Gauss-Hermite cohort population estimation of dexamethasone pharmacokinetic parameters in pregnant women using blood samples collected at birth
Authors: Krzyzanski Wojciech 
Published: February 2025

Objectives: Gauss-Hermite cohort population approximates normally distributed subject pharmacokinetic (PK) parameters with a discrete number of point distributions (cohorts) using the Gauss quadrature rules for nodes and weights [1]. This discretization interprets part of between subject variability as unexplained (residual) variability that permits applying the likelihood estimation of parameters from a single observation per subject data. Blood samples from the umbilical cord and mother are collected for assessment of the fetal to maternal drug plasma concentration ratio at birth. Such data are inherently single observation per subject. The objective of this project was to test robustness of the Gauss-Hermite estimation technique using the previously published PK data on dexamethasone (DEX) in pregnant women. Methods: DEX concentrations in plasma from umbilical and peripheral veins collected at birth after intramuscular injection of two 6 mg antenatal doses of dexamethasone phosphate in 14 pregnant women were obtained from [2]. The one compartment model with first-order input was used to describe the maternal DEX concentrations. The fetal DEX concentrations were assumed to be proportional to the maternal ones with the FMR parameter as the proportionality coefficient. The 3-cohort lognormal distribution was used to quantify intersubject individual variability (IIV) of CL/F and V/F whereas ka and FMR were single cohort parameters. The proportional residual error models were used. The likelihood of observations and Fisher Information Matrix (FIM) were coded as R functions OBJ and FIM using reference equations [1], [3]. The minimization of the objective function was performed by the Nelder-Mead algorithm implemented in R [4]. The standard errors of parameter estimates were calculated as the square roots of the diagonal elements of the FIM. The single cohort parameter distribution (naïve pooled data) was used as a reference model. Results: The minimization of OBJ resulted in estimates of PK parameters for both reference and 3-cohort population models. The estimates (%RSE) of typical values of CL/F and V/F were 38.0 L/h (12%), 12.6 L (87%) with their %IIV 62% (43%) and 87% (79%). The estimates of typical values of FMR and ka were 0.34 (8%) and 0.4 1/h (25%). Inclusion of IIV for FMR resulted in a singular FIM. While the estimates of CL/F and FMR were similar to the reference model, the estimates of V/F and ka were 8-fold and 5-fold higher. The model reasonably well described the observed data. The squared correlation coefficients between observed and population predicted values of DEX concentrations were 0.54 and 0.22 for mother and fetus, respectively. Conclusions: The Gauss-Hermite cohort population estimates can be obtained with reasonable precision for single observation per subject data when the standard maximum likelihood estimation methods fail due to non-identifiability of IIV and residual variability. Citations: [1] Pinheiro JC and Bates DM (1995) Approximations to the log-likelihood function in the nonlinear mixed-effects model. J Comp Graph Stat 4:12-35 [2] Tsuei SE, Petersen MC, Ashley JJ, McBride WG, Moore RG (1980) Disposition of synthetic glucocorticoids II. Dexamethasone in parturient women. Clin. Pharmacol. Ther. 28: 88-98 [3] Philppou AN and Roussas GG (1975) Asymptotic normality of the maximum likelihoodestimate in the independent but not identically distributed case. Annals Inst Stat Math 27:45-55 [4] Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran 77. The Art of Scientific Computing. Volume 1. Cambridge University Press, Cambridge.