PKNCA Training Sessions

19 November 2021

Introduction to PKNCA and Basics of Its Use

Creation of these materials were supported by funding from the Metrum Research Group.

Introduction to PKNCA

PKNCA is a tool for calculating noncompartmental analysis (NCA) results for pharmacokinetic (PK) data.

… but, you already knew that or you wouldn’t be here.

PKNCA has several foci:

be regulatory-ready
- it has approximately 100% test coverage.
be reproducible
- it has a focus on being scriptable.
get the right answer or none at all
- it will try to know what you want,
- but all decisions can be overridden, and
- if there is a question that may cause an error or an unanticipated result, either no result will output or an error will be raised.

Enjoy!

I hope that you have a whale of a good time during this training.

(Foreshadowing…)

Some NCA Definitions

C_max: The maximum observed concentration
T_max: The time of the maximum observed concentration
t_last: The time of the last concentration above the limit of quantification
AUC: Area under the concentration-time curve. Some important AUC variants are:
- AUC_last: AUC from time zero to t_last
- AUC_int: AUC from time zero to the end of an interval of time, often extrapolated or interpolated (e.g. AUC_0-24hr)
- AUC_∞: AUC from time zero to t_last then extrapolated from t_last to time infinity using the half life

Dataset Basics

NCA Data are Not Tidy as a Single Dataset

“Tidy datasets… have a specific structure: each variable is a column, each observation is a row, and each type of observational unit is a table.” - Hadley Wickham (https://doi.org/10.18637/jss.v059.i10)

CDISC has NCA tidied, and PKNCA follows that model:

concentration-time is a dataset (PC domain; PKNCAconc() object)
dose-time is a dataset (EX/EC domains; PKNCAdose() object)
NCA results are a dataset (PP domain; pk.nca() output)

Dataset Basics: Minimum data

PKNCA requires at minimum concentration, time, and what you want to calculate.

Dataset Basics: What columns are needed?

Column names are provided by the input to PKNCAconc() and PKNCAdose(); they are not hard-coded.

Columns that can be used include:

PKNCAconc(): concentration, time, groups; data exclusions; half-life inclusion and exclusion
PKNCAdose(): dose, time, groups; route, rate/duration of infusion; data exclusions
intervals given to PKNCAdata(): groups, start, end, and any NCA parameters to calculate

Dataset Basics: Example data

In the following slides, abbreviated data from an example study where two treatments (“A” and “B”) are administered to two subjects (1 and 2).

For PKNCA, the groups will be Treatment and Subject.
- PKNCA considers groups in order with the subject identifier as the last group (or the last group before a forward slash, /, if / is present).
- When indicated in order (...|Treatment+Subject), PKNCA automatically knows to keep Treatment and drop Subject for summaries (more on that later).

Dataset Basics: Example concentration data

Subject	Treatment	Time	Conc
1	A	0	0
1	A	2	2.143
1	A	8	0.4696
1	B	0	0
1	B	2	2.179
1	B	8	0.4852

Subject	Treatment	Time	Conc
2	A	0	0
2	A	2	1.937
2	A	8	0.4929
2	B	0	0
2	B	2	2.127
2	B	8	0.4804

Dataset Basics: Example dosing data

Subject	Treatment	Time	Dose
1	A	0	10
1	B	0	10

Subject	Treatment	Time	Dose
2	A	0	10
2	B	0	10

Dataset Basics: Example interval data

d_interval_1 <-
  data.frame(
    start=0, end=8,
    cmax=TRUE, tmax=TRUE, auclast=TRUE
  )

start	end	cmax	tmax	auclast
0	8	TRUE	TRUE	TRUE

Groups are not required, if you want the same intervals calculated for each group.

Hands-on: First NCA calculation with PKNCA

library(dplyr)
library(ggplot2)
library(tidyr)
library(purrr)
library(PKNCA)
# Concentration data setup
d_conc <-
  datasets::Theoph %>%
  filter(Subject %in% 1)
o_conc <- PKNCAconc(conc~Time, data=d_conc)
# Setup intervals for calculation
d_intervals <- data.frame(start=0, end=24, cmax=TRUE, tmax=TRUE, auclast=TRUE, aucint.inf.obs=TRUE)
# Combine concentration and dose
o_data <- PKNCAdata(o_conc, intervals=d_intervals)
# Calculate the results (suppressMessages() hides a message that isn't needed now)
o_result <- suppressMessages(pk.nca(o_data))
# summary(o_result)

PKNCA Functions

What functions are the most used?

PKNCAconc(): define a concentration-time PKNCAconc object
- All information about concentration data are given: concentration, time
- Optional information includes: grouping information (usually given), data to exclude, half-life inclusion and exclusion columns
PKNCAdose(): define a dose-time PKNCAdose object (optional)
- dose amount and time are both optional
- Optional information includes: rate or duration of infusion, data to exclude
PKNCAdata(): combine PKNCAconc, optionally PKNCAdose, and optionally intervals into a PKNCAdata object
- the PKNCAconc object must be given; the PKNCAdose object is optional; interval definitions are usually given; calculation options may be given
pk.nca(): calculate the NCA parameters from a data object into a PKNCAresult object

How do I do a simple calculation? all steps

We will break this down in subsequent slides.

