intervals¶

Parameters of the single dosing intervals of a multiple dose timecourse.

A dosing protocol with the dose times \(t_1 < \dots < t_K\) splits a timecourse into the dosing intervals \([t_k, t_{k+1}]\) and the last interval \([t_K, t_K + \tau_K]\), whose length comes from the protocol or from NCAOptions.tau. compute_intervals computes the exposure of every interval of every row of a batch, the analysis of a multiple dose curve of Gabrielsson & Weiner (2016, ch. 2.8) and Rowland & Tozer (2011, ch. 11):

• AUC(0-tau) of the interval, with the values at its bounds interpolated so that samples outside it add no area,
• Cmax, Tmax (relative to the start of the interval), Cmin,
• Ctrough, the value at the end of the interval, and Cstart, the value at its start (after an intravenous bolus the post-dose value; the pre-dose value of interval k is the Ctrough of interval k-1),
• Cavg = AUC(0-tau) / tau, fluctuation = (Cmax - Cmin) / Cavg and swing = (Cmax - Cmin) / Cmin,

and, for effect timecourses, AUEC(0-tau), Emax, TEmax, Emin, Eavg and the time above NCAOptions.effect_threshold.

The variables are named with the prefix interval_ and live over the extra dimension interval of a result, so that they do not clash with the single dose and the steady state parameters of the same curve.

The bounds of an interval. The value at the start and the value at the end are interpolated from the curve (pkpdutils.nca.auc.interpolate_at), which returns an observed value when a sample was taken at the bound. Two cases need more than an interpolation:

• after an intravenous bolus the concentration jumps at the dose. An interval which starts before the first sample of the curve therefore gets the log-linearly back-extrapolated C0 of its first two samples, the estimate compute_parameters uses for the single dose areas.
• an interval whose end carries the next bolus ends before that dose, so a sample recorded exactly at its end may be a post-dose sample of the next dose. It is taken as such only when it lies above the last sample inside the interval, which no decline can do; the trough is then the log-linear regression of the last (up to three) positive samples inside the interval evaluated at the end of the interval, and the row carries pkpdutils.nca.options.NCAFlag.EXTRAPOLATED_TROUGH. Every other sample at the end, and every interpolated end value, is the observed trough and is used as it is; the substitution never applies to another route, since only a bolus makes the concentration jump.
• an interval whose end is not covered by the data, or which holds no sample at all, is incomplete: its parameters are NaN and only the number of samples is reported (pkpdutils.nca.options.NCAFlag.INCOMPLETE_INTERVAL for the last interval).

interval_n_points counts the samples the interval uses; a sample at a boundary is used by both neighbouring intervals, so the counts of the intervals of a curve do not partition its samples.

interval_variables(options, *, has_dose)

compute_intervals(
    t, c, *, dose_amount, dose_time, tau, route, options
)