# Computing NCA Parameters for Theophylline

#### Bill Denney

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 | Time | Subject
--- | --- | --- | ---
1 | 4.02 | 0 | 1
12 | 4.40 | 0 | 2
23 | 4.53 | 0 | 3
34 | 4.40 | 0 | 4
45 | 5.86 | 0 | 5
56 | 4.00 | 0 | 6
67 | 4.95 | 0 | 7
78 | 4.53 | 0 | 8
89 | 3.10 | 0 | 9
100 | 5.50 | 0 | 10
111 | 4.92 | 0 | 11
122 | 5.30 | 0 | 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
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
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    knitr::kable(data_obj_automatic$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 | Subject
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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 | 10
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 | 10
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 | 11
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 | 11
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 | 12
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 | 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 AUC0-\(\infty\), 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 | start | end | PPTESTCD | PPORRES | exclude
--- | --- | --- | --- | --- | ---
1 | 0 | 24 | auclast | 92.365442 | NA
1 | 0 | Inf | cmax | 10.500000 | NA
1 | 0 | Inf | tmax | 1.120000 | NA
1 | 0 | Inf | tlast | 24.370000 | NA
1 | 0 | Inf | clast.obs | 3.280000 | NA
1 | 0 | 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 | start | end | PPTESTCD | PPORRES | exclude
--- | --- | --- | --- | --- | ---
6 | 0 | Inf | auclast | 71.6970150 | NA
6 | 0 | Inf | cmax | 6.4400000 | NA
6 | 0 | Inf | tmax | 1.1500000 | NA
6 | 0 | Inf | tlast | 23.8500000 | NA
6 | 0 | Inf | clast.obs | 0.9200000 | NA
6 | 0 | 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