4 AUC Types and Integration Methods

4.1 AUC types

PKNCA offers four families of AUC, each answering a different question:

flowchart LR
    A["AUClast\n0 → last measurable"]
    B["AUCall\n0 → last, zeros for BLQ"]
    C["AUCinf.obs\n0 → ∞ (observed Clast)"]
    D["AUCinf.pred\n0 → ∞ (predicted Clast)"]
    E["AUCint / partial\n0 → t (any t)"]

Parameter	End point	BLQ treatment	When to use
`auclast`	Last measurable concentration	BLQs after last non-BLQ are ignored	Default; most studies
`aucall`	Last measured time point	Post-last-measurable BLQs treated as 0	When you want to include the BLQ tail
`aucinf.obs`	Extrapolated to ∞ (using observed Clast)	—	When half-life is reliable
`aucinf.pred`	Extrapolated to ∞ (using predicted Clast from λz fit)	—	When Clast is noisy
`aucint.*`	Any user-defined time window	—	Partial AUC, bioequivalence

4.1.1 AUClast vs AUCall

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

o_data <- PKNCAdata(o_conc, o_dose, intervals = auc_compare)
o_nca  <- pk.nca(o_data)

as.data.frame(o_nca) |>
  filter(PPTESTCD %in% c("auclast", "aucall", "aucinf.obs", "aucpext.obs")) |>
  select(PPTESTCD, PPORRES)

# A tibble: 3 × 2
  PPTESTCD   PPORRES
  <chr>        <dbl>
1 auclast       147.
2 aucall        147.
3 aucinf.obs    215.

aucall ≥ auclast when there are post-last-measurable BLQ timepoints, since those are treated as 0 and add a small triangle to the AUC.

4.2 Partial AUC (AUCint)

For bioequivalence or exposure-in-a-window calculations, use aucint.* parameters. These calculate AUC over an exact time window, interpolating concentrations at the boundaries if needed.

# AUC from 0 to 4h and 0 to 12h on the same profile
partial_intervals <- data.frame(
  start         = c(0,  0),
  end           = c(4, 12),
  aucint.last   = TRUE,   # AUC to the last obs within window (or interpolated boundary)
  aucint.inf.obs = FALSE
)

o_data_partial <- PKNCAdata(o_conc, o_dose, intervals = partial_intervals)
o_nca_partial  <- pk.nca(o_data_partial)

as.data.frame(o_nca_partial) |>
  filter(PPTESTCD == "aucint.last") |>
  select(start, end, PPTESTCD, PPORRES)

# A tibble: 2 × 4
  start   end PPTESTCD    PPORRES
  <dbl> <dbl> <chr>         <dbl>
1     0     4 aucint.last    33.7
2     0    12 aucint.last    91.7

All partial AUC variants:

Parameter	End concentration	Dose-aware boundary	Extrapolation
`aucint.last`	Last observed in window	No	None
`aucint.all`	Last observed, BLQs as 0	No	None
`aucint.inf.obs`	Extrapolated to ∞, observed Clast	No	λz-based tail
`aucint.inf.pred`	Extrapolated to ∞, predicted Clast	No	λz-based tail
`aucint.last.dose`	Same as `.last`	Yes	None
`aucint.all.dose`	Same as `.all`	Yes	None
`aucint.inf.obs.dose`	Same as `.inf.obs`	Yes	λz-based tail
`aucint.inf.pred.dose`	Same as `.inf.pred`	Yes	λz-based tail

Note: aucint.inf.pred requires that lambda.z has been estimated (i.e., that the terminal slope is calculable from the data window).

The .dose variants use dose-aware interpolation (interp.extrap.conc.dose()) at the interval start and end. This matters when the interval boundary coincides with a dose time — the .dose variant correctly handles the before/after concentration jump.

