Bootstrap resampling of sparse PK data

sparse_bootstrap() makes a new sparse PKNCAconc() object holding the original data and n_boot bootstrap replicates of it, following the stratified nonparametric bootstrap of Shen and Machado (2017). Each replicate resamples the animals with replacement within each stratum, where the stratum is the set of times an animal was sampled: each sampling time with serial sacrifice, or each batch in a batch design. An animal's samples stay together, so the correlation between samples from the same animal is kept. pk.nca() then calculates every parameter for every replicate the same way as for the original data (from the arithmetic-mean profile, or with the sparse estimators). Its results summarize the replicates with summary(), and be_assess() compares groups with the percentile intervals of the replicates.

Usage

sparse_bootstrap(
  object,
  n_boot = 200,
  seed = NULL,
  paired = NULL,
  replicate_col = "bootstrap"
)

Arguments

object

A sparse PKNCAconc object

n_boot

The number of bootstrap replicates. The default of 200 is enough for the mean and standard deviation of the parameters (Takemoto et al. 2006); percentile confidence intervals need more replicates to be stable.

seed

The random seed for the resampling. When NULL, one is drawn (from the current random number stream) and stored in the result, so the replicates can always be reproduced. The random number state of the session is restored afterward.

paired

Group columns whose levels each animal has, so they are resampled together (for example, the treatment of a crossover design)

replicate_col

The name of the replicate group column to add

Value

A sparse PKNCAconc object with the original data and the replicates. Its bootstrap element records n_boot, seed, paired, replicate_col, and the original subject column.

Details

The replicates are a new group (replicate_col) with the values "original" (the data as given) and "bootstrap1" through "bootstrap<n_boot>". A resampled animal gets a new subject identifier (<replicate_col>_subject, the original subject with the draw number) so that an animal drawn twice counts as two animals.

Groups named in paired, and the analytes (the groups after / in the formula), are resampled together: an animal drawn for a replicate brings its samples from every level of those groups. Use paired for a crossover, where each animal (or eye, as in Shen and Machado 2017) receives each treatment. Other groups (such as the treatment of a parallel design) are resampled independently.

The "original" replicate holds the data as given, so the same pk.nca() run also gives the estimates.

References

Shen M, Machado SG. Bioequivalence evaluation of sparse sampling pharmacokinetics data using bootstrap resampling method. Journal of Biopharmaceutical Statistics. 2017;27(2):257-264. doi:10.1080/10543406.2016.1265543

Takemoto S, Yamaoka K, Nishikawa M, Takakura Y. Histogram analysis of pharmacokinetic parameters by bootstrap resampling from one-point sampling data in animal experiments. Drug Metabolism and Pharmacokinetics. 2006;21(6):458-464. doi:10.2133/dmpk.21.458

Wolfsegger MJ, Jaki T. Estimation of AUC from 0 to infinity in serial sacrifice designs. Journal of Pharmacokinetics and Pharmacodynamics. 2005;32(5-6):757-766. doi:10.1007/s10928-005-0044-0 (Bootstrap-t intervals on the analytical variance, where this bootstrap resamples the animals and takes the percentile or normal interval.)

See also

Other Sparse Methods: as_sparse_pk(), pk.calc.aucinf.obs_sparse(), pk.calc.aucivlast_sparse(), pk.calc.auclast_sparse(), pk.calc.sparse_auc(), pk.calc.sparse_aumc(), sparse_auc_weight_linear(), sparse_mean(), summary.PKNCAresults_sparse_bootstrap()

Examples

d_sparse <-
  data.frame(
    time = rep(c(0, 1, 2, 4, 8, 24), each = 3),
    conc = c(0, 0, 0, 5, 6, 4, 8, 7, 9, 6, 5, 7, 3, 2.5, 3.5, 0.6, 0.4, 0.5)
  )
d_sparse$animal <- seq_len(nrow(d_sparse))
o_conc <- PKNCAconc(d_sparse, conc ~ time | animal, sparse = TRUE)
o_conc_boot <- sparse_bootstrap(o_conc, n_boot = 20, seed = 1)
o_data_boot <-
  PKNCAdata(o_conc_boot, intervals = data.frame(start = 0, end = 24, auclast = TRUE, cmax = TRUE))
summary(pk.nca(o_data_boot))
#> The sparse estimators use the linear trapezoidal rule, so the auc.method option ("lin up/log down") does not apply to: auclast
#>  start end  N     auclast        cmax
#>      0  24 18 68.3 [5.01] 8.09 [5.61]
#> 
#> Caption: auclast, cmax: geometric mean and geometric coefficient of variation; N: number of animals in the study; summarized over 20 bootstrap replicates (seed 1)
#>