# Concentration data setup
d_conc <-
  datasets::Theoph %>%
  filter(Subject %in% 1)
o_conc <- PKNCAconc(conc~Time, data=d_conc)
# Dose data setup
d_dose <-
  datasets::Theoph %>%
  filter(Subject %in% 1) %>%
  filter(Time == 0)
o_dose <- PKNCAdose(Dose~Time, data=d_dose)
# Combine concentration and dose
o_data <- PKNCAdata(o_conc, o_dose)
# Calculate the results
o_result <- pk.nca(o_data)

How do I do a simple calculation? Concentration data

# Load your dataset as a data.frame
d_conc <-
  datasets::Theoph %>%
  filter(Subject %in% 1)
# Take a look at the data
pander::pander(head(d_conc, 2))

Subject	Wt	Dose	Time	conc
1	79.6	4.02	0	0.74
1	79.6	4.02	0.25	2.84

# Define the PKNCAconc object indicating the concentration and time columns, the
# dataset, and any other options.
o_conc <- PKNCAconc(conc~Time, data=d_conc)

How do I do a simple calculation? Dose data

# Load your dataset as a data.frame
d_dose <-
  datasets::Theoph %>%
  filter(Subject %in% 1) %>%
  filter(Time == 0)
# Take a look at the data
pander::pander(d_dose)

Subject	Wt	Dose	Time	conc
1	79.6	4.02	0	0.74

# Define the PKNCAdose object indicating the dose amount and time columns, the
# dataset, and any other options.
o_dose <- PKNCAdose(Dose~Time, data=d_dose)

How do I do a simple calculation? Calculate results

# Combine the PKNCAconc and PKNCAdose objects.  You can add interval
# specifications and calculation options here.
o_data <- PKNCAdata(o_conc, o_dose)
# Calculate the results
o_result <- pk.nca(o_data)

How do I do a simple calculation? Get results

To calculate summary statistics, use summary(); to extract all individual-level results, use as.data.frame().

The "caption" attribute of the summary describes how the summary statistics were calculated for each parameter. (Hint: pander::pander() knows how to use that to put the caption on a table in a report.)

The individual results contain the columns for start time, end time, grouping variables (none in this example), parameter names, values, and if the value should be excluded.

How do I do a simple calculation? Get summary results

# Look at summarized results
pander::pander(summary(o_result))

auclast, cmax, aucinf.obs: geometric mean and geometric coefficient of variation; tmax: median and range; half.life: arithmetic mean and standard deviation
start	end	N	auclast	cmax	tmax	half.life	aucinf.obs
0	24	1	92.4 [NC]	.	.	.	.
0	Inf	1	.	10.5 [NC]	1.12 [1.12, 1.12]	14.3 [NC]	215 [NC]

How do I do a simple calculation? Get individual results

end	PPTESTCD	PPORRES	exclude
24	auclast	92.37	NA
Inf	cmax	10.5	NA
Inf	tmax	1.12	NA

PKNCA datasets

How does PKNCA think about data?

Three types of data are inputs for calculation in PKNCA:

concentration-time (PKNCAconc),
dose-time (PKNCAdose), and
intervals.

PKNCAconc and PKNCAdose objects can optionally have groups. The groups in a PKNCAdose object must be the same or fewer than the groups in PKNCAconc object (for example, all subjects in a treatment arm may receive the same dose).

What is an “interval” and how is it different than a “group”?

A group separates one full concentration-time profile for a subject that you may ever want to consider at the same time. Usually, it groups by study, treatment, analyte, and subject (other groups can be useful depending on the study design).

An interval selects a time range within a group.

One time can be in zero or more intervals, but only zero or one group. Intervals can be adjacent (0-12 and 12-24) or overlap (0-12 and 0-24). In other words, one sample may be used in more than one interval, but one sample will never be used in more than one group.

Legend: The group contains all points on the figure. Shaded regions indicate intervals. Arrows indicate points shared between intervals within the group.

Common data management requirements before sending data to PKNCA

Time must not be missing for PKNCAconc (if given to PKNCAdose, it must not be missing).
Below the limit of quantification (BLQ) concentrations must be set to zero (not NA).
Imputation of time zero is required for AUC calculation.
Especially for actual-time calculations, imputation of the beginning of the interval is usually needed.

Columns must be created for:

Concentration or dose,
Time
Groups
- usually columns for study, treatment arm, subject;
- sometimes analyte, formulation, period (needed in case the same subject receives the same treatment arm multiple times)

Setup your concentration data

Concentration data must be numeric

Setup your concentration data

Concentration data must be numeric
Time must be numeric and not be missing

Setup your concentration data

Concentration data must be numeric
Time must be numeric and not be missing
Groups can be anything, setup at the level of the individual

Group: 🗸 a pod of killer whales

Setup your dosing data (if you have it and even if you don’t)

Normal dosing data setup: PKNCAdose(dose~time|actarm+usubjid, data=d_dose)

Dose amount must be numeric — or it can be omitted
- PKNCAdose(~time|actarm+usubjid, data=d_dose)
Time must be numeric and not be missing — or it can be omitted
- PKNCAdose(dose~.|actarm+usubjid, data=d_dose)
Groups can be anything — may be grouped at a higher level than the individual
- Useful when all dose amounts and times are the same within an arm: PKNCAdose(dose~time|actarm, data=d_dose)
- Useful dose amount is the same at all times within an arm: PKNCAdose(dose~.|actarm, data=d_dose)
- Useful when times are all the same within an arm but dose may differ: PKNCAdose(~time|actarm, data=d_dose)

Define your intervals

Intervals have columns for:

start and end times for the interval,
groups matching any level of grouping; intervals apply by a merge/join with the groups
parameters to calculate (TRUE means to calculate it; FALSE means don’t). The full list of available parameters is in the selection of calculation intervals vignette.
- You only have to specify the parameter you want, not all parameters.

