16 Dose-Aware Interpolation and Extrapolation

16.1 Why dose timing matters for interpolation

Standard concentration interpolation (e.g., interp.extrap.conc()) assumes a smooth concentration-time curve with no discontinuities. But when a dose is given at or near the interpolation target time, the correct value depends critically on whether you are asking about the concentration before or after that dose event.

interp.extrap.conc.dose() is the dose-aware version. It accounts for:

Whether the route is intravascular (bolus causes instantaneous jump) or extravascular (no instantaneous change)
Whether you want the concentration before (out.after = FALSE) or after (out.after = TRUE) the dose
Whether the dose is an infusion with a finite duration

16.2 The key argument: `out.after`

`out.after`	Meaning
`FALSE` (default)	Return the concentration just before the dose event
`TRUE`	Return the concentration just after the dose event

For extravascular doses, there is no instantaneous concentration change at the dose time, so out.after only affects the behaviour right at the dose time itself.

For IV bolus, the dose causes an instantaneous jump, so the before/after distinction is pharmacologically meaningful.

16.3 Shared example data

# Single-dose oral profile (absorption + elimination)
conc <- c(0.0, 2.5, 5.0, 4.2, 2.8, 1.5, 0.8)
time <- c(0,   1,   2,   3,   5,   7,   10 )

d <- data.frame(time = time, conc = conc)

ggplot(d, aes(x = time, y = conc)) +
  geom_line(colour = "steelblue") +
  geom_point(size = 3, colour = "steelblue") +
  labs(title = "Example single-dose oral profile",
       x = "Time (h)", y = "Concentration (mg/L)") +
  theme_minimal()

16.4 Basic interpolation (no dose at target time)

When the target time is between observed samples and does not coincide with a dose, the result equals standard log-linear interpolation.

# t = 4h falls between t=3 and t=5
interp.extrap.conc.dose(
  conc       = conc,
  time       = time,
  time.dose  = 0,          # dose was given at t=0
  route.dose = "extravascular",
  time.out   = 4
)

[1] 3.429286
attr(,"Method")
[1] "Interpolation"

Compare to dose-unaware interpolation:

interp.extrap.conc(conc = conc, time = time, time.out = 4)

[1] 3.429286

They agree when no dose occurs at the target time.

16.5 At the dose time: oral (extravascular)

For an oral dose, concentration does not change instantaneously at the dose time — absorption is gradual. So out.after does not change the interpolated value at the dose time itself.

# Oral: t=0, before dose
interp.extrap.conc.dose(
  conc       = conc, time = time,
  time.dose  = 0, route.dose = "extravascular",
  time.out   = 0, out.after  = FALSE
)

[1] 0
attr(,"Method")
[1] "Observed concentration"

# Oral: t=0, after dose (same — no jump)
interp.extrap.conc.dose(
  conc       = conc, time = time,
  time.dose  = 0, route.dose = "extravascular",
  time.out   = 0, out.after  = TRUE
)

[1] 0
attr(,"Method")
[1] "Interpolation"

16.6 At the dose time: IV bolus (intravascular)

For an IV bolus, the dose causes an instantaneous concentration jump. out.after = FALSE returns the pre-dose (trough) concentration; out.after = TRUE returns the post-dose concentration.

# IV profile: C0 = 10 after dose, declines monoexponentially
conc_iv <- c(10,  8,  6,  4,  2.5, 1.5)
time_iv <- c(0,   1,  2,  4,  6,   9  )

# Before second dose at t=6 — return the trough
interp.extrap.conc.dose(
  conc       = conc_iv, time = time_iv,
  time.dose  = 0, route.dose = "intravascular",
  time.out   = 6, out.after  = FALSE
)

[1] 2.5
attr(,"Method")
[1] "Observed concentration"

16.7 Multiple dose times

Provide a vector to time.dose when multiple doses were given during the sampling window.

# Oral doses at t=0 and t=6
conc_md <- c(0, 2.5, 5.0, 4.2, 2.8, 4.5, 6.0, 5.1, 3.5, 2.0)
time_md <- c(0, 1,   2,   3,   5,   6,   7,   8,   10,  12 )

# Concentration just before the second dose at t=6
interp.extrap.conc.dose(
  conc       = conc_md, time = time_md,
  time.dose  = c(0, 6), route.dose = "extravascular",
  time.out   = 6, out.after = FALSE
)

[1] 4.5
attr(,"Method")
[1] "Observed concentration"

# Concentration just after the second dose at t=6
interp.extrap.conc.dose(
  conc       = conc_md, time = time_md,
  time.dose  = c(0, 6), route.dose = "extravascular",
  time.out   = 6, out.after = TRUE
)

[1] 4.5
attr(,"Method")
[1] "Interpolation"

For extravascular doses, before and after are the same (no instantaneous jump).

