PKNCA provides functions to complete noncompartmental analysis (NCA) for pharmacokinetic (PK) data. Its intent is to provide a complete R-based solution enabling data provenance for NCA including tracking data cleaning, enabling calculations, exporting results, and reporting. The library is designed to give a reasonable answer without user intervention (load, calculate, and summarize), but it allows the user to override the automatic selections at any point.

The library design is modular to allow expansion based on needs unforseen by the authors including new NCA parameters, novel data cleaning methods, and modular summarization decisions. Expanding the library will be discussed in a separate vignette.

The simplest analysis requires concentration and dosing data, then five function calls can provide summarized results. (Please note that this and the other examples in this document are intended to show the typical workflow, but they are not intended to run directly. For an example to run directly, please see the theophylline example.)

```
library(PKNCA)
library(dplyr, quietly=TRUE)
## Load the PK concentration data
d.conc <- datasets::Theoph %>%
mutate(Subject=as.numeric(as.character(Subject)))
## Generate the dosing data
d.dose <- d.conc[d.conc$Time == 0,]
d.dose$Time <- 0
## Create a concentration object specifying the concentration, time, and
## subject columns. (Note that any number of grouping levels is
## supported; you are not restricted to just grouping by subject.)
my.conc <- PKNCAconc(d.conc,
conc~Time|Subject)
## Create a dosing object specifying the dose, time, and subject
## columns. (Note that the grouping factors should be the same as or a
## subset of the grouping factors for concentration, and the grouping
## columns must have the same names between concentration and dose
## objects.)
my.dose <- PKNCAdose(d.dose,
Dose~Time|Subject)
## Combine the concentration and dosing information both to
## automatically define the intervals for NCA calculation and provide
## doses for calculations requiring dose.
my.data <- PKNCAdata(my.conc, my.dose)
## Calculate the NCA parameters
my.results <- pk.nca(my.data)
## Summarize the results
summary(my.results)
```

```
## start end N auclast cmax tmax half.life
## 1 0 24 12 74.6 [24.3] . . .
## 2 0 Inf 12 . 8.65 [17.0] 1.14 [0.630, 3.55] 8.18 [2.12]
## aucinf.obs
## 1 .
## 2 115 [28.4]
```

After loading data, it must be in the right form. The minimum requirements are that concentration, dose, and time must all be numeric (and not factors). Grouping variables have no specific requirements; they can be any mode.

Values below the limit of quantificaiton are coded as zeros (`0`

), and missing values are coded as `NA`

.

Different organizations have different requirements for computation and summarization of NCA. Options for how to perform calculations and summaries are handled by the `PKNCA.options`

command.

Default options have been set to commonly-used standard parameters. The current value for options can be found by running the command with no arguments:

`PKNCA.options()`

```
## $adj.r.squared.factor
## [1] 1e-04
##
## $max.missing
## [1] 0.5
##
## $auc.method
## [1] "lin up/log down"
##
## $conc.na
## [1] "drop"
##
## $conc.blq
## $conc.blq$first
## [1] "keep"
##
## $conc.blq$middle
## [1] "drop"
##
## $conc.blq$last
## [1] "keep"
##
##
## $first.tmax
## [1] TRUE
##
## $allow.tmax.in.half.life
## [1] FALSE
##
## $min.hl.points
## [1] 3
##
## $min.span.ratio
## [1] 2
##
## $max.aucinf.pext
## [1] 20
##
## $min.hl.r.squared
## [1] 0.9
##
## $tau.choices
## [1] NA
##
## $single.dose.aucs
## start end auclast aucall aumclast aumcall aucint.last aucint.last.dose
## 1 0 24 TRUE FALSE FALSE FALSE FALSE FALSE
## 2 0 Inf FALSE FALSE FALSE FALSE FALSE FALSE
## aucint.all aucint.all.dose auclast.dn aucall.dn aumclast.dn aumcall.dn
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE
## cmax cmin tmax tlast tfirst clast.obs cl.last cl.all f mrt.last
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## mrt.iv.last vss.last vss.iv.last cav ctrough ptr tlag deg.fluc
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## swing ceoi ae clr.last clr.obs clr.pred fe half.life r.squared
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## adj.r.squared lambda.z lambda.z.time.first lambda.z.n.points clast.pred
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## span.ratio cmax.dn cmin.dn clast.obs.dn clast.pred.dn cav.dn ctrough.dn
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## thalf.eff.last thalf.eff.iv.last kel.last kel.iv.last aucinf.obs
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE TRUE
## aucinf.pred aumcinf.obs aumcinf.pred aucint.inf.obs aucint.inf.obs.dose
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## aucint.inf.pred aucint.inf.pred.dose aucinf.obs.dn aucinf.pred.dn
## 1 FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE
## aumcinf.obs.dn aumcinf.pred.dn aucpext.obs aucpext.pred cl.obs cl.pred
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE
## mrt.obs mrt.pred mrt.iv.obs mrt.iv.pred mrt.md.obs mrt.md.pred vz.obs
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## vz.pred vss.obs vss.pred vss.iv.obs vss.iv.pred vss.md.obs vss.md.pred
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## vd.obs vd.pred thalf.eff.obs thalf.eff.pred thalf.eff.iv.obs
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## thalf.eff.iv.pred kel.obs kel.pred kel.iv.obs kel.iv.pred
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
```

And, to reset the current values to the library defaults, run the function with the default argument set to `TRUE`

.

`PKNCA.options(default=TRUE)`

Each of the options is documented where it is used; for example, the first.tmax option is documented in the `pk.calc.tmax`

function.

On top of methods of calculation, summarization method preferences differ. Typical summarization preferences include selection of the measurement of central tendency and dispersion, handling of missing values, handling of values below the limit of quantification, and more. Beyond the method for summarization, presentation is managed through user preferences. Presentation is typically controlled by rounding to either a defined number of decimal places or significant figures.

An example is that C_{max} may be summarized by the geometric mean with the geometric CV using three significant figures, and having a summary result requires that at least half of the available values are present (not missing). The code below will set this example.

```
PKNCA.set.summary(name="cmax",
point=business.geomean,
spread=business.geocv,
rounding=list(signif=3))
```

Another example is that T_{max} is usually summarized by the median and range, and as measurements are often taken with minute resolution and recorded in hours, reporting is usually to the second decimal place.

```
PKNCA.set.summary(name="tmax",
point=business.median,
spread=business.range,
rounding=list(round=2))
```

If the functions or default rounding options provided in the library do not meet the summarization needs, a user-supplied function can be used for rounding.

```
median_na <- function(x) {
median(x, na.rm=TRUE)
}
quantprob_na <- function(x) {
quantile(x, probs=c(0.05, 0.95), na.rm=TRUE)
}
PKNCA.set.summary(name="auclast",
point=median_na,
spread=quantprob_na,
rounding=list(signif=3))
```

In some cases multiple parameters may need the same summary functions (as often occurs with simulated data). Many parameters can be set simultaneously by specifying a vector of `name`

s.

```
median_na <- function(x) {
median(x, na.rm=TRUE)
}
quantprob_na <- function(x) {
quantile(x, probs=c(0.05, 0.95), na.rm=TRUE)
}
PKNCA.set.summary(name=c("auclast", "cmax", "tmax", "half.life", "aucinf.pred"),
point=median_na,
spread=quantprob_na,
rounding=list(signif=3))
```

As described in the quick start, concentration and dose data are generally grouped to identify how to separate the data. Typical groups for concentration data include study, treatment, subject, and analyte. Typical groups for dose data include study, treatment, and subject. By default, summaries are produced based on the concentration groups dropping the subject (so that averages are taken across subjects within the other parameters).