Define your intervals: example

For time 0 to 24, calculate AUClast
For time 0 to infinity, calculate cmax, tmax, half.life, and aucinf.obs

start	end	auclast	cmax	tmax	half.life	aucinf.obs
0	24	TRUE	FALSE	FALSE	FALSE	FALSE
0	Inf	FALSE	TRUE	TRUE	TRUE	TRUE

Calculations above the hood

Prepare your data for calculation

d_conc <-
  datasets::Theoph %>%
  mutate(
    Treatment=
      case_when(
        Dose <= median(Dose)~"Low dose",
        TRUE~"High dose"
      )
  )
# The study was single-dose
d_dose <-
  d_conc %>%
  select(Treatment, Subject, Dose) %>%
  unique() %>%
  mutate(dose_time=0)

Calculate without dosing data

o_conc <- PKNCAconc(conc~Time|Treatment+Subject, data=d_conc)
try({
  o_data <- PKNCAdata(o_conc)
  summary(pk.nca(o_data))
})

## Error in PKNCAdata.default(data.conc = data.conc, data.dose = data.dose,  : 
##   If data.dose is not given, intervals must be given

Whoops! Without dosing, we need intervals.

Calculate without dosing data, try 2

o_conc <- PKNCAconc(conc~Time|Treatment+Subject, data=d_conc)
d_intervals <- data.frame(start=0, end=Inf, cmax=TRUE, tmax=TRUE, half.life=TRUE, aucinf.obs=TRUE)
o_data_manual_intervals <- PKNCAdata(o_conc, intervals=d_intervals)
summary(pk.nca(o_data_manual_intervals))

## No dose information provided, calculations requiring dose will return NA.

##  start end Treatment N        cmax               tmax   half.life aucinf.obs
##      0 Inf High dose 5 9.16 [19.4] 3.48 [0.980, 3.55] 7.73 [1.08] 120 [26.2]
##      0 Inf  Low dose 7 8.30 [15.2] 1.12 [0.630, 2.02] 8.50 [2.67] 111 [31.6]
## 
## Caption: cmax, aucinf.obs: geometric mean and geometric coefficient of variation; tmax: median and range; half.life: arithmetic mean and standard deviation

Dosing data helps with interval setup

o_conc <- PKNCAconc(conc~Time|Treatment+Subject, data=d_conc)
o_dose <- PKNCAdose(Dose~dose_time|Treatment+Subject, data=d_dose)
o_data_auto_intervals <- PKNCAdata(o_conc, o_dose)
o_data_auto_intervals$intervals$aucint.inf.obs <- TRUE
summary(pk.nca(o_data_auto_intervals))

##  start end Treatment N     auclast        cmax               tmax   half.life
##      0  24  Low dose 7 70.2 [14.4]           .                  .           .
##      0 Inf  Low dose 7           . 8.30 [15.2] 1.12 [0.630, 2.02] 8.50 [2.67]
##      0  24 High dose 5 81.3 [34.2]           .                  .           .
##      0 Inf High dose 5           . 9.16 [19.4] 3.48 [0.980, 3.55] 7.73 [1.08]
##  aucinf.obs aucint.inf.obs
##           .    94.1 [22.5]
##  111 [31.6]     111 [31.6]
##           .     105 [23.3]
##  120 [26.2]     120 [26.2]
## 
## Caption: auclast, cmax, aucinf.obs, aucint.inf.obs: geometric mean and geometric coefficient of variation; tmax: median and range; half.life: arithmetic mean and standard deviation

AUC considerations with PKNCA (1/3)

The considerations below mainly apply to actual-time data; nominal-time data usually have measurements at the start and end time for the interval.

With an interval start and end of 0 and 24 (and the last measurement time just after 24 hours):

AUC_last is calculated only based on points within the interval (the AUClast color in the figure)

AUC considerations with PKNCA (2/3)

The considerations below mainly apply to actual-time data; nominal-time data usually have measurements at the start and end time for the interval.

With an interval start and end of 0 and 24 (and the last measurement time just after 24 hours):

AUC_int looks at the points in the interval, and if there is no measurement at the interval end time, interpolates or extrapolates to the interval end time (the AUClast and AUCint color in the figure)

AUC considerations with PKNCA (2/3)

The considerations below mainly apply to actual-time data; nominal-time data usually have measurements at the start and end time for the interval.

With an interval start and end of 0 and 24 (and the last measurement time just after 24 hours):

AUC_∞ is calculated based on AUC_last, t_last, and the half-life from t_last, only using data within the interval– no data after the end of the interval.
Ensure that the interval used for calculating AUC_∞ includes all the points desired (usually, end=Inf).

