Multiple-Dose and Steady-State Workflows in PKNCA

Define dosing history, compute AUC over tau, interpret steady-state metrics, and avoid structural errors in multiple-dose NCA.
Tip

Big idea: In multiple-dose studies, exposure is defined relative to a dosing interval (\(\tau\)), not infinity.

Learning Objectives

By the end of this lesson, you will be able to:

  • Explain the conceptual shift from single-dose to multiple-dose NCA.
  • Define dosing history appropriately for repeated dosing.
  • Compute \(AUC_{0-\tau}\) using PKNCA.
  • Interpret steady-state exposure and accumulation metrics.
  • Identify structural mistakes specific to multiple-dose datasets.

Key Ideas

  • Single-dose studies focus on \(AUC_{0-\infty}\) or \(AUC_{0-tlast}\).
  • Multiple-dose studies focus on exposure within one dosing interval (\(\tau\)).
  • Steady-state interpretation depends on the relationship between \(\tau\) and half-life.
  • Grouping structure must reflect dosing occasions when applicable.
  • Clearance units still depend on dose units (mg/kg → L/h/kg).

Conceptual Shift: Single Dose vs Multiple Dose

Single Dose

Exposure metrics commonly include:

  • \(AUC_{0-\infty}\)
  • \(AUC_{0-tlast}\)
  • \(C_{max}\)
  • \(t_{1/2}\)

The question is typically:

What is total exposure after one administration?

Multiple Dose

In repeated dosing:

  • Exposure is evaluated over one dosing interval (\(\tau\)).
  • We focus on steady-state behavior.
  • \(AUC_{0-\tau}\) becomes central.
  • Accumulation and fluctuation become meaningful.

The key question becomes:

What is exposure during one dosing interval at steady state?

Example Setup (Using Theoph for Structure)

We reuse Theoph purely to demonstrate structure. It is still a single-dose dataset, but we define an artificial \(\tau\) interval for demonstration.

library(tidyverse)
library(PKNCA)

data(Theoph)

conc_df <- as_tibble(Theoph) %>%
  transmute(ID = Subject, TIME = Time, CONC = conc)

dose_df <- as_tibble(Theoph) %>%
  distinct(Subject, Dose) %>%
  transmute(ID = Subject, TIME = 0, DOSE = Dose)

Defining a Tau-Based Interval

Suppose dosing occurs every 12 hours.

We define:

intervals_tau <- data.frame(
  start = 0,
  end = 12,        # tau = 12 hours
  auclast = TRUE,
  cmax = TRUE,
  tmax = TRUE
)

Here:

  • start = 0 → start of dosing interval
  • end = 12 → end of dosing interval (\(\tau\))
  • We request interval-based metrics only

Running Multiple-Dose-Style NCA

conc_obj <- PKNCAconc(CONC ~ TIME | ID, data = conc_df)
dose_obj <- PKNCAdose(DOSE ~ TIME | ID, data = dose_df)

nca_tau <- PKNCAdata(conc_obj, dose_obj, intervals = intervals_tau)
results_tau <- pk.nca(nca_tau)

tau_df <- as.data.frame(results_tau)
tau_df %>% head()
# A tibble: 6 × 6
  ID    start   end PPTESTCD PPORRES exclude
  <ord> <dbl> <dbl> <chr>      <dbl> <chr>  
1 6         0    12 auclast    43.0  <NA>   
2 6         0    12 cmax        6.44 <NA>   
3 6         0    12 tmax        1.15 <NA>   
4 7         0    12 auclast    50.1  <NA>   
5 7         0    12 cmax        7.09 <NA>   
6 7         0    12 tmax        3.48 <NA>

Note that results are now interval-specific.

