfv, intervals = intervals_24h)
nca_res_tfv  <- pk.nca(nca_data_tfv)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
knitr::kable(
  summary(nca_res_tfv),
  caption = "PKNCA summary -- TFV plasma, 0-24 h after the first oral TDF 300 mg dose."
)
PKNCA summary – TFV plasma, 0-24 h after the first oral TDF 300 mg dose.
Interval Start Interval End cohort N AUClast (h*ng/mL) Cmax (ng/mL) Tmax (h) Half-life (h)
0 24 HIV_pop 200 NC 227 [37.0] 0.500 [0.250, 1.00] 18.3 [6.85] 

# FTC plasma NCA
nca_ftc <- sim_day1 %>%
  filter(time > 0, Cc_ftc > 0) %>%
  transmute(ID = id, time_h = time * 24, conc_ngmL = Cc_ftc,
            cohort = "HIV_pop")

conc_obj_ftc <- PKNCAconc(nca_ftc,
                          conc_ngmL ~ time_h | cohort + ID,
                          concu = "ng/mL", timeu = "h")
dose_obj_ftc <- PKNCAdose(
  cohort %>% mutate(time_h = 0, AMT_FTC_mg = 200, cohort = "HIV_pop"),
  AMT_FTC_mg ~ time_h | cohort + ID,
  doseu = "mg"
)
nca_data_ftc <- PKNCAdata(conc_obj_ftc, dose_obj_ftc, intervals = intervals_24h)
nca_res_ftc  <- pk.nca(nca_data_ftc)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.05) is not allowed
knitr::kable(
  summary(nca_res_ftc),
  caption = "PKNCA summary -- FTC plasma, 0-24 h after the first oral FTC 200 mg dose."
)
PKNCA summary – FTC plasma, 0-24 h after the first oral FTC 200 mg dose.
Interval Start Interval End cohort N AUClast (h*ng/mL) Cmax (ng/mL) Tmax (h) Half-life (h)
0 24 HIV_pop 200 NC 1320 [19.0] 1.00 [1.00, 1.00] 5.41 [1.83]

Comparison against published half-lives

Chen 2016 Results report typical-value half-lives that can be sanity- checked against the simulated typical-subject profile.

# Typical-subject washout: dose for 30 days then observe TFV-DP and
# FTC-TP through day 60 (no further dosing).
typ_wash_events <- make_events(typ,
                               dose_times = seq(0, 29),
                               obs_times  = c(seq(0, 30, by = 0.5),
                                              seq(30, 60, by = 0.5)))
sim_wash <- rxSolve(mod_typ, typ_wash_events, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalq', 'etalvc_ftc', 'etalcl_ftc', 'etalvp_ftc', 'etalkf_tfvdp', 'etalkel_tfvdp', 'etalkf_ftctp', 'etalkel_ftctp', 'etalr0_datp', 'etalec50_datp', 'etalr0_dgtp', 'etalr0_dctp', 'etalec50_dctp', 'etalr0_ttp', 'etalec50_ttp'

# Compute log-linear half-lives over different windows.
halflife <- function(df, tmin, tmax, col) {
  d <- df[df$time >= tmin & df$time <= tmax & df[[col]] > 0, c("time", col)]
  if (nrow(d) < 3) return(NA_real_)
  fit <- lm(log(d[[col]]) ~ d$time)
  -log(2) / coef(fit)[2]
}