Hands-on workshop

Steady-state intramuscular administration

The data for the exercise are from a PK study of amikacin in a killer whale and a beluga whale. (DOI: 10.1638/03-078)

(Callback…)

Steady-state intramuscular administration

library(PKNCA)

d_conc <- read.csv("c:/tmp/whale_conc.csv")
d_dose <- read.csv("c:/tmp/whale_dose.csv")
head(d_conc)
head(d_dose)

o_conc <- PKNCAconc(concentration~time|Animal, data=d_conc)
o_dose <- PKNCAdose(dose~time|Animal, data=d_dose)
o_data <- PKNCAdata(o_conc, o_dose)
o_data$intervals
o_nca <- pk.nca(o_data)
summary(o_nca)
summary(o_nca, drop.group=c())
as.data.frame(o_nca)

Day 2 Start

Control your data

Including and excluding data points

Data may be included/excluded in two ways:

Overall: excluded a row of data from all analyses
Half-life: excluded from half-life calculations, but included in all other analyses

For both ways of including/excluding data, it is defined by a column in the input data. The column is either NA or an empty string ("") to indicate “no” or any other text to indicate “yes”.

Exclude data points overall

Use the exclude argument for PKNCAconc() or PKNCAdose().

When you use exclude, this is how you give your data to PKNCA:

d_before_exclude <-
  data.frame(
    time=0:4,
    conc=c(0, 2, 1, 0.5, 0.25),
    not_this=c(NA, "Not this", NA, NA, NA)
  )
o_conc <-
  PKNCAconc(
    data=d_before_exclude,
    conc~time,
    exclude="not_this"
  )

And, this is how PKNCA thinks about it:

pander::pander(
  d_before_exclude %>%
    filter(is.na(not_this))
)

time	conc	not_this
0	0	NA
2	1	NA
3	0.5	NA
4	0.25	NA

Exclude data points overall

o_conc <- PKNCAconc(data=d_before_exclude, conc~time, exclude="not_this")

Hey babe, did you get my 5 rows of data?

I only saw 4 rows. Are you sure you sent 5?

Yep, definitely 5 check that last slide. 😠

…

New phone. Who dis?

Digression: How is λz automatically calculated?

Filter the data from the first point after t_max (or from t_max if allow.tmax.in.half.life=TRUE) to t_last and excluding BLQ in the middle.
Fit the semi-log line from 3 points before t_last (3 can be changed with the min.hl.points option) to t_last.
- Repeat for all sets of points from there to the first point included.
- If that 3 points are not available, it is not calculated.
Among the fits, select the best adjusted r² (within a tolerance of adj.r.squared.factor).
Require λz> 0.
If more than one fit is available at this point, select the one with the most points included.

Note: WinNonlin first requires λz> 0 then selects for adjusted r². Therefore, WinNonlin will occasionally provide a half-life when PKNCA will not, but the fit line is not as good (as measured by r²). The selection of filtering order is an intentional feature with PKNCA, and it generally has minimal impact on summary statistics because the quality of the half-life fit is usually low in this scenario.

λz control (manual exclusions and inclusions of data points)

Use the exclude_half.life or include_half.life argument for PKNCAconc(). The two arguments behave very differently in how points are selected for half-life.

exclude_half.life uses the same automatic point selection method of curve stripping (described before), but it excludes individual points from that calculation.

include_half.life uses no automatic point selection method, and only points specifically noted by the analyst are included.

Less-common calculations

Urine calculations

d_urine <-
  data.frame(
    conc=c(1, 2, 3),
    urine_volume=c(200, 100, 300),
    time=c(1, 2, 3)
  )
o_conc <- PKNCAconc(data=d_urine, conc~time, volume="urine_volume")
d_intervals <- data.frame(start=0, end=24, ae=TRUE)
o_data <- PKNCAdata(o_conc, intervals=d_intervals)
o_nca <- suppressMessages(pk.nca(o_data))
summary(o_nca)

##  start end N        ae
##      0  24 1 1300 [NC]
## 
## Caption: ae: geometric mean and geometric coefficient of variation

Urine calculations: understanding what is happening and potential hiccups

Intervals for urine are treated the same as any other interval type. Specifically, PKNCA does not look outside the start and end of the interval.

Watch out for e.g. a 24-hour urine amount to be included in more than one interval because start = 0 and end = 24.
Watch out for an actual start or end time to be outside of the interval and therefore to be omitted from calculations.

Calculations below the hood

PKNCA only calculates what is required, not every possible parameter (1 of 2)

If you don’t need a parameter, PKNCA won’t calculate it.

For example, if all you need is cmax, all you’ll get is cmax.

o_conc <- PKNCAconc(data=data.frame(conc=2^-(1:4), time=0:3), conc~time)
o_data <- PKNCAdata(o_conc, intervals=data.frame(start=0, end=Inf, cmax=TRUE))
o_nca <- suppressMessages(pk.nca(o_data))
as.data.frame(o_nca)

## # A tibble: 1 × 5
##   start   end PPTESTCD PPORRES exclude
##   <dbl> <dbl> <chr>      <dbl> <chr>  
## 1     0   Inf cmax         0.5 <NA>

PKNCA only calculates what is required, not every possible parameter (2 of 2)

If you need AUC_0-, PKNCA will calculate other required parameters behind the scenes.

o_data <-
  PKNCAdata(
    o_conc,
    intervals=
      data.frame(
        start=0, end=Inf,
        aucinf.obs=TRUE
      )
  )
o_nca <- suppressMessages(pk.nca(o_data))

as.data.frame(o_nca)

## # A tibble: 12 × 5
##    start   end PPTESTCD            PPORRES exclude
##    <dbl> <dbl> <chr>                 <dbl> <chr>  
##  1     0   Inf tmax                 0      <NA>   
##  2     0   Inf tlast                3      <NA>   
##  3     0   Inf clast.obs            0.0625 <NA>   
##  4     0   Inf lambda.z             0.693  <NA>   
##  5     0   Inf r.squared            1      <NA>   
##  6     0   Inf adj.r.squared        1      <NA>   
##  7     0   Inf lambda.z.time.first  1      <NA>   
##  8     0   Inf lambda.z.n.points    3      <NA>   
##  9     0   Inf clast.pred           0.0625 <NA>   
## 10     0   Inf half.life            1.00   <NA>   
## 11     0   Inf span.ratio           2.00   <NA>   
## 12     0   Inf aucinf.obs           0.721  <NA>

How to select the correct parameters for calculations (aka, why are there 32 types of AUC in PKNCA?)

