Data Imputation

Imputation may be required for noncompartmental analysis (NCA) calculations. Typical imputations may require setting the concentration before the first dose to zero or shifting actual time predose concentrations to the beginning of the dosing interval.

PKNCA supports imputation either for the full analysis dataset or per calculation interval.

The current list of imputation methods built into PKNCA can be found by looking at ?PKNCA_impute_method:

library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter
cat(paste(
  "*", ls("package:PKNCA", pattern = "^PKNCA_impute_method")
), sep = "\n")
#> * PKNCA_impute_method_end_conc_drop
#> * PKNCA_impute_method_start_cmin
#> * PKNCA_impute_method_start_conc0
#> * PKNCA_impute_method_start_predose

In brief, the built-in methods work as follows:

start_conc0 sets the concentration at the interval start time to 0. If an observation exists at the start time, its value is replaced with 0; otherwise, a new row is added (usually used with single-dose data).
start_predose shifts the most recent observation before the interval start to the interval start time. It applies only when no start-time observation exists, only when a pre-start observation exists, and only when the shift is no more than max_shift (by default, 5% of the interval duration or, for intervals with an infinite end, 5% of the time from the interval start to the last sample).
start_cmin adds the minimum concentration within the interval at the interval start time when no start-time observation exists (usually used with multiple-dose data).

The development version of PKNCA also adds PKNCA_impute_method_end_conc_drop (used as "end_conc_drop"), which drops a concentration observed exactly at the interval end – such as a predose sample for the next dose – from that interval’s calculation.

How does imputation occur?

(You can skip this section if you don’t desire the details of the methods of imputation.)

Imputation occurs just before calculations are performed within PKNCA. Imputation occurs only on a single interval definition at a time, so the same group (usually meaning the same subject with the same analyte) at the same time range can have different imputations for different parameter calculations.

The reason that this is done is to ensure that there are no unintentional modifications to the data. As an example, if an AUC_0-24 were calculated on Day 1 and Day 2 of a study with actual times, the nominal 24 hour sample may be collected at 23.5 hours. It may be preferable to keep the 23.5 hour sample at 23.5 hours for the Day 1 calculation, and at the same time, it may be preferred to shift the same 23.5 hr sample to 24 hours (time 0 on Day 2) for the Day 2 calculation.

How to select imputation methods to use

The selection of imputation methods uses a string of text with commas or spaces (or both) separating the imputation methods to use. No imputation will be performed if the imputation method is requested as NA or "".

To select no imputation (the default), indicate the imputation by NA or "".
To set imputation on the full dataset, use the impute argument to PKNCAdata() to specify the methods to use.
To set imputation by interval, use the impute argument to PKNCAdata() to specify the column in the intervals dataset to use for imputation.
You cannot specify imputation for both the full dataset and by interval at the same time. And, if a column name in the dataset matches the impute argument to PKNCAdata(), that will be used.

Imputation method functions are named PKNCA_impute_method_[method name]. For example, the method to impute a concentration of 0 at time 0 is named PKNCA_impute_method_start_conc0. When specifying the imputation method to use, give the [method name] part of the function name. So for the example above, use "start_conc0".

To specify more than one, give all the methods in order with a comma or space separating them (for example, "start_predose,start_conc0"), and the methods will be applied in order, each to the output of the previous method. Note that because start_conc0 sets the start-time concentration to 0 even when a start-time value already exists, the "start_predose,start_conc0" chain produces the same results as "start_conc0" alone: the concentration that start_predose shifts to the start time is then overwritten with 0. This overwriting is by design; the intent of start_conc0 is to force the start concentration to zero, and that can remove a nonzero predose concentration, too. To carry a predose concentration to the start time, use "start_predose" alone; to force the start concentration to zero, use "start_conc0"; and to use the predose concentration when one exists and 0 otherwise, write a custom imputation method (see the “Advanced” section below).

Imputation for the full dataset

If an imputation applies to the full dataset, it can be provided in the impute argument to PKNCAdata():

library(PKNCA)
# Remove time 0 to illustrate that imputation works
d_conc <- as.data.frame(datasets::Theoph)[!datasets::Theoph$Time == 0, ]
conc_obj <- PKNCAconc(d_conc, conc~Time|Subject)
d_dose <- unique(datasets::Theoph[datasets::Theoph$Time == 0,
                                  c("Dose", "Time", "Subject")])
dose_obj <- PKNCAdose(d_dose, Dose~Time|Subject)
data_obj <- PKNCAdata(conc_obj, dose_obj, impute = "start_predose,start_conc0")
nca_obj <- pk.nca(data_obj)
summary(nca_obj)
#>  start end  N     auclast        cmax               tmax   half.life aucinf.obs
#>      0  24 12 74.6 [24.2]           .                  .           .          .
#>      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

Imputation by calculation interval

If an imputation applies to specific intervals, the column in the interval data.frame can be provided in the impute argument to PKNCAdata():

library(PKNCA)
# Remove time 0 to illustrate that imputation works
d_conc <- as.data.frame(datasets::Theoph)[!datasets::Theoph$Time == 0, ]
conc_obj <- PKNCAconc(d_conc, conc~Time|Subject)
d_dose <- unique(datasets::Theoph[datasets::Theoph$Time == 0,
                                  c("Dose", "Time", "Subject")])
dose_obj <- PKNCAdose(d_dose, Dose~Time|Subject)

d_intervals <-
  data.frame(
    start=0, end=c(24, 24.1),
    auclast=TRUE,
    impute=c(NA, "start_conc0")
  )

data_obj <- PKNCAdata(conc_obj, dose_obj, intervals = d_intervals, impute = "impute")
nca_obj <- pk.nca(data_obj)
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.27) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.27) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.27) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.35) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.3) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.25) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.37) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.25) is not allowed
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.3) is not allowed
# PKNCA does not impute time 0 by default, so AUClast in the 0-24 interval is
# not calculated
summary(nca_obj)
#>  start  end  N     auclast
#>      0 24.0 12          NC
#>      0 24.1 12 76.4 [23.0]
#> 
#> Caption: auclast: geometric mean and geometric coefficient of variation; N: number of subjects

Advanced: Writing your own imputation functions

Writing your own imputation function is intended to be a simple process. To create an imputation function requires the following steps:

Write a function where the name starts with PKNCA_impute_method_ and the remainder of the function name is a brief description of the method. (Such as PKNCA_impute_method_start_conc0.)
The function should have 4 arguments: conc, time, ..., and options.
The function should return a single data.frame with two columns named conc and time. The rows in the data.frame must be sorted by time.

In addition to the above, the function may take named arguments of:

start and end to indicate the start and end time of the interval, and
conc.group and time.group to indicate the concentrations and times that have not been filtered for the interval.

Bill Denney

2026-08-21

How does imputation occur?

How to select imputation methods to use

Imputation for the full dataset

Imputation by calculation interval

Advanced: Writing your own imputation functions