# All partial AUC variants over a single window
all_partial <- data.frame(
  start                 = 0,
  end                   = 8,
  aucint.last           = TRUE,
  aucint.all            = TRUE,
  aucint.inf.obs        = TRUE,
  aucint.inf.pred       = TRUE,
  aucint.last.dose      = TRUE,
  aucint.all.dose       = TRUE,
  aucint.inf.obs.dose   = TRUE,
  aucint.inf.pred.dose  = TRUE
)

o_nca_all_partial <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = all_partial))
as.data.frame(o_nca_all_partial) |>
  filter(grepl("^aucint", PPTESTCD)) |>
  select(PPTESTCD, PPORRES)

# A tibble: 8 × 2
  PPTESTCD             PPORRES
  <chr>                  <dbl>
1 aucint.last             65.3
2 aucint.last.dose        65.3
3 aucint.all              65.3
4 aucint.all.dose         65.3
5 aucint.inf.obs          65.3
6 aucint.inf.obs.dose     65.3
7 aucint.inf.pred         65.3
8 aucint.inf.pred.dose    65.3

4.3 Percent extrapolation (%AUCextrap)

When using aucinf, you should check what fraction was extrapolated beyond the last observation. A high aucpext means the terminal phase was poorly characterised.

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

o_nca_pext <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = pext_interval))
as.data.frame(o_nca_pext) |>
  filter(grepl("^auc", PPTESTCD)) |>
  select(PPTESTCD, PPORRES)

# A tibble: 5 × 2
  PPTESTCD     PPORRES
  <chr>          <dbl>
1 auclast        147. 
2 aucinf.obs     215. 
3 aucinf.pred    215. 
4 aucpext.obs     31.5
5 aucpext.pred    31.5

The default threshold is max.aucinf.pext = 20 (%). Results where aucpext > 20% are flagged with an exclude message. Change the threshold via options:

# Stricter: flag if more than 10% is extrapolated
o_data_strict <- PKNCAdata(o_conc, o_dose, intervals = pext_interval,
                            options = list(max.aucinf.pext = 10))
o_nca_strict  <- pk.nca(o_data_strict)
as.data.frame(o_nca_strict) |>
  filter(PPTESTCD == "aucinf.obs") |>
  select(PPTESTCD, PPORRES, exclude)

# A tibble: 1 × 3
  PPTESTCD   PPORRES exclude
  <chr>        <dbl> <chr>  
1 aucinf.obs    215. <NA>

4.4 Integration methods

The integration method controls how the area of each trapezoid is computed between consecutive timepoints.

# Visual comparison of the three methods on one subject
methods <- c("linear", "lin-log", "lin up/log down")

results <- lapply(methods, function(m) {
  o <- pk.nca(PKNCAdata(o_conc, o_dose,
                        intervals = data.frame(start=0, end=Inf, auclast=TRUE),
                        options   = list(auc.method = m)))
  as.data.frame(o) |>
    filter(PPTESTCD == "auclast") |>
    mutate(method = m)
}) |> bind_rows()

results |> select(method, PPORRES) |>
  rename(auclast = PPORRES)

# A tibble: 3 × 2
  method          auclast
  <chr>             <dbl>
1 linear             149.
2 lin-log            147.
3 lin up/log down    147.

4.4.1 Method details

Linear trapezoidal ("linear")

Uses the standard trapezoidal rule throughout: \[\text{AUC}_{t_i \to t_{i+1}} = \frac{(C_i + C_{i+1})}{2} \times (t_{i+1} - t_i)\]

Overestimates during the descending phase (gives too much weight to the higher concentration).

Lin-log ("lin-log")

Uses linear integration from start up to Tmax, and log-linear integration from Tmax onward: \[\text{AUC}_{t_i \to t_{i+1}} = \frac{(C_i - C_{i+1})}{\ln C_i - \ln C_{i+1}} \times (t_{i+1} - t_i) \quad \text{(post-Tmax)}\]

The switch point is Tmax (not whether concentrations are rising or falling), so any post-Tmax secondary peak is integrated log-linearly even if concentrations are rising. Falls back to linear for any interval where either endpoint is zero. Not recommended — "lin up/log down" is strictly better for nearly all use cases as it switches on actual direction rather than Tmax.

Lin up / log down ("lin up/log down") — default

Hybrid: linear trapezoidal on the ascending phase (when $C_{i+1} \geq C_i$), log-linear on the descending phase (when $C_{i+1} < C_i$). Best of both worlds for most PK profiles.