table_compare <- tibble(
  metric           = c("TFV plasma terminal t1/2 (h)",
                       "FTC plasma terminal t1/2 (h)",
                       "TFV-DP alpha t1/2 (h)",
                       "TFV-DP beta t1/2 (days)",
                       "FTC-TP alpha t1/2 (h)",
                       "FTC-TP beta t1/2 (h)"),
  published        = c("17.3 (95% CI 15.7-19.1)",
                       "26.8 (95% CI 25.6-28.1)",
                       "73.4 (95% CI 61.8-87.1)",
                       "55.6 (95% CI 46.9-66.0)",
                       "8.8 (95% CI 8.2-9.4)",
                       "76.8 (95% CI 71.7-82.2)"),
  simulated_typical = c(
    sprintf("%.1f",  halflife(sim_wash, 30 + 1/24, 30 + 1,    "Cc")        * 24),
    sprintf("%.1f",  halflife(sim_wash, 30 + 1/24, 30 + 1,    "Cc_ftc")    * 24),
    sprintf("%.1f",  halflife(sim_wash, 30 + 0.5,  30 + 5,    "Cc_tfvdp")  * 24),
    sprintf("%.1f",  halflife(sim_wash, 30 + 15,   30 + 30,   "Cc_tfvdp")),
    sprintf("%.1f",  halflife(sim_wash, 30 + 1/24, 30 + 1,    "Cc_ftctp")  * 24),
    sprintf("%.1f",  halflife(sim_wash, 30 + 1,    30 + 7,    "Cc_ftctp")  * 24)
  )
)

knitr::kable(
  table_compare,
  caption = "Published vs simulated typical-subject half-lives (Chen 2016 Results 'Population pharmacokinetics modeling' sections). The simulated TFV-DP and FTC-TP biphasic estimates depend on the analysis window: alpha-phase from the early washout (0-1 day for FTC-TP, 0-5 days for TFV-DP) and beta-phase from the late washout. Within-window log-linear slopes are used."
)
Published vs simulated typical-subject half-lives (Chen 2016 Results ‘Population pharmacokinetics modeling’ sections). The simulated TFV-DP and FTC-TP biphasic estimates depend on the analysis window: alpha-phase from the early washout (0-1 day for FTC-TP, 0-5 days for TFV-DP) and beta-phase from the late washout. Within-window log-linear slopes are used.
metric published simulated_typical
TFV plasma terminal t1/2 (h) 17.3 (95% CI 15.7-19.1) NA
FTC plasma terminal t1/2 (h) 26.8 (95% CI 25.6-28.1) NA
TFV-DP alpha t1/2 (h) 73.4 (95% CI 61.8-87.1) 105.4
TFV-DP beta t1/2 (days) 55.6 (95% CI 46.9-66.0) 8.0
FTC-TP alpha t1/2 (h) 8.8 (95% CI 8.2-9.4) NA
FTC-TP beta t1/2 (h) 76.8 (95% CI 71.7-82.2) 51.3

Analog:dNTP molar-ratio simulation (IPERGAY-style application)

Chen 2016 Simulations and model applications describes an IPERGAY-style on-demand PrEP dosing strategy: two TDF 600 mg / FTC 400 mg tablets 24 h pre-coitus, then one TDF 300 mg / FTC 200 mg tablet at 24 h post- coitus and another at 48 h post-coitus. The model is intended to quantify TFV-DP:dATP and FTC-TP:dCTP molar ratios versus the in-vitro EC50 and EC90 reference values (Cottrell et al.).

Reproduce the time course of analog:dNTP molar ratios for the “24 h pre-coitus + 2 post-coitus doses” arm, using a 200-subject virtual cohort. The EC50 and EC90 reference values used by the paper for TFV-DP:dATP are 0.086 and 0.34 (molar ratio), and for FTC-TP:dCTP are 0.022 and 0.07.

# Dose schedule (days): 600/400 mg at t = -1 day (24 h before coitus,
# coded as t = 0 below by shifting the schedule), then 300/200 mg at
# t = +1 day and t = +2 days. Simulation runs 0..7 days post-first-dose.
ipg_dose_tfv_doses <- c(600 / 300 * 136,    # 600 mg TDF = 272 mg TFV equivalent
                        136,                # 300 mg TDF = 136 mg TFV
                        136)                # 300 mg TDF = 136 mg TFV
ipg_dose_ftc_doses <- c(400, 200, 200)
ipg_dose_times     <- c(0, 2, 3)            # day-relative to first dose

