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.)

```
##
## Attaching package: 'dplyr'
```

```
## The following objects are masked from 'package:stats':
##
## filter, lag
```

```
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
```

```
## Load the PK concentration data
d_conc <-
as.data.frame(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.)
conc_obj <-
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.)
dose_obj <-
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.
data_obj <- PKNCAdata(conc_obj, dose_obj)
## Calculate the NCA parameters
results_obj <- pk.nca(data_obj)
## Summarize the results
summary(results_obj)
```

```
## start end N auclast cmax tmax half.life aucinf.obs
## 0 24 12 74.6 [24.3] . . . .
## 0 Inf 12 . 8.65 [17.0] 1.14 [0.630, 3.55] 8.18 [2.12] 115 [28.4]
##
## Caption: auclast, cmax, aucinf.obs: geometric mean and geometric coefficient of variation; tmax: median and range; half.life: arithmetic mean and standard deviation; N: number of subjects
```

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 quantification 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:

```
## $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
##
## $keep_interval_cols
## NULL
##
## $min.hl.points
## [1] 3
##
## $min.span.ratio
## [1] 2
##
## $max.aucinf.pext
## [1] 20
##
## $min.hl.r.squared
## [1] 0.9
##
## $progress
## [1] TRUE
##
## $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 c0 cmax cmin tmax tlast tfirst clast.obs
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## cl.last cl.all f mrt.last mrt.iv.last vss.last vss.iv.last cav
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## cav.int.last cav.int.all ctrough cstart ptr tlag deg.fluc swing ceoi
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## aucabove.predose.all aucabove.trough.all count_conc totdose ae clr.last
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE
## clr.obs clr.pred fe sparse_auclast sparse_auc_se sparse_auc_df time_above
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## aucivlast aucivall aucivint.last aucivint.all aucivpbextlast aucivpbextall
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE
## aucivpbextint.last aucivpbextint.all half.life r.squared adj.r.squared
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE TRUE FALSE FALSE
## lambda.z lambda.z.time.first lambda.z.n.points clast.pred span.ratio
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## thalf.eff.last thalf.eff.iv.last kel.last kel.iv.last aucinf.obs aucinf.pred
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE TRUE FALSE
## aumcinf.obs aumcinf.pred aucint.inf.obs aucint.inf.obs.dose aucint.inf.pred
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## aucint.inf.pred.dose aucivinf.obs aucivinf.pred aucivpbextinf.obs
## 1 FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE
## aucivpbextinf.pred aucpext.obs aucpext.pred cl.obs cl.pred mrt.obs mrt.pred
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## mrt.iv.obs mrt.iv.pred mrt.md.obs mrt.md.pred vz.obs vz.pred vss.obs vss.pred
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## vss.iv.obs vss.iv.pred vss.md.obs vss.md.pred cav.int.inf.obs
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## cav.int.inf.pred thalf.eff.obs thalf.eff.pred thalf.eff.iv.obs
## 1 FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE
## thalf.eff.iv.pred kel.obs kel.pred kel.iv.obs kel.iv.pred auclast.dn
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE
## aucall.dn aucinf.obs.dn aucinf.pred.dn aumclast.dn aumcall.dn aumcinf.obs.dn
## 1 FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE
## aumcinf.pred.dn 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
```

And, to reset the current values to the library defaults, run the
function with the default argument set to `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",
description = "geometric mean and geometric coefficient of variation",
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",
description = "median and range",
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",
description = "median and 5th to 95th percentile",
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"),
description = "median and 5th to 95th percentile",
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.)
conc_obj <- 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.)
dose_obj <- PKNCAdose(d_dose_both,
Dose~Time|Study+Subject)
# Perform and summarize the PK data as previously described
data_obj <- PKNCAdata(conc_obj, dose_obj)
results_obj <- pk.nca(data_obj)
summary(results_obj)
```

All NCA calculations require the interval 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 treatment– 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 | c0 | cmax | cmin | tmax | tlast | tfirst | clast.obs | cl.last | cl.all | f | mrt.last | mrt.iv.last | vss.last | vss.iv.last | cav | cav.int.last | cav.int.all | ctrough | cstart | ptr | tlag | deg.fluc | swing | ceoi | aucabove.predose.all | aucabove.trough.all | count_conc | totdose | ae | clr.last | clr.obs | clr.pred | fe | sparse_auclast | sparse_auc_se | sparse_auc_df | time_above | aucivlast | aucivall | aucivint.last | aucivint.all | aucivpbextlast | aucivpbextall | aucivpbextint.last | aucivpbextint.all | half.life | r.squared | adj.r.squared | lambda.z | lambda.z.time.first | lambda.z.n.points | clast.pred | span.ratio | 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 | aucivinf.obs | aucivinf.pred | aucivpbextinf.obs | aucivpbextinf.pred | 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 | cav.int.inf.obs | cav.int.inf.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 | auclast.dn | aucall.dn | aucinf.obs.dn | aucinf.pred.dn | aumclast.dn | aumcall.dn | aumcinf.obs.dn | aumcinf.pred.dn | cmax.dn | cmin.dn | clast.obs.dn | clast.pred.dn | cav.dn | ctrough.dn |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

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 | 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 | 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 | 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 | 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 |

For multiple-dose studies, PKNCA selects one group at a time and
compares the concentration and dosing times. When there is a
concentration 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`

`## [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`

`## [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. 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.

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

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

When computing NCA using actual times, grouping by start and end time
in summaries (see layer) is less helpful because everyone could have
different start and end times. So, you may keep the interval columns
using the option `"keep_interval_cols"`

as follows (where
“dosetype” must be a column name in the intervals):

When NCA has been calculated, you can summarize the results with the
`summary()`

function.

By default, it will count the number of unique subjects
(`N`

) in the summary, and when the number of subjects differs
from the number of measurements included in a summary (`n`

),
it will summarize `n`

for the given parameters. Note that
counting of “n” includes all non-missing values that were not excluded
from summarization; this will included all zeros that are e.g. excluded
from geometric statistics.

Edge cases like two unique subjects where one has an excluded value
and one has duplicated values (`N = 2`

and `n = 2`

even though both measurements come from a single subject) are to be
handled by the user.