16.8 IV infusion: dose duration

For IV infusions, supply duration.dose (the infusion duration in the same time units).

# 30-minute (0.5h) infusion starting at t=0
conc_inf <- c(0, 3,  5,  4.5, 3,  2,  1  )
time_inf <- c(0, 0.25, 0.5, 1, 2, 4, 8  )

# At end of infusion (t=0.5): concentration is the measured peak
interp.extrap.conc.dose(
  conc          = conc_inf, time = time_inf,
  time.dose     = 0,
  route.dose    = "intravascular",
  duration.dose = 0.5,
  time.out      = 0.5, out.after = FALSE
)

[1] 5
attr(,"Method")
[1] "Observed concentration"

16.9 How PKNCA uses `interp.extrap.conc.dose()` internally

PKNCA calls this function automatically whenever an interval boundary (the start or end of an interval in your intervals data frame) falls at a dose time. You normally never call it directly.

Understanding its behaviour helps diagnose unusual NCA results when dosing and sampling times coincide — for example, when start = tau (the trough time) is also the time of the next dose.

16.10 Argument reference

Argument	Required	Meaning
`conc`	Yes	Observed concentrations
`time`	Yes	Observation times (same units as `time.dose`)
`time.dose`	Yes	Time(s) at which doses were given
`route.dose`	Yes	`"extravascular"` or `"intravascular"`
`duration.dose`	No	Infusion duration (NA = bolus)
`time.out`	Yes	Target time at which to interpolate/extrapolate
`out.after`	No (default `FALSE`)	`FALSE` = before dose; `TRUE` = after dose
`options`	No	PKNCA options list (controls AUC method / interpolation rule)

pkgdown reference: interp.extrap.conc.dose() · interp.extrap.conc()

