Examples simplify understanding. Below is an example of how to use the theophylline dataset to generate NCA parameters.

Load the data

## It is always a good idea to look at the data
knitr::kable(head(datasets::Theoph))

Subject	Wt	Dose	Time	conc
1	79.6	4.02	0.00	0.74
1	79.6	4.02	0.25	2.84
1	79.6	4.02	0.57	6.57
1	79.6	4.02	1.12	10.50
1	79.6	4.02	2.02	9.66
1	79.6	4.02	3.82	8.58

The columns that we will be interested in for our analysis are conc, Time, and Subject in the concentration data set and Dose, Time, and Subject for the dosing data set.

## By default it is groupedData; convert it to a data frame for use
conc_obj <- PKNCAconc(as.data.frame(datasets::Theoph), conc~Time|Subject)

## Dosing data needs to only have one row per dose, so subset for
## that first.
d_dose <- unique(datasets::Theoph[datasets::Theoph$Time == 0,
                                  c("Dose", "Time", "Subject")])
knitr::kable(d_dose,
             caption="Example dosing data extracted from theophylline data set")

Example dosing data extracted from theophylline data set
	Dose	Subject
1	4.02	1
12	4.40	2
23	4.53	3
34	4.40	4
45	5.86	5
56	4.00	6
67	4.95	7
78	4.53	8
89	3.10	9
100	5.50	10
111	4.92	11
122	5.30	12

dose_obj <- PKNCAdose(d_dose, Dose~Time|Subject)

Merge the Concentration and Dose

After loading the data, they must be combined to prepare for parameter calculation. Intervals for calculation will automatically be selected based on the single.dose.aucs setting in PKNCA.options

data_obj_automatic <- PKNCAdata(conc_obj, dose_obj)
knitr::kable(PKNCA.options("single.dose.aucs"))

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	count_conc_measured	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.time.last	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	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	FALSE	TRUE	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	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE

knitr::kable(data_obj_automatic$intervals)

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	count_conc_measured	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.time.last	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	Subject
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	FALSE	FALSE	1
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	FALSE	TRUE	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	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	1
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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	FALSE	TRUE	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	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	5
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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	FALSE	TRUE	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	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	11
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	FALSE	FALSE	12
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	FALSE	TRUE	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	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	12

Intervals for calculation can also be specified manually. Manual specification requires at least columns for start time, end time, and the parameters requested. The manual specification can also include any grouping factors from the concentration data set. Column order of the intervals is not important. When intervals are manually specified, they are expanded to the full interval set when added to a PKNCAdata object (in other words, a column is created for each parameter. Also, PKNCA automatically calculates parameters required for the NCA, so while lambda.z is required for calculating AUC_0-\(\infty\), you do not have to specify it in the parameters requested.

intervals_manual <- data.frame(start=0,
                               end=Inf,
                               cmax=TRUE,
                               tmax=TRUE,
                               aucinf.obs=TRUE,
                               auclast=TRUE)
data_obj_manual <- PKNCAdata(conc_obj, dose_obj,
                             intervals=intervals_manual)
knitr::kable(data_obj_manual$intervals)

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	count_conc_measured	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.time.last	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	Inf	TRUE	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	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	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE	FALSE

Compute the parameters

Parameter calculation will automatically split the data by the grouping factor(s), subset by the interval, calculate all required parameters, record all options used for the calculations, and include data provenance to show that the calculation was performed as described. For all this, just call the pk.nca function with your PKNCAdata object.

results_obj_automatic <- pk.nca(data_obj_automatic)
knitr::kable(head(as.data.frame(results_obj_automatic)))

Subject	end	PPTESTCD	PPORRES	exclude
1	24	auclast	92.365442	NA
1	Inf	cmax	10.500000	NA
1	Inf	tmax	1.120000	NA
1	Inf	tlast	24.370000	NA
1	Inf	clast.obs	3.280000	NA
1	Inf	lambda.z	0.048457	NA

summary(results_obj_automatic)

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]

results_obj_manual <- pk.nca(data_obj_manual)
knitr::kable(head(as.data.frame(results_obj_manual)))

Subject	end	PPTESTCD	PPORRES	exclude
6	Inf	auclast	71.6970150	NA
6	Inf	cmax	6.4400000	NA
6	Inf	tmax	1.1500000	NA
6	Inf	tlast	23.8500000	NA
6	Inf	clast.obs	0.9200000	NA
6	Inf	lambda.z	0.0877957	NA

summary(results_obj_manual)

start	end	N	auclast	cmax	tmax	aucinf.obs
0	Inf	12	98.7 [22.5]	8.65 [17.0]	1.14 [0.630, 3.55]	115 [28.4]

Multiple Dose Example

Assessing multiple dose pharmacokinetics is conceptually the same as single-dose in PKNCA.