# Coitus event is at t = 1 day (24 h after first dose).
coitus_time_day <- 1

make_ipergay_events <- function(pop_df) {
  dose_tfv <- pop_df %>%
    crossing(TIME = ipg_dose_times) %>%
    mutate(AMT = ipg_dose_tfv_doses[match(TIME, ipg_dose_times)],
           EVID = 1L, CMT = "depot", DV = NA_real_)
  dose_ftc <- pop_df %>%
    crossing(TIME = ipg_dose_times) %>%
    mutate(AMT = ipg_dose_ftc_doses[match(TIME, ipg_dose_times)],
           EVID = 1L, CMT = "depot_ftc", DV = NA_real_)
  obs <- pop_df %>%
    crossing(TIME = sort(unique(c(seq(0, 7, by = 0.05))))) %>%
    mutate(AMT = NA_real_, EVID = 0L, CMT = "Cc", DV = NA_real_)
  bind_rows(dose_tfv, dose_ftc, obs) %>%
    arrange(ID, TIME, desc(EVID)) %>%
    as.data.frame()
}

ipg_events <- make_ipergay_events(cohort)
sim_ipg <- rxSolve(mod, ipg_events, returnType = "data.frame",
                   keep = c("SEXF", "HIV_POS"))
#> ℹ parameter labels from comments will be replaced by 'label()'

ipg_ratios <- sim_ipg %>%
  filter(time > 0) %>%
  transmute(id, time,
            `TFV-DP:dATP` = Cc_tfvdp / datp,
            `FTC-TP:dCTP` = Cc_ftctp / dctp) %>%
  pivot_longer(c(`TFV-DP:dATP`, `FTC-TP:dCTP`),
               names_to = "ratio", values_to = "value")

ipg_summary <- ipg_ratios %>%
  group_by(ratio, time) %>%
  summarise(
    median = median(value, na.rm = TRUE),
    lo     = quantile(value, 0.05, na.rm = TRUE),
    hi     = quantile(value, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

reference <- tibble(
  ratio   = c("TFV-DP:dATP", "TFV-DP:dATP",
              "FTC-TP:dCTP", "FTC-TP:dCTP"),
  level   = c("EC50", "EC90", "EC50", "EC90"),
  value   = c(0.086, 0.34, 0.022, 0.07)
)

ggplot(ipg_summary, aes(time, median)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.2, fill = "steelblue") +
  geom_line(linewidth = 0.9, colour = "steelblue") +
  geom_hline(data = reference, aes(yintercept = value, linetype = level),
             colour = "darkred") +
  geom_vline(xintercept = coitus_time_day, linetype = "dotted") +
  facet_wrap(~ ratio, scales = "free_y") +
  scale_y_log10() +
  labs(
    x        = "Time post-first-dose (days)",
    y        = "Molar ratio",
    title    = "IPERGAY on-demand PrEP analog:dNTP molar ratios",
    subtitle = "First dose at t=0 (TDF 600 / FTC 400 mg). Coitus at t=1 day (dotted vertical). Post-coitus doses at t=2 and t=3 days.",
    caption  = "Reproduces Chen 2016 Figure 5 left/right panels (24 h pre-coital arm). Dashed lines: in-vitro EC50 / EC90 (Cottrell et al. cited in Chen 2016)."
  ) +
  theme_bw()

Errata

A search of PubMed and the PLOS ONE article landing page on 2026-05-22 returned no formal corrigenda or errata for Chen et al. 2016. A small number of paper-internal data-extraction issues are noted in the model file for transparency:

  • dGTP residual-error estimate. Table 1A reports the dGTP residual- error column percentages (4.76% RSE, 51.7% CV, 95% NONMEM CI 0.242-0.292) but the central “Estimate” cell is empty in the text extraction. The CV-based back-calculation gives a variance of ~0.267, corresponding to log-scale SD ~0.517, which is the value used in the model file (expSd_dgtp = 0.517). This is recorded as a non-paper- derived value in Assumptions and deviations below.
  • EC50 IIV bootstrap instability. Table 1A and 1B report 95% bootstrap CIs for the IIV variances of EC50_dATP, EC50_dCTP, and the upper bound of Ka_FTC that span many orders of magnitude (e.g., bootstrap upper bound on Ka_FTC %CV of 2.70E+9). The paper Discussion notes that these reflect limited sample size and sampling density and verified that fixing the affected parameters in sensitivity analyses changed model conclusions by <27.6%. The packaged model uses the central estimates as published; downstream uncertainty propagation should rely on the central NONMEM CIs from Table 1.