# Visualise the three profiles for one subject
d_plot <- d_one |>
  filter(conc > 0) |>
  arrange(time)

# Illustrate the interpolated concentration between two points
t_seq <- seq(min(d_plot$time), max(d_plot$time), length.out = 200)

ggplot(d_plot, aes(x = time, y = conc)) +
  geom_line(colour = "steelblue", linewidth = 1) +
  geom_point(size = 3, colour = "steelblue") +
  geom_area(alpha = 0.15, fill = "steelblue") +
  labs(title = "Concentration-time profile (shaded area = AUClast)",
       x = "Time (h)", y = "Concentration (mg/L)") +
  theme_minimal()

4.4.2 When to use which method

Study type	Recommended method	Notes
Most oral/extravascular	`"lin up/log down"` (default)	Linear on ascending phase, log-linear on declining phase
IV bolus	`"lin up/log down"` (default)	Profile is entirely declining, so log-linear is used throughout — equivalent to `"lin-log"` for pure bolus but without the Tmax ambiguity
IV infusion with smooth decline	`"lin up/log down"`	Concentrations rise during infusion (linear) then fall after end of infusion (log-linear)
Regulatory (some agencies)	`"linear"`	Some health authorities require the linear trapezoidal rule throughout
Highly irregular profiles with zeros	`"linear"`	Log-linear is undefined when either endpoint is zero; `"linear"` is the safe fallback
Never recommended	`"lin-log"`	Switches at Tmax rather than on direction of change — gives wrong method for post-Tmax secondary peaks

4.5 AUMC — area under the first moment curve

The AUMC is used to compute MRT. It weights concentrations by time: \[\text{AUMC} = \int_0^{t} t \cdot C(t) \, dt\]

aumc_interval <- data.frame(
  start        = 0,
  end          = Inf,
  aumclast     = TRUE,
  aumcinf.obs  = TRUE
)

o_nca_aumc <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = aumc_interval))
as.data.frame(o_nca_aumc) |>
  filter(grepl("^aumc", PPTESTCD)) |>
  select(PPTESTCD, PPORRES)

# A tibble: 2 × 2
  PPTESTCD    PPORRES
  <chr>         <dbl>
1 aumclast      1499.
2 aumcinf.obs   4546.

4.6 AUC above a threshold (`aucabove.*`)

aucabove.* computes the area under the curve above a reference concentration — useful for quantifying time above a minimum effective concentration or below a toxicity threshold.

Parameter	Reference concentration
`aucabove.trough.all`	Ctrough (concentration at end of interval)
`aucabove.predose.all`	Cpredose (concentration at interval start)

above_interval <- data.frame(
  start              = 0,
  end                = 24,
  aucabove.trough.all  = TRUE,
  aucabove.predose.all = TRUE,
  ctrough              = TRUE,
  cstart               = TRUE
)

o_nca_above <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = above_interval))

as.data.frame(o_nca_above) |>
  filter(PPTESTCD %in% c("aucabove.trough.all", "aucabove.predose.all", "ctrough", "cstart")) |>
  select(PPTESTCD, PPORRES)

# A tibble: 4 × 2
  PPTESTCD             PPORRES
  <chr>                  <dbl>
1 ctrough                NA   
2 cstart                  0.74
3 aucabove.predose.all   83.4 
4 aucabove.trough.all    NA

4.7 Time above a threshold (`time_above`)

time_above computes the total duration (in time units) for which the concentration exceeds a specified threshold. The threshold is set via the conc_above column in the intervals data frame.

# Time above 2 mg/L
time_above_interval <- data.frame(
  start      = 0,
  end        = Inf,
  time_above = TRUE,
  conc_above = 2       # threshold concentration (same units as your data)
)

o_nca_ta <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = time_above_interval))

as.data.frame(o_nca_ta) |>
  filter(PPTESTCD == "time_above") |>
  select(PPTESTCD, PPORRES)

# A tibble: 1 × 2
  PPTESTCD   PPORRES
  <chr>        <dbl>
1 time_above    24.2

4.8 Total dose (`totdose`)

totdose is the total amount administered within the analysis interval — it is extracted from the dose object rather than computed from concentrations. Useful as a reference column in your results data frame.

totdose_interval <- data.frame(
  start    = 0,
  end      = Inf,
  totdose  = TRUE,
  auclast  = TRUE
)

o_nca_td <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = totdose_interval))

as.data.frame(o_nca_td) |>
  filter(PPTESTCD %in% c("totdose", "auclast")) |>
  select(PPTESTCD, PPORRES)

# A tibble: 2 × 2
  PPTESTCD PPORRES
  <chr>      <dbl>
1 auclast     147.
2 totdose     320.

4.9 AUMC variants

The area under the first-moment curve (AUMC) is used to calculate MRT.