To assess multiple dose PK, the theophylline data will be extended from single to multiple doses using superposition (see the superposition vignette for more information).

d_conc <- PKNCAconc(as.data.frame(Theoph), conc~Time|Subject)
conc_obj_multi <-
  PKNCAconc(
    superposition(d_conc,
                  tau=168,
                  dose.times=seq(0, 144, by=24),
                  n.tau=1,
                  check.blq=FALSE),
    conc~time|Subject)
conc_obj_multi

## Formula for concentration:
##  conc ~ time | Subject
## Data are dense PK.
## With 12 subjects defined in the 'Subject' column.
## Nominal time column is not specified.
## 
## First 6 rows of concentration data:
##  Subject     conc time exclude volume duration
##        1  0.74000 0.00    <NA>     NA        0
##        1  2.84000 0.25    <NA>     NA        0
##        1  4.23875 0.37    <NA>     NA        0
##        1  6.57000 0.57    <NA>     NA        0
##        1 10.50000 1.12    <NA>     NA        0
##        1  9.66000 2.02    <NA>     NA        0

dose_obj_multi <- PKNCAdose(expand.grid(Subject=unique(as.data.frame(conc_obj_multi)$Subject),
                                      time=seq(0, 144, by=24)),
                          ~time|Subject)
dose_obj_multi

## Formula for dosing:
##  ~time | Subject
## Nominal time column is not specified.
## 
## First 6 rows of dosing data:
##  Subject time exclude         route duration
##        1    0    <NA> extravascular        0
##        2    0    <NA> extravascular        0
##        3    0    <NA> extravascular        0
##        4    0    <NA> extravascular        0
##        5    0    <NA> extravascular        0
##        6    0    <NA> extravascular        0

The superposition-simulated scenario is not especially realistic as it includes dense sampling on every day. With this scenario, the intervals automatically selected have an interval for every subject on every day.

data_obj <- PKNCAdata(conc_obj_multi, dose_obj_multi)
data_obj$intervals[,c("Subject", "start", "end")]

## # A tibble: 84 × 3
##    Subject start   end
##    <ord>   <dbl> <dbl>
##  1 1           0    24
##  2 1          24    48
##  3 1          48    72
##  4 1          72    96
##  5 1          96   120
##  6 1         120   144
##  7 1         144   168
##  8 2           0    24
##  9 2          24    48
## 10 2          48    72
## # ℹ 74 more rows

In a more realistic scenario, dense PK sampling occurs for every subject on the first and last days. To select those intervals manually, specify the intervals of interest in the intervals argument to the PKNCAdata function call. The intervals are automatically expanded not to calculate anything that was not requested.

intervals_manual <- data.frame(start=c(0, 144),
                               end=c(24, 168),
                               cmax=TRUE,
                               auclast=TRUE)
data_obj <- PKNCAdata(conc_obj_multi, dose_obj_multi,
                      intervals=intervals_manual)
data_obj$intervals

