AUCinf vs Partial AUC: Choosing the Right Interval in NCA

Understand the computational difference between AUC to infinity and partial AUC. Learn how interval definition affects stability, extrapolation, and interpretation.

Tip

Big idea: AUC is defined over an interval. Choosing 0–Inf versus 0–T is not cosmetic — it changes how much extrapolation you accept.

Learning Objectives

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

Explain the computational difference between AUCinf and partial AUC.
Define multiple intervals in PKNCA.
Compare AUC0–T (e.g., 0–24) with AUC0–Inf.
Interpret extrapolation fraction in the context of interval choice.

Conceptual Bridge

In a previous lesson we evaluated whether the terminal phase is reliable enough to estimate $\lambda_z$ and half-life.

Here we examine how that decision affects the exposure metric you report — specifically the choice between AUC$_{0-\infty}$ and partial AUC.

Key Ideas

AUC0–Tlast (partial AUC) integrates only observed data.
AUC0–Inf integrates observed data plus extrapolated tail area.
Extrapolation depends on the estimated terminal slope ($\lambda_z$).
If terminal slope is unstable, AUCinf is unstable.
Partial AUC is often more robust when sampling is limited.

Setup: Run NCA on Theoph

library(tidyverse)
library(PKNCA)

data(Theoph)

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

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

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

Step 1: Define the Intervals You Want

We will compute an observed AUC-to-last metric and AUCinf in the same run.

intervals_df <- data.frame(
  start = 0,
  end = Inf,
  auclast = TRUE,
  aucinf.obs = TRUE
)

nca_data <- PKNCAdata(conc_obj, dose_obj, intervals = intervals_df)
results_obj <- pk.nca(nca_data)
raw_df <- as.data.frame(results_obj)

sort(unique(raw_df$PPTESTCD))

 [1] "adj.r.squared"       "aucinf.obs"          "auclast"            
 [4] "clast.obs"           "clast.pred"          "half.life"          
 [7] "lambda.z"            "lambda.z.n.points"   "lambda.z.time.first"
[10] "lambda.z.time.last"  "r.squared"           "span.ratio"         
[13] "tlast"               "tmax"

Step 2: Extract AUC Outputs

We extract the two AUC metrics returned by PKNCA:

auclast
aucinf.obs

auc_tbl <- raw_df %>%
  filter(PPTESTCD %in% c("auclast", "aucinf.obs")) %>%
  select(ID, PPTESTCD, PPORRES) %>%
  pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

auc_tbl %>%
  select(ID, auclast, aucinf.obs) %>%
  head()

# A tibble: 6 × 3
  ID    auclast aucinf.obs
  <ord>   <dbl>      <dbl>
1 6        71.7       82.2
2 7        88.0      101. 
3 8        86.8      102. 
4 11       77.9       86.9
5 3        95.9      106. 
6 2        88.7       97.4

Step 3: Compute Extrapolated Fraction

\[ \text{Extrapolated Fraction} = \frac{AUC_{0-\infty} - AUC_{0-tlast}}{AUC_{0-\infty}} \]

auc_tbl <- auc_tbl %>%
  mutate(
    extrap_fraction = (aucinf.obs - auclast) / aucinf.obs
  )

auc_tbl %>%
  select(ID, extrap_fraction) %>%
  head()

# A tibble: 6 × 2
  ID    extrap_fraction
  <ord>           <dbl>
1 6              0.128 
2 7              0.129 
3 8              0.150 
4 11             0.104 
5 3              0.0966
6 2              0.0888

Interpretation

If extrapolated fraction is small (e.g., <20%), AUCinf is close to observed exposure.
If extrapolated fraction is large, AUCinf relies heavily on the terminal slope.
In sparse sampling, AUCinf may be less stable than partial AUC.

Partial AUC avoids extrapolation entirely.

When Partial AUC Is Preferable

Fixed dosing interval (e.g., AUC0–24)
Sparse terminal sampling
Unstable lambda_z / unreliable half-life
When your decision is about observed exposure within a window

Computational Takeaway

In PKNCA, interval choice is controlled in intervals_df.

Changing:

end = Inf

to something like:

end = 24

changes the exposure definition you compute.

Strategies

Compute both AUC0–T (or AUC0–Tlast) and AUC0–Inf during exploratory work.
Examine extrapolated fraction before reporting AUCinf.
Document interval definitions in your reporting layer.
Keep interval choice consistent across groups.

Practice Problems

Executable: Compute AUC0–12 by setting end = 12 and requesting auclast = TRUE.
Executable: Identify subjects with extrapolated fraction > 0.25.
Conceptual: Why might partial AUC be more stable in sparse designs?

Step-by-Step Solutions

1. AUC0–12:

intervals_0_12 <- data.frame(
  start = 0,
  end = 12,
  auclast = TRUE
)

nca_0_12 <- PKNCAdata(conc_obj, dose_obj, intervals = intervals_0_12)

as.data.frame(pk.nca(nca_0_12)) %>%
  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 7         0    12 auclast     50.1 <NA>   
3 8         0    12 auclast     51.5 <NA>   
4 11        0    12 auclast     49.0 <NA>   
5 3         0    12 auclast     57.1 <NA>   
6 2         0    12 auclast     67.2 <NA>

2. Extrapolation > 25%:

auc_tbl %>%
  filter(!is.na(extrap_fraction), extrap_fraction > 0.25)

# A tibble: 1 × 4
  ID    auclast aucinf.obs extrap_fraction
  <ord>   <dbl>      <dbl>           <dbl>
1 1        147.       215.           0.315

3. Conceptual answer:
Partial AUC does not depend on terminal slope estimation. Sparse terminal data can destabilize $\lambda_z$ and inflate extrapolated area, making AUCinf less reliable.

Summary

AUC depends on the interval you define.

AUC0–Tlast uses only observed data.
AUC0–Inf adds extrapolated tail area.
Extrapolation depends on terminal slope quality.
In PKNCA, interval choice is controlled explicitly in intervals_df.

Quick Tips

Start by checking available outputs using unique(raw_df$PPTESTCD).
Extrapolated fraction is a practical reliability flag for AUCinf.
Partial AUC is often more robust when terminal data are weak.
Document interval definitions in every report.