Time to steady-state (TSS) can be estimated with PKNCA using either a monoexponential increase toward an asymptote or by a linear regression of the last points. According to Maganti (2008), the monoexponential method is preferred.
TSS can be estimated using either method using the
pk.tss()
function in PKNCA.
Illustrating time to steady-state, the example from the superposition vignette will be used.
library(PKNCA)
theoph_corrected <- as.data.frame(datasets::Theoph)
theoph_corrected$conc[theoph_corrected$Time == 0] <- 0
conc_obj <- PKNCAconc(theoph_corrected, conc~Time|Subject)
steady_state <- superposition(conc_obj, dose.times = seq(0, 168 - 12, by=12), tau=168, n.tau=1)
# Add some noise to the data so that it seems more reasonable
steady_state_noise <- steady_state
steady_state_noise$conc <-
withr::with_seed(
seed = 5,
steady_state_noise$conc*exp(rnorm(nrow(steady_state_noise), mean = 0, sd = 0.1))
)
Examine the data graphically.
The below code estimates four different types of monoexponential time to steady-state:
tss_mono <-
pk.tss.monoexponential(
conc = steady_state_noise$conc,
time = steady_state_noise$time,
subject = steady_state_noise$Subject,
time.dosing = seq(0, 168 - 12, by=12)
)
#> Warning in nlme.formula(conc ~ ctrough.ss * (1 - exp(tss.constant * time/tss)),
#> : Iteration 1, LME step: nlminb() did not converge (code = 1). Do increase
#> 'msMaxIter'!
tss_mono
#> subject tss.monoexponential.population tss.monoexponential.popind
#> 1 1 26.41702 36.94338
#> 2 10 26.41702 31.95332
#> 3 11 26.41702 22.79701
#> 4 12 26.41702 26.59811
#> 5 2 26.41702 23.53971
#> 6 3 26.41702 24.72296
#> 7 4 26.41702 25.73772
#> 8 5 26.41702 26.93370
#> 9 6 26.41702 23.21927
#> 10 7 26.41702 25.39845
#> 11 8 26.41702 24.54317
#> 12 9 26.41702 24.61744
#> tss.monoexponential.individual tss.monoexponential.single
#> 1 40.65290 27.87592
#> 2 24.72591 27.87592
#> 3 20.18663 27.87592
#> 4 22.58610 27.87592
#> 5 25.45251 27.87592
#> 6 29.97015 27.87592
#> 7 21.60401 27.87592
#> 8 25.04023 27.87592
#> 9 23.53884 27.87592
#> 10 31.37369 27.87592
#> 11 32.02870 27.87592
#> 12 26.01334 27.87592
The fraction of steady-state required for time to steady-state can be
changed with the tss.fraction
argument (see
?pk.tss.monoexponential
).
The stepwise linear method estimates if the slope of the predose concentrations is statistically significant starting from the last measurement and moving backward in time. It has bias in that more individuals will move the time to steady-state to a late time point.