Parameter	Meaning
`aumclast`	AUMC from 0 to last measurable concentration
`aumcall`	AUMC from 0 to last, treating BLQ as 0
`aumcinf.obs`	AUMC extrapolated to ∞, observed Clast
`aumcinf.pred`	AUMC extrapolated to ∞, predicted Clast

aumc_interval <- data.frame(
  start         = 0,
  end           = Inf,
  aumclast      = TRUE,
  aumcall       = TRUE,
  aumcinf.obs   = TRUE,
  aumcinf.pred  = TRUE
)

o_nca_aumc <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = aumc_interval))

as.data.frame(o_nca_aumc) |>
  filter(grepl("^aumc", PPTESTCD)) |>
  select(PPTESTCD, PPORRES)

# A tibble: 4 × 2
  PPTESTCD     PPORRES
  <chr>          <dbl>
1 aumclast       1499.
2 aumcall        1499.
3 aumcinf.obs    4546.
4 aumcinf.pred   4546.

4.10 Cav over a specific interval (`cav.int.*`)

cav.int.* computes the average concentration over a specified window using the trapezoidal rule, without requiring a full dosing-interval design.

Parameter	Window
`cav.int.last`	0 to last measurable
`cav.int.all`	0 to last, BLQ = 0
`cav.int.inf.obs`	0 to ∞, observed Clast
`cav.int.inf.pred`	0 to ∞, predicted Clast

cav_interval <- data.frame(
  start             = 0,
  end               = Inf,
  cav.int.last      = TRUE,
  cav.int.all       = TRUE,
  cav.int.inf.obs   = TRUE,
  cav.int.inf.pred  = TRUE
)

o_nca_cav <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = cav_interval))

as.data.frame(o_nca_cav) |>
  filter(grepl("^cav.int", PPTESTCD)) |>
  select(PPTESTCD, PPORRES)

# A tibble: 4 × 2
  PPTESTCD         PPORRES
  <chr>              <dbl>
1 cav.int.last           0
2 cav.int.all            0
3 cav.int.inf.obs        0
4 cav.int.inf.pred       0

4.11 Concentration interpolation at interval boundaries

When a requested interval boundary (e.g., end = 8) falls between two observed timepoints, PKNCA interpolates the concentration at that boundary before computing AUC.

The interpolation method matches the AUC method: - "linear" → linear interpolation - "lin up/log down" → log-linear interpolation on the descending phase

# end=5h falls between t=4 and t=7.02 in the Theoph dataset
interp_interval <- data.frame(start = 0, end = 5, auclast = TRUE)
o_nca_interp <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = interp_interval))
as.data.frame(o_nca_interp) |>
  filter(PPTESTCD == "auclast") |>
  select(start, end, PPTESTCD, PPORRES)

# A tibble: 1 × 4
  start   end PPTESTCD PPORRES
  <dbl> <dbl> <chr>      <dbl>
1     0     5 auclast     32.1

pkgdown reference: PKNCAconc() · PKNCAdose() · PKNCAdata() · pk.nca() · interp.extrap.conc.dose() · interp.extrap.conc()

