Sparse NCA Calculations
Sparse noncompartmental analysis (NCA) is performed when multiple individuals contribute to a single concentration-time profile due to the fact that there are only one or a subset of the full profile samples taken per animal. A typical example is when three mice have PK drawn per time point, but no animals have more than one sample drawn. Another typical example is when animals may have two or three samples during an interval, but no animal has the full profile.
Sparse NCA Setup
Sparse NCA is setup similarly to how normal, dense PK sampling is
setup with PKNCA. The only difference are that you give the
sparse option to PKNCAconc(), and in your
interval calculations, you will request the sparse variants of the
parameters. As of the writing of this vignette, the only sparse
parameter for calculation is sparse_auclast. Any of the
non-sparse parameters will be calculated based on the mean profile of
the animals in a group.
The example below uses data extracted from Holder D. J., Hsuan F., Dixit R. and Soper K. (1999). A method for estimating and testing area under the curve in serial sacrifice, batch, and complete data designs. Journal of Biopharmaceutical Statistics, 9(3):451-464.
# Setup the data
d_sparse <-
data.frame(
id = c(1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 4L, 5L, 6L, 4L, 5L, 6L, 7L, 8L, 9L, 7L, 8L, 9L),
conc = c(0, 0, 0, 1.75, 2.2, 1.58, 4.63, 2.99, 1.52, 3.03, 1.98, 2.22, 3.34, 1.3, 1.22, 3.54, 2.84, 2.55, 0.3, 0.0421, 0.231),
time = c(0, 0, 0, 1, 1, 1, 6, 6, 6, 2, 2, 2, 10, 10, 10, 4, 4, 4, 24, 24, 24),
dose = c(100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100)
)Look at your data. (This is not technically a required step, but it’s good practice.)
library(ggplot2)
ggplot(d_sparse, aes(x=time, y=conc, group=id)) +
geom_point() +
geom_line() +
scale_x_continuous(breaks=seq(0, 24, by=6))
Data Setup Note
Sparse NCA requires that subject numbers (or animal numbers) are given, even if each subject only contributes a single sample. The reason for this requirement is that which subject contributes to which time point changes the standard error calculation. If all individuals contribute a single sample, a simple way to handle this is by setting a column with sequential numbers and giving that as the subject identifier:
d_sparse$id <- 1:nrow(d_sparse)How Subjects Are Grouped for Sparse Calculations
With dense (normal) PK, every subject has a full concentration-time profile, so NCA parameters are calculated one subject at a time. Sparse parameters are different: they are calculated from the pooled samples of every subject that belongs to the same group. Knowing what defines a “group” is therefore important.
The groups are taken from the grouping variables on the right of the
| in the PKNCAconc() formula, with the
subject column removed. Every subject that shares the same
combination of the remaining (non-subject) grouping variables
contributes to a single pooled sparse concentration-time profile.
In the simple example above, the formula is
conc~time|id. Here id is the subject, and
removing it leaves no other grouping variables, so all of the data form
a single sparse group.
The behavior is easier to see with more grouping variables. Suppose the concentration and dose objects are created with the formulas below (illustrative code; not run here):
o_conc_sparse <- PKNCAconc(d_conc, conc~time|matrix+drug+usubjid/analyte, sparse=TRUE)
o_dose_sparse <- PKNCAdose(d_dose, dose~time|drug+usubjid)usubjid is the subject because, by default, the subject
is the last grouping variable before any / (or the last
grouping variable when there is no /). After dropping the
subject, the grouping variables that remain are matrix,
drug, and analyte. Sparse parameters are
therefore calculated by combining all subjects within each unique
combination of matrix, drug, and
analyte.
In other words, with that formula PKNCA does not
keep each usubjid separate, and it does
not group by matrix, drug, or
analyte alone. It pools subjects using the full set of
non-subject grouping variables together (matrix +
drug + analyte).
Because subjects are pooled within a group, all subjects in a group must share the same dosing. If subjects in the same group have different dosing information (for example, different dose amounts or dose times), PKNCA stops with an error identifying the inconsistent group.
Calculate!
Setup PKNCA for calculations and then calculate!
##
## Attaching package: 'PKNCA'## The following object is masked from 'package:stats':
##
## filter
o_conc_sparse <- PKNCAconc(d_sparse, conc~time|id, sparse=TRUE)
d_intervals <-
data.frame(
start=0,
end=24,
aucinf.obs=TRUE,
cmax=TRUE,
sparse_auclast=TRUE
)
o_data_sparse <- PKNCAdata(o_conc_sparse, intervals=d_intervals)
o_nca <- pk.nca(o_data_sparse)## No dose information provided, calculations requiring dose will return NA.## Warning: Too few points for half-life calculation (min.hl.points=3 with only 2
## points)## Warning: Cannot yet calculate sparse degrees of freedom for multiple samples
## per subjectResults
As with any other PKNCA result, the data are available through the
summary() function:
summary(o_nca)## start end cmax sparse_auclast aucinf.obs
## 0 24 3.05 39.5 NC
##
## Caption: cmax, sparse_auclast, aucinf.obs: geometric mean and geometric coefficient of variationor individual results are available through the
as.data.frame() function:
as.data.frame(o_nca)## # A tibble: 18 × 6
## start end PPTESTCD PPORRES PPANMETH exclude
## <dbl> <dbl> <chr> <dbl> <chr> <chr>
## 1 0 24 cmax 3.05 "" NA
## 2 0 24 tmax 6 "" NA
## 3 0 24 tlast 24 "" NA
## 4 0 24 clast.obs 0.191 "" NA
## 5 0 24 lambda.z NA "" Too few point…
## 6 0 24 r.squared NA "" Too few point…
## 7 0 24 adj.r.squared NA "" Too few point…
## 8 0 24 lambda.z.corrxy NA "" Too few point…
## 9 0 24 lambda.z.time.first NA "" Too few point…
## 10 0 24 lambda.z.time.last NA "" Too few point…
## 11 0 24 lambda.z.n.points NA "" Too few point…
## 12 0 24 clast.pred NA "" Too few point…
## 13 0 24 half.life NA "" Too few point…
## 14 0 24 span.ratio NA "" Too few point…
## 15 0 24 aucinf.obs NA "AUC: lin up/log down" Too few point…
## 16 0 24 sparse_auclast 39.5 "" NA
## 17 0 24 sparse_auc_se 7.31 "" NA
## 18 0 24 sparse_auc_df NA "" NA