Equation 7.vii in Nedelman and Jia, 1998 is used for this calculation:
Arguments
- sparse_pk
A sparse_pk object from
as_sparse_pk()
Details
$$var\left(\hat{AUC}\right) = \sum\limits_{i=0}^m\left(\frac{w_i^2 s_i^2}{r_i}\right) + 2\sum\limits_{i<j}\left(\frac{w_i w_j r_{ij} s_{ij}}{r_i r_j}\right)$$
The degrees of freedom are the Satterthwaite approximation of equation 6 of
the same paper for any sampling design, including subjects with more than
one sample (see the "df" attribute of the return value and Details of
cov_holder() for the covariance).
When the animals form groups sampled at exactly the same times, with no time sampled in more than one group (serial sacrifice, batch, and complete designs), the same variance and degrees of freedom are calculated from the weighted sum of each animal's samples, which is much faster for many animals. For serial sacrifice, the degrees of freedom are then equation 6a of Nedelman, Gibiansky, and Lau (1995).
References
Nedelman JR, Jia X. An extension of Satterthwaite’s approximation applied to pharmacokinetics. Journal of Biopharmaceutical Statistics. 1998;8(2):317-328. doi:10.1080/10543409808835241
Holder DJ. Comments on Nedelman and Jia’s Extension of Satterthwaite’s Approximation Applied to Pharmacokinetics. Journal of Biopharmaceutical Statistics. 2001;11(1-2):75-79. doi:10.1081/BIP-100104199
Nedelman JR, Gibiansky E, Lau DTW. Applying Bailer's method for AUC confidence intervals to sparse sampling. Pharmaceutical Research. 1995;12(1):124-128.