--- title: "AUC Types and Integration Methods" --- ```{r setup, include=FALSE} library(PKNCA) library(dplyr) library(ggplot2) conflicted::conflicts_prefer(dplyr::filter, dplyr::select, .quiet = TRUE) # Shared dataset for this page: oral theophylline, subject 1 d_one <- as.data.frame(Theoph) |> filter(Subject == "1") |> rename(time = Time, subject = Subject) d_dose <- data.frame(subject = "1", dose = Theoph$Dose[1] * Theoph$Wt[1], time = 0) o_conc <- PKNCAconc(d_one, conc ~ time | subject) o_dose <- PKNCAdose(d_dose, dose ~ time | subject, route = "extravascular") ``` ## AUC types PKNCA offers four families of AUC, each answering a different question: ```{mermaid} flowchart LR A["AUClast\n0 → last measurable"] B["AUCall\n0 → last, zeros for BLQ"] C["AUCinf.obs\n0 → ∞ (observed Clast)"] D["AUCinf.pred\n0 → ∞ (predicted Clast)"] E["AUCint / partial\n0 → t (any t)"] ``` | Parameter | End point | BLQ treatment | When to use | |---|---|---|---| | `auclast` | Last measurable concentration | BLQs after last non-BLQ are ignored | Default; most studies | | `aucall` | Last measured time point | Post-last-measurable BLQs treated as 0 | When you want to include the BLQ tail | | `aucinf.obs` | Extrapolated to ∞ (using observed Clast) | — | When half-life is reliable | | `aucinf.pred` | Extrapolated to ∞ (using predicted Clast from λz fit) | — | When Clast is noisy | | `aucint.*` | Any user-defined time window | — | Partial AUC, bioequivalence | ### AUClast vs AUCall ```{r} auc_compare <- data.frame( start = 0, end = Inf, auclast = TRUE, aucall = TRUE, aucinf.obs = TRUE ) o_data <- PKNCAdata(o_conc, o_dose, intervals = auc_compare) o_nca <- pk.nca(o_data) as.data.frame(o_nca) |> filter(PPTESTCD %in% c("auclast", "aucall", "aucinf.obs", "aucpext.obs")) |> select(PPTESTCD, PPORRES) ``` > `aucall` ≥ `auclast` when there are post-last-measurable BLQ timepoints, since those are treated as 0 and add a small triangle to the AUC. --- ## Partial AUC (AUCint) For bioequivalence or exposure-in-a-window calculations, use `aucint.*` parameters. These calculate AUC over an exact time window, interpolating concentrations at the boundaries if needed. ```{r} # AUC from 0 to 4h and 0 to 12h on the same profile partial_intervals <- data.frame( start = c(0, 0), end = c(4, 12), aucint.last = TRUE, # AUC to the last obs within window (or interpolated boundary) aucint.inf.obs = FALSE ) o_data_partial <- PKNCAdata(o_conc, o_dose, intervals = partial_intervals) o_nca_partial <- pk.nca(o_data_partial) as.data.frame(o_nca_partial) |> filter(PPTESTCD == "aucint.last") |> select(start, end, PPTESTCD, PPORRES) ``` **All partial AUC variants:** | Parameter | End concentration | Dose-aware boundary | Extrapolation | |---|---|---|---| | `aucint.last` | Last observed in window | No | None | | `aucint.all` | Last observed, BLQs as 0 | No | None | | `aucint.inf.obs` | Extrapolated to ∞, observed Clast | No | λz-based tail | | `aucint.inf.pred` | Extrapolated to ∞, predicted Clast | No | λz-based tail | | `aucint.last.dose` | Same as `.last` | **Yes** | None | | `aucint.all.dose` | Same as `.all` | **Yes** | None | | `aucint.inf.obs.dose` | Same as `.inf.obs` | **Yes** | λz-based tail | | `aucint.inf.pred.dose` | Same as `.inf.pred` | **Yes** | λz-based tail | > **Note:** `aucint.inf.pred` requires that `lambda.z` has been estimated (i.e., that the terminal slope is calculable from the data window). The `.dose` variants use **dose-aware interpolation** (`interp.extrap.conc.dose()`) at the interval start and end. This matters when the interval boundary coincides with a dose time — the `.dose` variant correctly handles the before/after concentration jump. ```{r} # All partial AUC variants over a single window all_partial <- data.frame( start = 0, end = 8, aucint.last = TRUE, aucint.all = TRUE, aucint.inf.obs = TRUE, aucint.inf.pred = TRUE, aucint.last.dose = TRUE, aucint.all.dose = TRUE, aucint.inf.obs.dose = TRUE, aucint.inf.pred.dose = TRUE ) o_nca_all_partial <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = all_partial)) as.data.frame(o_nca_all_partial) |> filter(grepl("^aucint", PPTESTCD)) |> select(PPTESTCD, PPORRES) ``` --- ## Percent extrapolation (%AUCextrap) When using `aucinf`, you should check what fraction was extrapolated beyond the last observation. A high `aucpext` means the terminal phase was poorly characterised. ```{r} pext_interval <- data.frame( start = 0, end = Inf, auclast = TRUE, aucinf.obs = TRUE, aucpext.obs = TRUE, aucpext.pred = TRUE ) o_nca_pext <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = pext_interval)) as.data.frame(o_nca_pext) |> filter(grepl("^auc", PPTESTCD)) |> select(PPTESTCD, PPORRES) ``` The default threshold is `max.aucinf.pext = 20` (%). Results where `aucpext > 20%` are flagged with an `exclude` message. Change the threshold via options: ```{r} # Stricter: flag if more than 10% is extrapolated o_data_strict <- PKNCAdata(o_conc, o_dose, intervals = pext_interval, options = list(max.aucinf.pext = 10)) o_nca_strict <- pk.nca(o_data_strict) as.data.frame(o_nca_strict) |> filter(PPTESTCD == "aucinf.obs") |> select(PPTESTCD, PPORRES, exclude) ``` --- ## Integration methods The integration method controls how the area of each trapezoid is computed between consecutive timepoints. ```{r} # Visual comparison of the three methods on one subject methods <- c("linear", "lin-log", "lin up/log down") results <- lapply(methods, function(m) { o <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = data.frame(start=0, end=Inf, auclast=TRUE), options = list(auc.method = m))) as.data.frame(o) |> filter(PPTESTCD == "auclast") |> mutate(method = m) }) |> bind_rows() results |> select(method, PPORRES) |> rename(auclast = PPORRES) ``` ### Method details **Linear trapezoidal (`"linear"`)** Uses the standard trapezoidal rule throughout: $$\text{AUC}_{t_i \to t_{i+1}} = \frac{(C_i + C_{i+1})}{2} \times (t_{i+1} - t_i)$$ Overestimates during the descending phase (gives too much weight to the higher concentration). **Lin-log (`"lin-log"`)** Uses **linear** integration from start up to Tmax, and **log-linear** integration from Tmax onward: $$\text{AUC}_{t_i \to t_{i+1}} = \frac{(C_i - C_{i+1})}{\ln C_i - \ln C_{i+1}} \times (t_{i+1} - t_i) \quad \text{(post-Tmax)}$$ The switch point is Tmax (not whether concentrations are rising or falling), so any post-Tmax secondary peak is integrated log-linearly even if concentrations are rising. Falls back to linear for any interval where either endpoint is zero. Not recommended — `"lin up/log down"` is strictly better for nearly all use cases as it switches on actual direction rather than Tmax. **Lin up / log down (`"lin up/log down"`) — default** Hybrid: linear trapezoidal on the ascending phase (when $C_{i+1} \geq C_i$), log-linear on the descending phase (when $C_{i+1} < C_i$). Best of both worlds for most PK profiles. ```{r} # Visualise the three profiles for one subject d_plot <- d_one |> filter(conc > 0) |> arrange(time) # Illustrate the interpolated concentration between two points t_seq <- seq(min(d_plot$time), max(d_plot$time), length.out = 200) ggplot(d_plot, aes(x = time, y = conc)) + geom_line(colour = "steelblue", linewidth = 1) + geom_point(size = 3, colour = "steelblue") + geom_area(alpha = 0.15, fill = "steelblue") + labs(title = "Concentration-time profile (shaded area = AUClast)", x = "Time (h)", y = "Concentration (mg/L)") + theme_minimal() ``` ### When to use which method | Study type | Recommended method | Notes | |---|---|---| | Most oral/extravascular | `"lin up/log down"` (default) | Linear on ascending phase, log-linear on declining phase | | IV bolus | `"lin up/log down"` (default) | Profile is entirely declining, so log-linear is used throughout — equivalent to `"lin-log"` for pure bolus but without the Tmax ambiguity | | IV infusion with smooth decline | `"lin up/log down"` | Concentrations rise during infusion (linear) then fall after end of infusion (log-linear) | | Regulatory (some agencies) | `"linear"` | Some health authorities require the linear trapezoidal rule throughout | | Highly irregular profiles with zeros | `"linear"` | Log-linear is undefined when either endpoint is zero; `"linear"` is the safe fallback | | Never recommended | `"lin-log"` | Switches at Tmax rather than on direction of change — gives wrong method for post-Tmax secondary peaks | --- ## AUMC — area under the first moment curve The AUMC is used to compute MRT. It weights concentrations by time: $$\text{AUMC} = \int_0^{t} t \cdot C(t) \, dt$$ ```{r} aumc_interval <- data.frame( start = 0, end = Inf, aumclast = TRUE, aumcinf.obs = TRUE ) o_nca_aumc <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = aumc_interval)) as.data.frame(o_nca_aumc) |> filter(grepl("^aumc", PPTESTCD)) |> select(PPTESTCD, PPORRES) ``` --- ## AUC above a threshold (`aucabove.