##   start end auclast aucall aumclast aumcall aucint.last aucint.last.dose
## 1     0  24    TRUE  FALSE    FALSE   FALSE       FALSE            FALSE
## 2   144 168    TRUE  FALSE    FALSE   FALSE       FALSE            FALSE
##   aucint.all aucint.all.dose    c0 cmax  cmin  tmax tlast tfirst clast.obs
## 1      FALSE           FALSE FALSE TRUE FALSE FALSE FALSE  FALSE     FALSE
## 2      FALSE           FALSE FALSE TRUE FALSE FALSE 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 count_conc_measured
## 1                FALSE               FALSE      FALSE               FALSE
## 2                FALSE               FALSE      FALSE               FALSE
##   totdose    ae clr.last clr.obs clr.pred    fe sparse_auclast sparse_auc_se
## 1   FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE         FALSE
## 2   FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE         FALSE
##   sparse_auc_df time_above aucivlast aucivall aucivint.last aucivint.all
## 1         FALSE      FALSE     FALSE    FALSE         FALSE        FALSE
## 2         FALSE      FALSE     FALSE    FALSE         FALSE        FALSE
##   aucivpbextlast aucivpbextall aucivpbextint.last aucivpbextint.all half.life
## 1          FALSE         FALSE              FALSE             FALSE     FALSE
## 2          FALSE         FALSE              FALSE             FALSE     FALSE
##   r.squared adj.r.squared lambda.z lambda.z.time.first lambda.z.time.last
## 1     FALSE         FALSE    FALSE               FALSE              FALSE
## 2     FALSE         FALSE    FALSE               FALSE              FALSE
##   lambda.z.n.points clast.pred span.ratio thalf.eff.last thalf.eff.iv.last
## 1             FALSE      FALSE      FALSE          FALSE             FALSE
## 2             FALSE      FALSE      FALSE          FALSE             FALSE
##   kel.last kel.iv.last aucinf.obs aucinf.pred aumcinf.obs aumcinf.pred
## 1    FALSE       FALSE      FALSE       FALSE       FALSE        FALSE
## 2    FALSE       FALSE      FALSE       FALSE       FALSE        FALSE
##   aucint.inf.obs aucint.inf.obs.dose aucint.inf.pred aucint.inf.pred.dose
## 1          FALSE               FALSE           FALSE                FALSE
## 2          FALSE               FALSE           FALSE                FALSE
##   aucivinf.obs aucivinf.pred aucivpbextinf.obs aucivpbextinf.pred aucpext.obs
## 1        FALSE         FALSE             FALSE              FALSE       FALSE
## 2        FALSE         FALSE             FALSE              FALSE       FALSE
##   aucpext.pred cl.obs cl.pred mrt.obs mrt.pred mrt.iv.obs mrt.iv.pred
## 1        FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
## 2        FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
##   mrt.md.obs mrt.md.pred vz.obs vz.pred vss.obs vss.pred vss.iv.obs vss.iv.pred
## 1      FALSE       FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
## 2      FALSE       FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
##   vss.md.obs vss.md.pred cav.int.inf.obs cav.int.inf.pred thalf.eff.obs
## 1      FALSE       FALSE           FALSE            FALSE         FALSE
## 2      FALSE       FALSE           FALSE            FALSE         FALSE
##   thalf.eff.pred thalf.eff.iv.obs thalf.eff.iv.pred kel.obs kel.pred kel.iv.obs
## 1          FALSE            FALSE             FALSE   FALSE    FALSE      FALSE
## 2          FALSE            FALSE             FALSE   FALSE    FALSE      FALSE
##   kel.iv.pred auclast.dn aucall.dn aucinf.obs.dn aucinf.pred.dn aumclast.dn
## 1       FALSE      FALSE     FALSE         FALSE          FALSE       FALSE
## 2       FALSE      FALSE     FALSE         FALSE          FALSE       FALSE
##   aumcall.dn aumcinf.obs.dn aumcinf.pred.dn cmax.dn cmin.dn clast.obs.dn
## 1      FALSE          FALSE           FALSE   FALSE   FALSE        FALSE
## 2      FALSE          FALSE           FALSE   FALSE   FALSE        FALSE
##   clast.pred.dn cav.dn ctrough.dn
## 1         FALSE  FALSE      FALSE
## 2         FALSE  FALSE      FALSE

After the data is ready, the calculations and summary can progress.

results_obj <- pk.nca(data_obj)
print(results_obj)