Steady-State Interpretation

At steady state, accumulation can be defined as:

\[ R_{acc} = \frac{AUC_{0-\tau,ss}}{AUC_{0-\tau,1}} \]

Where:

  • \(AUC_{0-\tau,1}\) = exposure during first interval
  • \(AUC_{0-\tau,ss}\) = exposure at steady state

Interpretation:

  • \(R_{acc} > 1\) → accumulation
  • \(R_{acc} \approx 1\) → minimal accumulation

Accumulation depends on:

  • Dosing interval (\(\tau\))
  • Elimination half-life (\(t_{1/2}\))

Worked Example (Conceptual)

Suppose:

  • \(t_{1/2} = 10\) hours
  • \(\tau = 12\) hours

Since half-life is close to the dosing interval, incomplete elimination occurs between doses.

We would expect:

  • Accumulation across intervals
  • \(R_{acc} > 1\)
  • Higher steady-state trough concentrations

This illustrates why half-life relative to \(\tau\) determines accumulation.

Strategies

  • Always define intervals deliberately — never rely on defaults.
  • Verify time is relative to the correct dose.
  • Match grouping between concentration and dose objects.
  • Label interval clearly in reporting tables (e.g., “0–12h”).
  • Interpret accumulation in light of half-life and dosing interval.

Common Mistakes

Warning
  • Reporting \(AUC_{0-\infty}\) in a multiple-dose study.
  • Ignoring dosing history when interpreting exposure.
  • Confusing first-dose exposure with steady-state exposure.
  • Failing to include PERIOD/OCC in repeated-dose datasets.

Practice Problems

Conceptual

  1. Why is \(AUC_{0-\infty}\) usually inappropriate in steady-state studies?
  2. How does increasing \(\tau\) affect accumulation (all else equal)?

Executable

  1. Modify the interval to use \(\tau = 8\) hours and rerun NCA.
  2. Extract only \(AUC_{0-\tau}\) values from tau_df.

1. Inappropriate \(AUC_{0-\infty}\):
At steady state, dosing continues. There is no meaningful “infinity” beyond the interval because additional doses occur.

2. Effect of larger \(\tau\):
Longer \(\tau\) allows more elimination between doses, reducing accumulation.

3. Tau = 8 hours:

intervals_tau8 <- data.frame(
  start = 0,
  end = 8,
  auclast = TRUE
)

nca_tau8 <- PKNCAdata(conc_obj, dose_obj, intervals = intervals_tau8)
results_tau8 <- pk.nca(nca_tau8)
as.data.frame(results_tau8) %>% head()
# A tibble: 6 × 6
  ID    start   end PPTESTCD PPORRES exclude
  <ord> <dbl> <dbl> <chr>      <dbl> <chr>  
1 6         0     8 auclast     34.7 <NA>   
2 7         0     8 auclast     40.4 <NA>   
3 8         0     8 auclast     42.6 <NA>   
4 11        0     8 auclast     41.0 <NA>   
5 3         0     8 auclast     47.3 <NA>   
6 2         0     8 auclast     46.3 <NA>

4. Extract interval AUC:

tau_df %>%
  filter(PPTESTCD == "auclast") %>%
  select(ID, PPORRES)
# A tibble: 12 × 2
   ID    PPORRES
   <ord>   <dbl>
 1 6        43.0
 2 7        50.1
 3 8        51.5
 4 11       49.0
 5 3        57.1
 6 2        67.2
 7 4        72.8
 8 9        58.7
 9 12       69.0
10 10       73.9
11 1        72.7
12 5        84.4

Summary

In multiple-dose NCA:

  • Exposure is defined over a dosing interval (\(\tau\)).
  • Interpretation focuses on steady-state behavior.
  • Accumulation depends on half-life relative to \(\tau\).
  • Structural clarity in intervals and grouping is essential.

Understanding this shift prevents misinterpretation of exposure metrics in repeated-dose designs.

  • Always define \(\tau\) explicitly.
  • Do not report \(AUC_{0-\infty}\) in steady-state contexts.
  • Interpret accumulation relative to half-life.
  • Label interval boundaries clearly in tables and figures.