CDISC has one set of names, but they are not precise (e.g. AUCINT doesn’t tell the interpolation/extrapolation method).

PKNCA tries to be everything to everyone (in terms of parameters calculated), and it simultaneously tries to be precise. That yields many parameters.

See the Selection of Calculation Intervals vignette in the Parameters Available for Calculation in an Interval section for all available parameters.

When are intervals (partly) ignored?

Very few parameters reach outside of the start and end of an interval for additional information about what is being calculated. As of the writing of these training materials (PKNCA version 0.9.5), the only parameters that look outside are the aucint class of parameters.

AUC_int may look after the end of the interval to calculate the concentration at end.

Note: Watch out for a dose before the next concentration (e.g. a dose at 24 hours but the prior sample is around 12 and the next is around 25):

Control your results

Excluding results (Not the best way)

A simple way to exclude a value from results is to convert the results to a data.frame and then drop the rows you don’t want:

as.data.frame(o_nca) %>%
  filter(PPTESTCD != "half.life")

## # A tibble: 11 × 5
##    start   end PPTESTCD            PPORRES exclude
##    <dbl> <dbl> <chr>                 <dbl> <chr>  
##  1     0   Inf tmax                 0      <NA>   
##  2     0   Inf tlast                3      <NA>   
##  3     0   Inf clast.obs            0.0625 <NA>   
##  4     0   Inf lambda.z             0.693  <NA>   
##  5     0   Inf r.squared            1      <NA>   
##  6     0   Inf adj.r.squared        1      <NA>   
##  7     0   Inf lambda.z.time.first  1      <NA>   
##  8     0   Inf lambda.z.n.points    3      <NA>   
##  9     0   Inf clast.pred           0.0625 <NA>   
## 10     0   Inf span.ratio           2.00   <NA>   
## 11     0   Inf aucinf.obs           0.721  <NA>

But, parameters derived from half-life remain.

Excluding results (The best way, 1/2)

When you use the exclude() function, parameters that are dependent on an excluded parameter will be excluded.

o_nca_excluded <-
  o_nca %>%
  exclude(FUN=exclude_nca_span.ratio(3))
as.data.frame(o_nca_excluded)

## # A tibble: 12 × 5
##    start   end PPTESTCD            PPORRES exclude       
##    <dbl> <dbl> <chr>                 <dbl> <chr>         
##  1     0   Inf tmax                 0      <NA>          
##  2     0   Inf tlast                3      <NA>          
##  3     0   Inf clast.obs            0.0625 <NA>          
##  4     0   Inf lambda.z             0.693  Span ratio < 3
##  5     0   Inf r.squared            1      Span ratio < 3
##  6     0   Inf adj.r.squared        1      Span ratio < 3
##  7     0   Inf lambda.z.time.first  1      Span ratio < 3
##  8     0   Inf lambda.z.n.points    3      Span ratio < 3
##  9     0   Inf clast.pred           0.0625 Span ratio < 3
## 10     0   Inf half.life            1.00   Span ratio < 3
## 11     0   Inf span.ratio           2.00   Span ratio < 3
## 12     0   Inf aucinf.obs           0.721  Span ratio < 3

Excluding results (The best way, 2/2)

Now, everything dependent on the half-life is excluded in summaries.

summary(o_nca)

##  start end N aucinf.obs
##      0 Inf 1 0.721 [NC]
## 
## Caption: aucinf.obs: geometric mean and geometric coefficient of variation

summary(o_nca_excluded)

##  start end N aucinf.obs
##      0 Inf 1         NC
## 
## Caption: aucinf.obs: geometric mean and geometric coefficient of variation

NCA-related calculations

Superposition

Superposition assumes linear kinetics and can convert a single-dose profile to multi-dose.

# Subject 2 is selected for a BLQ time=0 concentration
d_prep <-
  datasets::Theoph %>%
  filter(Subject == 2)
# Superposition to steady-state is the default
d_ss <-
  superposition(
    conc=d_prep$conc,
    time=d_prep$Time,
    tau=24
  )
# Going to steady-state is also an option
# (n.tau=2 means the second dose)
d_second_dose <-
  superposition(
    conc=d_prep$conc,
    time=d_prep$Time,
    tau=24,
    n.tau=2
  )

# Want the profile for the first two doses
# together?
d_first_two <-
  superposition(
    conc=d_prep$conc,
    time=d_prep$Time,
    tau=48, # 48 hours
    n.tau=1, # One tau interval (0 to 48 hours)
    dose.times=c(0, 24)
  )

Time-to-Steady-state calculations

Time-to-steady-state (tss) can be useful as a method to confirm that a subject is at steady-state. PKNCA can calculate tss using trough concentrations either with a monoexponential increase toward steady-state (preferred) or a linear trend back from the final point.