## $result
## # A tibble: 48 × 6
##    Subject start   end PPTESTCD PPORRES exclude
##    <ord>   <dbl> <dbl> <chr>      <dbl> <chr>  
##  1 6           0    24 auclast    71.8  <NA>   
##  2 6           0    24 cmax        6.44 <NA>   
##  3 6         144   168 auclast    82.2  <NA>   
##  4 6         144   168 cmax        7.37 <NA>   
##  5 7           0    24 auclast    89.0  <NA>   
##  6 7           0    24 cmax        7.09 <NA>   
##  7 7         144   168 auclast   101.   <NA>   
##  8 7         144   168 cmax        8.07 <NA>   
##  9 8           0    24 auclast    86.7  <NA>   
## 10 8           0    24 cmax        7.56 <NA>   
## # ℹ 38 more rows
## 
## $data
## Formula for concentration:
##  conc ~ time | Subject
## Data are dense PK.
## With 12 subjects defined in the 'Subject' column.
## Nominal time column is not specified.
## 
## First 6 rows of concentration data:
##  Subject     conc time exclude volume duration
##        1  0.74000 0.00    <NA>     NA        0
##        1  2.84000 0.25    <NA>     NA        0
##        1  4.23875 0.37    <NA>     NA        0
##        1  6.57000 0.57    <NA>     NA        0
##        1 10.50000 1.12    <NA>     NA        0
##        1  9.66000 2.02    <NA>     NA        0
## Formula for dosing:
##  ~time | Subject
## Nominal time column is not specified.
## 
## First 6 rows of dosing data:
##  Subject time exclude         route duration
##        1    0    <NA> extravascular        0
##        2    0    <NA> extravascular        0
##        3    0    <NA> extravascular        0
##        4    0    <NA> extravascular        0
##        5    0    <NA> extravascular        0
##        6    0    <NA> extravascular        0
## 
## With 2 rows of interval specifications.
## With imputation: NA
## Options changed from default are:
## $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"
## 
## 
## $debug
## NULL
## 
## $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 count_conc_measured
## 1                FALSE               FALSE      FALSE               FALSE
## 2                FALSE               FALSE      FALSE               FALSE
##   totdose    ae clr.last clr.obs clr.pred    fe sparse_auclast sparse_auc_se
## 1   FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE         FALSE
## 2   FALSE FALSE    FALSE   FALSE    FALSE FALSE          FALSE         FALSE
##   sparse_auc_df time_above aucivlast aucivall aucivint.last aucivint.all
## 1         FALSE      FALSE     FALSE    FALSE         FALSE        FALSE
## 2         FALSE      FALSE     FALSE    FALSE         FALSE        FALSE
##   aucivpbextlast aucivpbextall aucivpbextint.last aucivpbextint.all half.life
## 1          FALSE         FALSE              FALSE             FALSE     FALSE
## 2          FALSE         FALSE              FALSE             FALSE      TRUE
##   r.squared adj.r.squared lambda.z lambda.z.time.first lambda.z.time.last
## 1     FALSE         FALSE    FALSE               FALSE              FALSE
## 2     FALSE         FALSE    FALSE               FALSE              FALSE
##   lambda.z.n.points clast.pred span.ratio thalf.eff.last thalf.eff.iv.last
## 1             FALSE      FALSE      FALSE          FALSE             FALSE
## 2             FALSE      FALSE      FALSE          FALSE             FALSE
##   kel.last kel.iv.last aucinf.obs aucinf.pred aumcinf.obs aumcinf.pred
## 1    FALSE       FALSE      FALSE       FALSE       FALSE        FALSE
## 2    FALSE       FALSE       TRUE       FALSE       FALSE        FALSE
##   aucint.inf.obs aucint.inf.obs.dose aucint.inf.pred aucint.inf.pred.dose
## 1          FALSE               FALSE           FALSE                FALSE
## 2          FALSE               FALSE           FALSE                FALSE
##   aucivinf.obs aucivinf.pred aucivpbextinf.obs aucivpbextinf.pred aucpext.obs
## 1        FALSE         FALSE             FALSE              FALSE       FALSE
## 2        FALSE         FALSE             FALSE              FALSE       FALSE
##   aucpext.pred cl.obs cl.pred mrt.obs mrt.pred mrt.iv.obs mrt.iv.pred
## 1        FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
## 2        FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
##   mrt.md.obs mrt.md.pred vz.obs vz.pred vss.obs vss.pred vss.iv.obs vss.iv.pred
## 1      FALSE       FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
## 2      FALSE       FALSE  FALSE   FALSE   FALSE    FALSE      FALSE       FALSE
##   vss.md.obs vss.md.pred cav.int.inf.obs cav.int.inf.pred thalf.eff.obs
## 1      FALSE       FALSE           FALSE            FALSE         FALSE
## 2      FALSE       FALSE           FALSE            FALSE         FALSE
##   thalf.eff.pred thalf.eff.iv.obs thalf.eff.iv.pred kel.obs kel.pred kel.iv.obs
## 1          FALSE            FALSE             FALSE   FALSE    FALSE      FALSE
## 2          FALSE            FALSE             FALSE   FALSE    FALSE      FALSE
##   kel.iv.pred auclast.dn aucall.dn aucinf.obs.dn aucinf.pred.dn aumclast.dn
## 1       FALSE      FALSE     FALSE         FALSE          FALSE       FALSE
## 2       FALSE      FALSE     FALSE         FALSE          FALSE       FALSE
##   aumcall.dn aumcinf.obs.dn aumcinf.pred.dn cmax.dn cmin.dn clast.obs.dn
## 1      FALSE          FALSE           FALSE   FALSE   FALSE        FALSE
## 2      FALSE          FALSE           FALSE   FALSE   FALSE        FALSE
##   clast.pred.dn cav.dn ctrough.dn
## 1         FALSE  FALSE      FALSE
## 2         FALSE  FALSE      FALSE
## 
## $allow_partial_missing_units
## [1] FALSE
## 
## 
## $columns
## $columns$exclude
## [1] "exclude"
## 
## 
## attr(,"class")
## [1] "PKNCAresults" "list"        
## attr(,"provenance")
## Provenance hash ee687a520af821aa354fef62aa53cba0 generated on 2025-08-18 20:37:10.490161 with R version 4.5.0 (2025-04-11 ucrt).

summary(results_obj)

##  start end  N     auclast        cmax
##      0  24 12 98.8 [23.0] 8.65 [17.0]
##    144 168 12  115 [28.4] 10.0 [21.0]
## 
## Caption: auclast, cmax: geometric mean and geometric coefficient of variation; N: number of subjects

Computing NCA Parameters for Theophylline

Bill Denney

Load the data

Merge the Concentration and Dose

Compute the parameters

Multiple Dose Example