The quick start example can be extended to include multiple analytes as follows. The only difference is the `/analyte`

formula element in the concentration data. The reason for the slash instead of the plus is that the last element before a slash is assumed to be the subject, and as noted before, the subject is (by default) excluded from the summary grouping (so that summaries are grouped by study, treatment, etc., but not by subject).

```
## Generate a faux multi-study, multi-analyte dataset.
d.conc.parent <- d.conc
d.conc.parent$Subject <- as.numeric(as.character(d.conc.parent$Subject))
d.conc.parent$Study <- d.conc.parent$Subject <= 6
d.conc.parent$Analyte <- "Parent"
d.conc.metabolite <- d.conc.parent
d.conc.metabolite$conc <- d.conc.metabolite$conc/2
d.conc.metabolite$Analyte <- "Metabolite"
d.conc.both <- rbind(d.conc.parent, d.conc.metabolite)
d.conc.both <- d.conc.both[with(d.conc.both, order(Study, Subject, Time, Analyte)),]
d.dose.both <- d.conc.both[d.conc.both$Time == 0 & d.conc.both$Analyte %in% "Parent",
c("Study", "Subject", "Dose", "Time")]
## Create a concentration object specifying the concentration, time,
## study, and subject columns. (Note that any number of grouping
## levels is supporting; you are not restricted to this list.)
my.conc <- PKNCAconc(d.conc.both,
conc~Time|Study+Subject/Analyte)
## Create a dosing object specifying the dose, time, study, and
## subject columns. (Note that the grouping factors should be a
## subset of the grouping factors for concentration, and the columns
## must have the same names between concentration and dose objects.)
my.dose <- PKNCAdose(d.dose.both,
Dose~Time|Study+Subject)
# Perform and summarize the PK data as previously described
my.data <- PKNCAdata(my.conc, my.dose)
my.results <- pk.nca(my.data)
summary(my.results)
```

All NCA calculations require the inverval over which they are calculated. When the concentration and dosing information are combined to the PKNCAdata object, intervals are automatically determined. The exception to this automatic determination is if the user provides intervals.

When selected either automatically or manually, intervals define at minimum a start time, an end time, and the parameters to be calculated. The parameter list is available from the `get.interval.cols`

function. The parameters requested are specified by setting the entry in a data.frame as requested.

```
intervals <-
data.frame(start=0, end=c(24, Inf),
cmax=c(FALSE, TRUE),
tmax=c(FALSE, TRUE),
auclast=TRUE,
aucinf.obs=c(FALSE, TRUE))
```

Intervals like the above is sufficient for designs with a single type of treatmentâ€“ like single doses. For more complex treatments in a single analysis, like the combination of single and multiple doses, include a treatment column matching the treatment column name from the concentration data set. See the Manual Interval Specification section below for more details.

When choosing which data is used for a calculation, PKNCA will never look beyond the data specified in the group and interval. Groups are defined by the call to the `PKNCAconc`

function, and they will typically define the measurement of a single analyte from a single individual receiving a single treatment. Intervals are subsets within a group by start and end time. PKNCA never examines data outside of the group and interval for standard NCA calculations. As an example, with data from 0 to 48 hours and an interval set to `start`

at 0 and `end`

at 24 with the calculation of `aucinf.obs`

, any data after 24 hours will not be used for the half-life or AUC_{inf} calculations.

A few functions look at data outside of a single interval, but these functions do not look at data outside of a single group, and these functions are typically used during preparation for NCA calculations not for the calculations themselves. Functions that look a group as a whole include `choose.auc.intervals`

, `find.tau`

, and `pk.tss`

.

If intervals are not specified when combining the concentration and dosing data, they will automatically be found from the concentration and dosing data.