dose_times <- seq(0, 96-1, by=6)
d_multidose <-
  superposition(
    conc=d_prep$conc,
    time=d_prep$Time,
    tau=96, # 48 hours
    n.tau=1, # One tau interval (0 to 48 hours)
    dose.times=dose_times
  )
pk.tss.monoexponential(
  conc=d_multidose$conc, time=d_multidose$time, subject=rep(1, nrow(d_multidose)),
  time.dosing=dose_times, subject.dosing=rep(1, length(dose_times)),
  output="single"
)

##   tss.monoexponential.single
## 1                   22.53005

Reporting

Graphics are intentionally not part of PKNCA, but there are some tricks that can help…

Generate all individual profiles using the groups that you defined:

o_conc <- PKNCAconc(conc~Time|Subject, data=datasets::Theoph)
d_plot <-
  grouped_df(data=datasets::Theoph, vars=names(getGroups(o_conc))) %>%
  nest() %>%
  mutate(
    figure=
      lapply(
        pmap(
          .l=list(data=data),
          .f=ggplot,
          aes(x=Time, y=conc)
        ),
        FUN="+",
        geom_line()
      )
  )
# d_plot$figure

Best practices for Data -> PKNCA -> knitr

Make summary tables using the summary() function on the NCA results, and use pander::pander() to make a pretty table with captions.

pander::pander(summary(o_nca))

aucinf.obs: geometric mean and geometric coefficient of variation
start	end	N	aucinf.obs
0	Inf	1	0.721 [NC]

Make an NCA data listing using the as.data.frame() function on the NCA results.

pander::pander(as.data.frame(o_nca))

Limitations

Units (especially clearance)

PKNCA does not (yet) support units. The most common place where that becomes an issue is with clearance which ends up having unusual units like “mg/(hr*ng/mL)” (with units of mg for dosing, hr for time, and ng/mL for concentration).

Data imputation

Some data points are required for inputs such as:

the start of the interval for AUC,
the end of the interval for some calculations (e.g. AUC_last vs AUC_int), and
interpolated concentrations at the end of a urine interval for urinary PK calculations.

IV bolus AUC (need to add C0)

PKNCA does not have an IV-aware AUC calculation (yet). So, C0 must be separately imputed.

Combined, multi-subject data (e.g. sparse animal sampling)

Averaging the concentration at a time point will allow for the mean sparse sampling result. But general sparse sampling methods are not (yet) implemented.

Secondary parameters (e.g. bioavailability and renal clearance)

PKNCA does not (yet) have the ability to calculate secondary PK parameters that require looking at more than one group/interval at a time. (If you have good ideas for how to define the intervals for that, please let me know.)

Hands-on

Single- and Multiple-dose, single analyte: Setup the underlying datasets

d_conc <-
  datasets::Theoph %>%
  rename(time=Time) %>%
  mutate(
    Subject=as.character(Subject)
  )
d_multidose <-
  PKNCAconc(conc~time|Subject, data=d_conc) %>%
  superposition(tau=24, check.blq=FALSE)
d_singledose_single_analyte <-
  d_conc %>%
  mutate(
    Study_Part="Single"
  )
d_multidose_single_analyte <-
  d_conc %>%
  mutate(Day=1) %>%
  bind_rows(
    d_multidose %>% mutate(time=time + 120, Day=6)
  ) %>%
  mutate(
    Study_Part="Multiple"
  )

Single- and Multiple-dose, single analyte: Setup the concentration and dose datasets

d_single_multi_conc <- bind_rows(d_singledose_single_analyte, d_multidose_single_analyte)
d_single_multi_dose <-
  d_single_multi_conc %>%
  filter(
    (Study_Part %in% "Single" & time == 0) |
      (Study_Part %in% "Multiple" & (time %% 24) == 0)
  )

Single- and Multiple-dose, single analyte: Perform basic analysis

o_conc <- PKNCAconc(data=d_single_multi_conc, conc~time|Study_Part+Subject)
o_dose <- PKNCAdose(data=d_single_multi_dose, Dose~time|Study_Part+Subject)
o_data <- PKNCAdata(o_conc, o_dose)
o_data$intervals %>% select(-Subject) %>% unique() %>% as.data.frame()