--- title: "Dose-Aware Interpolation and Extrapolation" --- ```{r setup, include=FALSE} library(PKNCA) library(dplyr) library(ggplot2) conflicted::conflicts_prefer(dplyr::filter, dplyr::select, .quiet = TRUE) ``` ## Why dose timing matters for interpolation Standard concentration interpolation (e.g., `interp.extrap.conc()`) assumes a smooth concentration-time curve with no discontinuities. But when a dose is given **at** or **near** the interpolation target time, the correct value depends critically on whether you are asking about the concentration *before* or *after* that dose event. **`interp.extrap.conc.dose()`** is the dose-aware version. It accounts for: - Whether the route is intravascular (bolus causes instantaneous jump) or extravascular (no instantaneous change) - Whether you want the concentration before (`out.after = FALSE`) or after (`out.after = TRUE`) the dose - Whether the dose is an infusion with a finite duration --- ## The key argument: `out.after` | `out.after` | Meaning | |---|---| | `FALSE` (default) | Return the concentration just **before** the dose event | | `TRUE` | Return the concentration just **after** the dose event | For extravascular doses, there is no instantaneous concentration change at the dose time, so `out.after` only affects the behaviour right at the dose time itself. For IV bolus, the dose causes an instantaneous jump, so the before/after distinction is pharmacologically meaningful. --- ## Shared example data ```{r} # Single-dose oral profile (absorption + elimination) conc <- c(0.0, 2.5, 5.0, 4.2, 2.8, 1.5, 0.8) time <- c(0, 1, 2, 3, 5, 7, 10 ) d <- data.frame(time = time, conc = conc) ggplot(d, aes(x = time, y = conc)) + geom_line(colour = "steelblue") + geom_point(size = 3, colour = "steelblue") + labs(title = "Example single-dose oral profile", x = "Time (h)", y = "Concentration (mg/L)") + theme_minimal() ``` --- ## Basic interpolation (no dose at target time) When the target time is **between** observed samples and does not coincide with a dose, the result equals standard log-linear interpolation. ```{r} # t = 4h falls between t=3 and t=5 interp.extrap.conc.dose( conc = conc, time = time, time.dose = 0, # dose was given at t=0 route.dose = "extravascular", time.out = 4 ) ``` Compare to dose-unaware interpolation: ```{r} interp.extrap.conc(conc = conc, time = time, time.out = 4) ``` They agree when no dose occurs at the target time. --- ## At the dose time: oral (extravascular) For an oral dose, concentration does not change instantaneously at the dose time — absorption is gradual. So `out.after` does not change the interpolated value at the dose time itself. ```{r} # Oral: t=0, before dose interp.extrap.conc.dose( conc = conc, time = time, time.dose = 0, route.dose = "extravascular", time.out = 0, out.after = FALSE ) ``` ```{r} # Oral: t=0, after dose (same — no jump) interp.extrap.conc.dose( conc = conc, time = time, time.dose = 0, route.dose = "extravascular", time.out = 0, out.after = TRUE ) ``` --- ## At the dose time: IV bolus (intravascular) For an IV bolus, the dose causes an instantaneous concentration jump. `out.after = FALSE` returns the pre-dose (trough) concentration; `out.after = TRUE` returns the post-dose concentration. ```{r} # IV profile: C0 = 10 after dose, declines monoexponentially conc_iv <- c(10, 8, 6, 4, 2.5, 1.5) time_iv <- c(0, 1, 2, 4, 6, 9 ) # Before second dose at t=6 — return the trough interp.extrap.conc.dose( conc = conc_iv, time = time_iv, time.dose = 0, route.dose = "intravascular", time.out = 6, out.after = FALSE ) ``` --- ## Multiple dose times Provide a vector to `time.dose` when multiple doses were given during the sampling window. ```{r} # Oral doses at t=0 and t=6 conc_md <- c(0, 2.5, 5.0, 4.2, 2.8, 4.5, 6.0, 5.1, 3.5, 2.0) time_md <- c(0, 1, 2, 3, 5, 6, 7, 8, 10, 12 ) # Concentration just before the second dose at t=6 interp.extrap.conc.dose( conc = conc_md, time = time_md, time.dose = c(0, 6), route.dose = "extravascular", time.out = 6, out.after = FALSE ) ``` ```{r} # Concentration just after the second dose at t=6 interp.extrap.conc.dose( conc = conc_md, time = time_md, time.dose = c(0, 6), route.dose = "extravascular", time.out = 6, out.after = TRUE ) ``` For extravascular doses, before and after are the same (no instantaneous jump). --- ## IV infusion: dose duration For IV infusions, supply `duration.dose` (the infusion duration in the same time units). ```{r} # 30-minute (0.5h) infusion starting at t=0 conc_inf <- c(0, 3, 5, 4.5, 3, 2, 1 ) time_inf <- c(0, 0.25, 0.5, 1, 2, 4, 8 ) # At end of infusion (t=0.5): concentration is the measured peak interp.extrap.conc.dose( conc = conc_inf, time = time_inf, time.dose = 0, route.dose = "intravascular", duration.dose = 0.5, time.out = 0.5, out.after = FALSE ) ``` --- ## How PKNCA uses `interp.extrap.conc.dose()` internally PKNCA calls this function automatically whenever an interval boundary (the `start` or `end` of an interval in your intervals data frame) falls at a dose time. You normally never call it directly. Understanding its behaviour helps diagnose unusual NCA results when dosing and sampling times coincide — for example, when `start = tau` (the trough time) is also the time of the next dose. --- ## Argument reference | Argument | Required | Meaning | |---|---|---| | `conc` | Yes | Observed concentrations | | `time` | Yes | Observation times (same units as `time.dose`) | | `time.dose` | Yes | Time(s) at which doses were given | | `route.dose` | Yes | `"extravascular"` or `"intravascular"` | | `duration.dose` | No | Infusion duration (NA = bolus) | | `time.out` | Yes | Target time at which to interpolate/extrapolate | | `out.after` | No (default `FALSE`) | `FALSE` = before dose; `TRUE` = after dose | | `options` | No | PKNCA options list (controls AUC method / interpolation rule) | --- ::: {.callout-note icon=false appearance="minimal"} **pkgdown reference:** [interp.extrap.conc.dose()](https://humanpred.github.io/pknca/reference/interp.extrap.conc.dose.html) · [interp.extrap.conc()](https://humanpred.github.io/pknca/reference/interp.extrap.conc.html) :::

16.1 Why dose timing matters for interpolation

16.2 The key argument: out.after

16.3 Shared example data

16.4 Basic interpolation (no dose at target time)

16.5 At the dose time: oral (extravascular)

16.6 At the dose time: IV bolus (intravascular)

16.7 Multiple dose times

16.8 IV infusion: dose duration

16.9 How PKNCA uses interp.extrap.conc.dose() internally

16.10 Argument reference

16.2 The key argument: `out.after`

16.9 How PKNCA uses `interp.extrap.conc.dose()` internally