Single dose data has a simple interval selection: the option `single.dose.aucs`

is used from the `PKNCA.options`

.

start | end | auclast | aucall | aumclast | aumcall | aucint.last | aucint.last.dose | aucint.all | aucint.all.dose | auclast.dn | aucall.dn | aumclast.dn | aumcall.dn | cmax | cmin | tmax | tlast | tfirst | clast.obs | cl.last | cl.all | f | mrt.last | mrt.iv.last | vss.last | vss.iv.last | cav | ctrough | ptr | tlag | deg.fluc | swing | ceoi | ae | clr.last | clr.obs | clr.pred | fe | half.life | r.squared | adj.r.squared | lambda.z | lambda.z.time.first | lambda.z.n.points | clast.pred | span.ratio | cmax.dn | cmin.dn | clast.obs.dn | clast.pred.dn | cav.dn | ctrough.dn | thalf.eff.last | thalf.eff.iv.last | kel.last | kel.iv.last | aucinf.obs | aucinf.pred | aumcinf.obs | aumcinf.pred | aucint.inf.obs | aucint.inf.obs.dose | aucint.inf.pred | aucint.inf.pred.dose | aucinf.obs.dn | aucinf.pred.dn | aumcinf.obs.dn | aumcinf.pred.dn | aucpext.obs | aucpext.pred | cl.obs | cl.pred | mrt.obs | mrt.pred | mrt.iv.obs | mrt.iv.pred | mrt.md.obs | mrt.md.pred | vz.obs | vz.pred | vss.obs | vss.pred | vss.iv.obs | vss.iv.pred | vss.md.obs | vss.md.pred | vd.obs | vd.pred | thalf.eff.obs | thalf.eff.pred | thalf.eff.iv.obs | thalf.eff.iv.pred | kel.obs | kel.pred | kel.iv.obs | kel.iv.pred |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 24 | TRUE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE |

0 | Inf | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | TRUE | FALSE | TRUE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | TRUE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | TRUE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE |

For multiple-dose studies, PKNCA selects one group at a time and compares the concentration and dosing times. When there is a concentation measurement between doses, an interval row is added. The dosing interval (\(\tau\)) is determined by looking for pattern repeats within the dosing data using the `find.tau`

function.

```
## find.tau can work when all doses have the same interval...
dose.times <- seq(0, 168, by=24)
print(dose.times)
```

`## [1] 0 24 48 72 96 120 144 168`

`PKNCA::find.tau(dose.times)`

`## [1] 24`

```
## or when the doses have mixed intervals (10 and 24 hours).
dose.times <- sort(c(seq(0, 168, by=24),
seq(10, 178, by=24)))
print(dose.times)
```

`## [1] 0 10 24 34 48 58 72 82 96 106 120 130 144 154 168 178`

`PKNCA::find.tau(dose.times)`

`## [1] 24`

After finding \(\tau\), PKNCA will also look after the last dose (or the beginning of the last dosing interval), and two additional intervals may be added:

- one interval for the dosing interval after the beginning of the last dosing interval (if there are concentrations measured in the interval)
- one interval for the half-life after the last dosing interval (if there are concentration more than \(\tau\) after the beginning of the last interval).

One consequence of automatic interval selection is that many rows are generated for intervals; one row is generated per interval per subject. The benefit of the method producing a large number of rows is that it is fully flexible to the actual study results. If a subject has a different schedule than the others for the same treatment (e.g.Â measurements that were nominally scheduled for day 14 occurred on day 13), those differences will be found.

Intervals can also be specified manually. Two use cases are common for manual specification: fully manual (never requesting the automatic intervals) and updating the automatic intervals.

Fully manual intervals can be specified by providing it to the `PKNCAdata`

call.

```
my.intervals <-
data.frame(start=0, end=c(24, Inf),
cmax=c(FALSE, TRUE),
tmax=c(FALSE, TRUE),
auclast=TRUE,
aucinf.obs=c(FALSE, TRUE))
my.data <- PKNCAdata(my.conc, my.dose,
intervals=my.intervals)
```

To update the automatically-selected intervals, extract the intervals, modify them, and put them back.

```
my.data <- PKNCAdata(my.conc, my.dose)
my.intervals <- my.data$intervals
my.intervals$aucinf.obs[1] <- TRUE
my.data$intervals <- my.intervals
```