##   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
## 3     0 120    TRUE  FALSE    FALSE   FALSE       FALSE            FALSE
## 4   120 144    TRUE  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
## 3      FALSE           FALSE FALSE  TRUE FALSE  TRUE FALSE  FALSE     FALSE
## 4      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 ctrough
## 1   FALSE  FALSE FALSE    FALSE       FALSE    FALSE       FALSE FALSE   FALSE
## 2   FALSE  FALSE FALSE    FALSE       FALSE    FALSE       FALSE FALSE   FALSE
## 3   FALSE  FALSE FALSE    FALSE       FALSE    FALSE       FALSE FALSE   FALSE
## 4   FALSE  FALSE FALSE    FALSE       FALSE    FALSE       FALSE FALSE   FALSE
##   cstart   ptr  tlag deg.fluc swing  ceoi aucabove.predose.all
## 1  FALSE FALSE FALSE    FALSE FALSE FALSE                FALSE
## 2  FALSE FALSE FALSE    FALSE FALSE FALSE                FALSE
## 3  FALSE FALSE FALSE    FALSE FALSE FALSE                FALSE
## 4  FALSE FALSE FALSE    FALSE FALSE FALSE                FALSE
##   aucabove.trough.all    ae clr.last clr.obs clr.pred    fe sparse_auclast
## 1               FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE
## 2               FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE
## 3               FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE
## 4               FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE
##   time_above aucivlast aucivall aucivint.last aucivint.all aucivpbextlast
## 1      FALSE     FALSE    FALSE         FALSE        FALSE          FALSE
## 2      FALSE     FALSE    FALSE         FALSE        FALSE          FALSE
## 3      FALSE     FALSE    FALSE         FALSE        FALSE          FALSE
## 4      FALSE     FALSE    FALSE         FALSE        FALSE          FALSE
##   aucivpbextall aucivpbextint.last aucivpbextint.all half.life r.squared
## 1         FALSE              FALSE             FALSE     FALSE     FALSE
## 2         FALSE              FALSE             FALSE      TRUE     FALSE
## 3         FALSE              FALSE             FALSE     FALSE     FALSE
## 4         FALSE              FALSE             FALSE     FALSE     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
## 3         FALSE    FALSE               FALSE             FALSE      FALSE
## 4         FALSE    FALSE               FALSE             FALSE      FALSE
##   span.ratio thalf.eff.last thalf.eff.iv.last kel.last kel.iv.last aucinf.obs
## 1      FALSE          FALSE             FALSE    FALSE       FALSE      FALSE
## 2      FALSE          FALSE             FALSE    FALSE       FALSE       TRUE
## 3      FALSE          FALSE             FALSE    FALSE       FALSE      FALSE
## 4      FALSE          FALSE             FALSE    FALSE       FALSE      FALSE
##   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
## 3       FALSE       FALSE        FALSE          FALSE               FALSE
## 4       FALSE       FALSE        FALSE          FALSE               FALSE
##   aucint.inf.pred aucint.inf.pred.dose aucivinf.obs aucivinf.pred
## 1           FALSE                FALSE        FALSE         FALSE
## 2           FALSE                FALSE        FALSE         FALSE
## 3           FALSE                FALSE        FALSE         FALSE
## 4           FALSE                FALSE        FALSE         FALSE
##   aucivpbextinf.obs aucivpbextinf.pred aucpext.obs aucpext.pred cl.obs cl.pred
## 1             FALSE              FALSE       FALSE        FALSE  FALSE   FALSE
## 2             FALSE              FALSE       FALSE        FALSE  FALSE   FALSE
## 3             FALSE              FALSE       FALSE        FALSE  FALSE   FALSE
## 4             FALSE              FALSE       FALSE        FALSE  FALSE   FALSE
##   mrt.obs mrt.pred mrt.iv.obs mrt.iv.pred mrt.md.obs mrt.md.pred vz.obs vz.pred
## 1   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
## 2   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
## 3   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
## 4   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
##   vss.obs vss.pred vss.iv.obs vss.iv.pred vss.md.obs vss.md.pred vd.obs vd.pred
## 1   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
## 2   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
## 3   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
## 4   FALSE    FALSE      FALSE       FALSE      FALSE       FALSE  FALSE   FALSE
##   thalf.eff.obs thalf.eff.pred thalf.eff.iv.obs thalf.eff.iv.pred kel.obs
## 1         FALSE          FALSE            FALSE             FALSE   FALSE
## 2         FALSE          FALSE            FALSE             FALSE   FALSE
## 3         FALSE          FALSE            FALSE             FALSE   FALSE
## 4         FALSE          FALSE            FALSE             FALSE   FALSE
##   kel.pred kel.iv.obs kel.iv.pred auclast.dn aucall.dn aucinf.obs.dn
## 1    FALSE      FALSE       FALSE      FALSE     FALSE         FALSE
## 2    FALSE      FALSE       FALSE      FALSE     FALSE         FALSE
## 3    FALSE      FALSE       FALSE      FALSE     FALSE         FALSE
## 4    FALSE      FALSE       FALSE      FALSE     FALSE         FALSE
##   aucinf.pred.dn aumclast.dn aumcall.dn aumcinf.obs.dn aumcinf.pred.dn cmax.dn
## 1          FALSE       FALSE      FALSE          FALSE           FALSE   FALSE
## 2          FALSE       FALSE      FALSE          FALSE           FALSE   FALSE
## 3          FALSE       FALSE      FALSE          FALSE           FALSE   FALSE
## 4          FALSE       FALSE      FALSE          FALSE           FALSE   FALSE
##   cmin.dn clast.obs.dn clast.pred.dn cav.dn ctrough.dn Study_Part
## 1   FALSE        FALSE         FALSE  FALSE      FALSE     Single
## 2   FALSE        FALSE         FALSE  FALSE      FALSE     Single
## 3   FALSE        FALSE         FALSE  FALSE      FALSE   Multiple
## 4   FALSE        FALSE         FALSE  FALSE      FALSE   Multiple

o_nca <- pk.nca(o_data)

Single- and Multiple-dose, single analyte: Use intervals for fewer subjects

d_intervals <-
  data.frame(
    start=0,
    end=24,
    Subject=c("1", "2"),
    Study_Part="Single",
    aucinf.obs=TRUE
  )
o_data <- PKNCAdata(o_conc, o_dose, intervals=d_intervals)
o_nca <- pk.nca(o_data)

