Compute the half-life and associated parameters

The terminal elimination half-life is estimated from the final points in the concentration-time curve using semi-log regression (log(conc)~time, the "log-linear" method) or Tobit regression ("tobit" method) with automated selection of the points for calculation (unless manually.selected.points is TRUE).

Usage

pk.calc.half.life(
  conc,
  time,
  tmax,
  tlast,
  time.dose = NULL,
  duration.dose = 0,
  lloq = NULL,
  hl_method = c("log-linear", "tobit"),
  manually.selected.points = FALSE,
  options = list(),
  min.hl.points = NULL,
  max.hl.points = NULL,
  min.hl.start.time = NULL,
  adj.r.squared.factor = NULL,
  r.squared.factor = NULL,
  tobit_n_points_penalty = NULL,
  tobit_optim_control = NULL,
  conc.blq = NULL,
  conc.na = NULL,
  first.tmax = NULL,
  allow.tmax.in.half.life = NULL,
  check = TRUE
)

Arguments

conc: Measured concentrations
time: Time of the measurement of the concentrations
tmax: Time of maximum concentration (will be calculated and included in the return data frame if not given)
tlast: Time of last concentration above the limit of quantification (will be calculated and included in the return data frame if not given)
time.dose: Time of the dose for the current interval (must be the same length as dose)
duration.dose: The duration of the dose administration for the current interval (typically zero for extravascular and intravascular bolus and nonzero for intravascular infusion)
lloq: Lower limit of quantification. A scalar or a vector the same length as conc. Required when hl_method = "tobit".
hl_method: The method used to estimate the half-life. "log-linear" (default) uses ordinary least-squares regression on log-transformed concentrations. "tobit" uses maximum-likelihood Tobit regression that properly accounts for BLQ observations. The global default can be changed via PKNCA.options(hl_method = "tobit").
manually.selected.points: Have the input points (conc and time) been manually selected? The impact of setting this to TRUE is that no selection for the best points will be done. When TRUE, this option causes the options of adj.r.squared.factor, r.squared.factor, min.hl.points, max.hl.points, min.hl.start.time, and allow.tmax.in.half.life to be ignored.
options: List of changes to the default PKNCA options (see PKNCA.options())
min.hl.points: The minimum number of points that must be included to calculate the half-life. For hl_method = "tobit" this counts only above-LLOQ points.
max.hl.points: The maximum number of points that automatic point selection may use (Inf, the default, for no maximum). It must be more than min.hl.points. For hl_method = "tobit" this counts only above-LLOQ points.
min.hl.start.time: The earliest time at which automatic point selection may start the half-life: points before it are not used. It is on the scale of time, which within pk.nca() is the time since the start of the interval. The default, 0, does not restrict the points.
adj.r.squared.factor: The allowance in adjusted r-squared for adding another point (log-linear method only). Giving it takes r.squared.factor out of use, and setting it to NA selects points with r.squared.factor instead.
r.squared.factor: The allowance in r-squared for adding another point (log-linear method only). Giving it takes adj.r.squared.factor out of use, so exactly one of the two is ever in use; NA (the default) selects points with adj.r.squared.factor. Unlike the adjusted r-squared, the r-squared does not reward more points, so it generally selects fewer of them; with min.hl.points = 2 the two-point fit has an r-squared of 1 and is therefore always selected.
tobit_n_points_penalty: The penalty exponent on the number of points for Tobit window selection. See PKNCA.options().
tobit_optim_control: A list of control parameters passed to stats::optim() for the Tobit fit. See PKNCA.options().
conc.blq: How to handle a BLQ value that is between above LOQ values? See details for description.
conc.na: How to handle NA concentrations. (See clean.conc.na())
first.tmax: If there is more than one time point with the maximum value (Cmax or ERmax), which time should be selected for Tmax/ERTmax? If 'TRUE', the first will be selected. If not, then the last is considered Tmax/ERTmax.
allow.tmax.in.half.life: Allow the concentration point for tmax to be included in the half-life slope calculation.
check: Run assert_conc_time()?

Value

A data frame with one row. Columns depend on hl_method:

Columns returned by both methods:

tmax: Time of maximum observed concentration (only included if not given as an input)
tlast: Time of last observed concentration above the LOQ (only included if not given as an input)
lambda.z: elimination rate
lambda.z.time.first: first time for half-life calculation
lambda.z.time.last: last time for half-life calculation
lambda.z.n.points: number of points in half-life calculation (all points for Tobit, including BLQ)
clast.pred: Concentration at tlast as predicted by the half-life line
half.life: half-life
span.ratio: ratio of the above-LLOQ time span to the half-life

Additional columns for hl_method = "log-linear":

r.squared: coefficient of determination
adj.r.squared: adjusted coefficient of determination
lambda.z.corrxy: correlation between time and log-conc for the half-life points

Additional columns for hl_method = "tobit":

lambda.z.n.points_blq: number of BLQ points included in the fit
tobit_residual: estimated residual standard deviation from the Tobit fit (on the log-concentration scale)
adj_tobit_residual: adjusted Tobit residual (analogous to adjusted r-squared; penalizes smaller windows)

Details

See the "Half-Life Calculation" and "Half-Life Calculation with Tobit Regression" vignettes for more details on the calculation methods.

If manually.selected.points is FALSE (default), the half-life is calculated by computing the best fit line for all points at or after tmax (based on the value of allow.tmax.in.half.life).

For hl_method = "log-linear", the best half-life is chosen by the following rules in order:

At least min.hl.points and at most max.hl.points points included, the first of them no earlier than min.hl.start.time
A lambda.z > 0 and at the same time the best adjusted r-squared (within adj.r.squared.factor) or, when adj.r.squared.factor is NA, the best r-squared (within r.squared.factor)
The one with the most points included

For hl_method = "tobit", BLQ observations are retained and treated as left-censored. The best window is the one minimizing tobit_residual * n ^ tobit_n_points_penalty (default: raw tobit_residual) among windows with lambda.z > 0, at least min.hl.points and at most max.hl.points above-LLOQ points, and a first point no earlier than min.hl.start.time. On ties the largest window (most total points) is preferred.

If manually.selected.points is TRUE, the conc and time data are used as-is without any form of point selection. When TRUE, adj.r.squared.factor, r.squared.factor, min.hl.points, max.hl.points, min.hl.start.time, and allow.tmax.in.half.life are ignored.

References

Gabrielsson J, Weiner D. "Section 2.8.4 Strategies for estimation of lambda-z." Pharmacokinetic & Pharmacodynamic Data Analysis: Concepts and Applications, 4th Edition. Stockholm, Sweden: Swedish Pharmaceutical Press, 2000. 167-9.