*`) `aucabove.*` computes the area under the curve above a reference concentration — useful for quantifying time above a minimum effective concentration or below a toxicity threshold. | Parameter | Reference concentration | |---|---| | `aucabove.trough.all` | Ctrough (concentration at end of interval) | | `aucabove.predose.all` | Cpredose (concentration at interval start) | ```{r} above_interval <- data.frame( start = 0, end = 24, aucabove.trough.all = TRUE, aucabove.predose.all = TRUE, ctrough = TRUE, cstart = TRUE ) o_nca_above <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = above_interval)) as.data.frame(o_nca_above) |> filter(PPTESTCD %in% c("aucabove.trough.all", "aucabove.predose.all", "ctrough", "cstart")) |> select(PPTESTCD, PPORRES) ``` --- ## Time above a threshold (`time_above`) `time_above` computes the total duration (in time units) for which the concentration exceeds a specified threshold. The threshold is set via the `conc_above` column in the intervals data frame. ```{r} # Time above 2 mg/L time_above_interval <- data.frame( start = 0, end = Inf, time_above = TRUE, conc_above = 2 # threshold concentration (same units as your data) ) o_nca_ta <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = time_above_interval)) as.data.frame(o_nca_ta) |> filter(PPTESTCD == "time_above") |> select(PPTESTCD, PPORRES) ``` --- ## Total dose (`totdose`) `totdose` is the total amount administered within the analysis interval — it is extracted from the dose object rather than computed from concentrations. Useful as a reference column in your results data frame. ```{r} totdose_interval <- data.frame( start = 0, end = Inf, totdose = TRUE, auclast = TRUE ) o_nca_td <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = totdose_interval)) as.data.frame(o_nca_td) |> filter(PPTESTCD %in% c("totdose", "auclast")) |> select(PPTESTCD, PPORRES) ``` --- ## AUMC variants The **area under the first-moment curve** (AUMC) is used to calculate MRT. | Parameter | Meaning | |---|---| | `aumclast` | AUMC from 0 to last measurable concentration | | `aumcall` | AUMC from 0 to last, treating BLQ as 0 | | `aumcinf.obs` | AUMC extrapolated to ∞, observed Clast | | `aumcinf.pred` | AUMC extrapolated to ∞, predicted Clast | ```{r} aumc_interval <- data.frame( start = 0, end = Inf, aumclast = TRUE, aumcall = TRUE, aumcinf.obs = TRUE, aumcinf.pred = TRUE ) o_nca_aumc <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = aumc_interval)) as.data.frame(o_nca_aumc) |> filter(grepl("^aumc", PPTESTCD)) |> select(PPTESTCD, PPORRES) ``` --- ## Cav over a specific interval (`cav.int.*`) `cav.int.*` computes the average concentration over a specified window using the trapezoidal rule, without requiring a full dosing-interval design. | Parameter | Window | |---|---| | `cav.int.last` | 0 to last measurable | | `cav.int.all` | 0 to last, BLQ = 0 | | `cav.int.inf.obs` | 0 to ∞, observed Clast | | `cav.int.inf.pred` | 0 to ∞, predicted Clast | ```{r} cav_interval <- data.frame( start = 0, end = Inf, cav.int.last = TRUE, cav.int.all = TRUE, cav.int.inf.obs = TRUE, cav.int.inf.pred = TRUE ) o_nca_cav <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = cav_interval)) as.data.frame(o_nca_cav) |> filter(grepl("^cav.int", PPTESTCD)) |> select(PPTESTCD, PPORRES) ``` --- ## Concentration interpolation at interval boundaries When a requested interval boundary (e.g., `end = 8`) falls between two observed timepoints, PKNCA interpolates the concentration at that boundary before computing AUC. The interpolation method matches the AUC method: - `"linear"` → linear interpolation - `"lin up/log down"` → log-linear interpolation on the descending phase ```{r} # end=5h falls between t=4 and t=7.02 in the Theoph dataset interp_interval <- data.frame(start = 0, end = 5, auclast = TRUE) o_nca_interp <- pk.nca(PKNCAdata(o_conc, o_dose, intervals = interp_interval)) as.data.frame(o_nca_interp) |> filter(PPTESTCD == "auclast") |> select(start, end, PPTESTCD, PPORRES) ``` --- ::: {.callout-note icon=false appearance="minimal"} **pkgdown reference:** [PKNCAconc()](https://humanpred.github.io/pknca/reference/PKNCAconc.html) · [PKNCAdose()](https://humanpred.github.io/pknca/reference/PKNCAdose.html) · [PKNCAdata()](https://humanpred.github.io/pknca/reference/PKNCAdata.html) · [pk.nca()](https://humanpred.github.io/pknca/reference/pk.nca.html) · [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) :::