## Warning: Study_Part=Single; Subject=3: No intervals for data

## Warning: Study_Part=Single; Subject=4: No intervals for data

## Warning: Study_Part=Single; Subject=5: No intervals for data

## Warning: Study_Part=Single; Subject=6: No intervals for data

## Warning: Study_Part=Single; Subject=7: No intervals for data

## Warning: Study_Part=Single; Subject=8: No intervals for data

## Warning: Study_Part=Single; Subject=9: No intervals for data

## Warning: Study_Part=Single; Subject=10: No intervals for data

## Warning: Study_Part=Single; Subject=11: No intervals for data

## Warning: Study_Part=Single; Subject=12: No intervals for data

## Warning: Study_Part=Multiple; Subject=1: No intervals for data

## Warning: Study_Part=Multiple; Subject=2: No intervals for data

## Warning: Study_Part=Multiple; Subject=3: No intervals for data

## Warning: Study_Part=Multiple; Subject=4: No intervals for data

## Warning: Study_Part=Multiple; Subject=5: No intervals for data

## Warning: Study_Part=Multiple; Subject=6: No intervals for data

## Warning: Study_Part=Multiple; Subject=7: No intervals for data

## Warning: Study_Part=Multiple; Subject=8: No intervals for data

## Warning: Study_Part=Multiple; Subject=9: No intervals for data

## Warning: Study_Part=Multiple; Subject=10: No intervals for data

## Warning: Study_Part=Multiple; Subject=11: No intervals for data

## Warning: Study_Part=Multiple; Subject=12: No intervals for data

summary(o_nca)

##  start end Study_Part N aucinf.obs
##      0  24     Single 2 144 [69.0]
## 
## Caption: aucinf.obs: geometric mean and geometric coefficient of variation

Single- and Multiple-dose, single analyte: Use custom intervals per subjects

# Find the time closest to 12 hours
d_intervals_prep <-
  d_single_multi_conc %>%
  filter(Study_Part == "Single") %>%
  mutate(
    time_deviation=abs(time-12)
  ) %>%
  group_by(Subject, Study_Part) %>%
  filter(time %in% time[time_deviation == min(time_deviation)])
d_intervals <-
  d_intervals_prep %>%
  select(Study_Part, Subject, end=time) %>%
  mutate(
    start=0,
    aucinf.obs=TRUE
  )
o_data <- PKNCAdata(o_conc, o_dose, intervals=d_intervals)

o_nca <- pk.nca(o_data)

## Warning: Study_Part=Multiple; Subject=1: No intervals for data

## Warning: Study_Part=Multiple; Subject=2: No intervals for data

## Warning: Study_Part=Multiple; Subject=3: No intervals for data

## Warning: Study_Part=Multiple; Subject=4: No intervals for data

## Warning: Study_Part=Multiple; Subject=5: No intervals for data

## Warning: Study_Part=Multiple; Subject=6: No intervals for data

## Warning: Study_Part=Multiple; Subject=7: No intervals for data

## Warning: Study_Part=Multiple; Subject=8: No intervals for data

## Warning: Study_Part=Multiple; Subject=9: No intervals for data

## Warning: Study_Part=Multiple; Subject=10: No intervals for data

## Warning: Study_Part=Multiple; Subject=11: No intervals for data

## Warning: Study_Part=Multiple; Subject=12: No intervals for data

summary(o_nca, drop.group=c("Subject", "end"))

## Warning in summary.PKNCAresults(o_nca, drop.group = c("Subject", "end")):
## drop.group including start or end may result in incorrect groupings (such as
## inaccurate comparison of intervals).  Drop these with care.

##  start Study_Part  N aucinf.obs
##      0     Single 12 120 [29.5]
## 
## Caption: aucinf.obs: geometric mean and geometric coefficient of variation

Single- and Multiple-dose, parent and metabolite

d_single_multi_conc_multi_analyte <-
  bind_rows(
    d_single_multi_conc %>% mutate(Analyte="Parent"),
    d_single_multi_conc %>%
      mutate(
        Analyte="Metabolite",
        conc=conc/2
      )
  )
o_conc <-
  PKNCAconc(
    data=d_single_multi_conc_multi_analyte,
    conc~time|Study_Part+Subject/Analyte
  )
o_dose <- PKNCAdose(data=d_single_multi_dose, Dose~time|Study_Part+Subject)
o_data <- PKNCAdata(o_conc, o_dose)
o_nca <- pk.nca(o_data)
summary(o_nca)

##  start end Study_Part    Analyte  N     auclast        cmax               tmax
##      0  24     Single     Parent 12 74.6 [24.3]           .                  .
##      0 Inf     Single     Parent 12           . 8.65 [17.0] 1.14 [0.630, 3.55]
##      0 120   Multiple     Parent 12  237 [38.0] 8.65 [17.0] 1.14 [0.630, 3.55]
##    120 144   Multiple     Parent 12  115 [28.4] 10.0 [21.0] 1.09 [0.630, 3.55]
##      0  24     Single Metabolite 12 37.3 [24.3]           .                  .
##      0 Inf     Single Metabolite 12           . 4.32 [17.0] 1.14 [0.630, 3.55]
##      0 120   Multiple Metabolite 12  118 [38.0] 4.32 [17.0] 1.14 [0.630, 3.55]
##    120 144   Multiple Metabolite 12 57.4 [28.4] 5.02 [21.0] 1.09 [0.630, 3.55]
##    half.life  aucinf.obs
##            .           .
##  8.18 [2.12]  115 [28.4]
##            .           .
##            .           .
##            .           .
##  8.18 [2.12] 57.4 [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