cov_holder {PKNCA} | R Documentation |
Calculate the covariance for two time points with sparse sampling
Description
The calculation follows equation A3 in Holder 2001 (see references below):
Usage
cov_holder(sparse_pk)
Arguments
sparse_pk |
A sparse_pk object from |
Details
If , then
is
defined as zero (rather than dividing by zero).
Where:
The covariance of times i and j
and
The number of subjects (usually animals) at times i and j, respectively
The number of subjects (usually animals) at both times i and j
and
The concentration measured for animal k at times i and j, respectively
and
The mean of the concentrations at times i and j, respectively
The Cauchy-Schwartz inequality is enforced for covariances to keep correlation coefficients between -1 and 1, inclusive, as described in equations 8 and 9 of Nedelman and Jia 1998.
Value
A matrix with one row and one column for each element of
sparse_pk_attribute
. The covariances are on the off diagonals, and for
simplicity of use, it also calculates the variance on the diagonal
elements.
References
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, Jia X. An extension of Satterthwaite’s approximation applied to pharmacokinetics. Journal of Biopharmaceutical Statistics. 1998;8(2):317-328. doi:10.1080/10543409808835241