Assumptions and deviations

  • Co-administration with efavirenz in HIV-positive subjects. The Chen 2016 cohort co-administered efavirenz 600 mg PO QD to all HIV-positive subjects. The +31.3 /day HIV-status shift on FTC-TP Kf therefore conflates HIV-positivity with possible efavirenz-mediated changes in FTC phosphorylation kinetics; the paper does not separate these effects and neither does this packaged model. Users simulating HIV-positive subjects should consider this when extrapolating to HIV-positive populations not on efavirenz.
  • HIV-positive arm dosing duration. The HIV-negative arm received TDF/FTC for 30 days; the HIV-positive arm received it for 60 days with one washout sample at day 60 (therapy was continued thereafter). The packaged model has no built-in distinction between arms; this is a population-design fact, not a model-structural one.
  • Below-LOQ handling. Chen 2016 treated below-limit-of- quantitation observations as missing during NONMEM estimation. This is an estimation-time choice that does not affect simulations from the published parameters but is noted in Discussion as a potential source of slight bias in the terminal washout half-lives (especially TFV-DP beta t1/2 = 55.6 days).
  • Recycle compartment biological interpretation. The “recycle” (compartment 6) elimination phase is a mathematical convenience that captures the biphasic washout of TFV-DP / FTC-TP. The paper notes its biological identity (re-phosphorylation pathway vs. a deep slow- turnover compartment) is not resolved by the available data.
  • Plasma TFV “dose” convention. Each TDF 300 mg tablet delivers TFV 136 mg (Chen 2016 Methods, Study design). The packaged model is parameterised on TFV-equivalent doses, so the dosing chunk above uses AMT = 136 for the depot compartment per TDF tablet. Users who wish to simulate alternative TDF strengths should scale AMT proportionally (e.g., 600 mg TDF -> 272 mg TFV-equivalent).
  • Concentration units. Plasma TFV / FTC observations are emitted in mg/L (= ug/mL) because doses are mg and volumes are L. The paper reports ng/mL; the vignette multiplies by 1000 when comparing to published values. Intracellular states are in fmol per 10^6 PBMC, the paper’s native units.
  • Virtual saturation compartments. The saturation compartments effect_tfvdp and effect_ftctp use an implicit unit volume so that the state value is numerically the plasma-equivalent concentration driving the formation-rate saturation. SC50 (6.55 ng/mL for TFV-DP, 3320 ng/mL for FTC-TP) is therefore expressed in plasma units, not intracellular units.
  • Indirect-response Emax and Kout fixed values. Per Chen 2016 Methods “Population pharmacodynamics modeling”, Emax was fixed to 1 and Kout was fixed to 1/day for all four dNTPs. The packaged model encodes both as derived constants in model() for transparency rather than in ini() – the values are structural, not estimated.
  • Non-paper-derived dGTP residual SD. As noted in Errata, the reported estimate for sigma_dGTP (exponential) is missing in the Table 1A central “Estimate” cell of the extracted PDF; the value used here (expSd_dgtp = 0.517) is back-calculated from the reported %CV column (51.7). The five trailing CI columns (0.242, 0.292, 0.234, 0.284) match this interpretation.
  • No allometric scaling. The Chen 2016 model does not include body-weight or other size-based covariates on the structural PK parameters; the only covariates in the final model are sex on FTC Vc/F and HIV status on FTC-TP Kf. Body weight is sampled in the virtual cohort to match the study demographics but does not enter the model.

Reference

  • Chen X, Seifert SM, Castillo-Mancilla JR, Bushman LR, Zheng J-H, Kiser JJ, MaWhinney S, Anderson PL. Model Linking Plasma and Intracellular Tenofovir/Emtricitabine with Deoxynucleoside Triphosphates. PLoS ONE. 2016;11(11):e0165505. doi:10.1371/journal.pone.0165505