Wojciech Krzyzanski1
1University at Buffalo
Introduction: Cohort population approximates multivariate normal distribution with a discrete number of point distributions (cohorts) so that their first and second moments are identical. This discretization interprets part of between subject variability (BSV) as unexplained (residual) variability that permits applying the likelihood estimation of parameters from a single observation per subject data. For a cohort population, BSV is reduced to the variability between a finite number of cohorts and the residual variability accounts for the reminder of unexplained variability. The Gauss quadrature rules naturally define the distribution of model parameters for a cohort population as the sum of weighted delta functions centered at the quadrature nodes [1]. We previously applied the Gauss-Hermite cohort population to approximate the multivariate normal distribution with the diagonal covariance matrix [2]. Objectives: •To represent a cohort population as a mixture of populations with zero variances •To compare estimates of population parameters for cohort and FOCE methods •To demonstrate that cohort population permits estimates of the full covariance matrix for one compartment model with simulated sparse data Methods: One compartment model was used to simulate drug plasma concentrations in 60 subjects at times 0.5, 1, 2, 4, 8, and 16 h. The log(CL) and log(V) values were normally distributed with mean (log(0.3), log(3)) (L/h, L) and variance O=(?CLCL, ?CLV, ?VCL, ?VV)=(0.04, 0.01,0.01,0.09). The constant residual error was assumed with s2 = 0.09. Simulations were performed using R version 4.3.2. The sparse dat consisted of one observation per subject such that each observation time was shared by 10 subjects. The Gauss-Hermite cohort distributions for CL and V consisted of 1 and 3 cohorts. The 1-cohort population model was implemented as naïve pooled data. For the 3-cohhort model O=L’L, where L was the lower triangular matrix. The 3-cohort model was coded using mixture of 9 populations representing the product of 3×3 cohorts of means determined by the Gauss-Hermite quadrature nodes and zero variances. The mixing parameters were calculated from the quadrature weights. The cohort models were implemented in NONMEM 7.5 (ICON plc). For assessment of multinormal distribution estimates of CL and V, one compartment model used for simulations was coded in NONMEM. The 1-cohort model parameters were estimated by the first-order (FO) method and 3-cohort by the first-order conditional estimation (FOCE) method. Metrics used for comparison of all estimation methods included parameter estimates, their relative standard errors (RSEs), and objective function values (OFVs). Results: The single cohort estimates of (CL, V, s2) using the dense simulated data obtained by FO method were (0.32, 3.1, 0.15) with %RSEs (2.6, 2.9, 7.5). For the sparse dataset, the single cohort estimates of (CL, V, s2) were (0.35, 3.3, 0.13) with %RESs (5.9, 6.5, 14.8). The 3-cohort estimates of (CL, V, L11, L21, L22, s2) for the dense data were (0.31, 3.0, 0.11, 0.064, 0.26,0.11) with %RSEs (2.9, 4.4, 26, 90, 13, 7.3). The O calculated from matrix L were (?CLCL, ?CLV, ?VCL, ?VV) = (0.016, 0.016, 0.016 , 0.065). The sparse data 3-cohort estimates of (CL, V, L11, L21, L22, s2) were (0.33, 3.3, 0.25, 0.18, 0.30,0.03) with %RSEs (6.9, 6.2, 15, 37, 20, 53). The calculated values of (?CLCL, ?CLV, ?VV} were (0.093,0.054,0.088). The dense data FOCE estimates of {CL, V, ?CLCL, ?CLV, ?VV, s2} were (0.32, 3.1, 0.013, 0.012, 0.073, 0.11) with %RSEs (2.7, 4.3, 53, 66, 24, 78). The sparse data FOCE estimates of (CL, V, ?CLCL, ?CLV, ?VV, s2) were (0.35, 3.3, 0.025, 0.020, 0.061, 0.081). The RSEs were not calculated. The absolute difference between OFVs for 3-cohort and FOCE estimates for both dense and sparse data were less than 1.1. Conclusions. The 1-cohort estimation method yielded accurate estimates of typical values of CL and V for both dense and sparse data. The 3-cohort and FOCE estimates of all model parameters were similar for the dense data with similar %RSEs. The FOCE estimates for the sparse data were more accurate but the %RSE were not available. The 3-cohort estimates for dense data were less accurate but their %RSEs were relatively small. The cohort population estimates of typical values and covariance matrix can be obtained with reasonable precision for sparse data when the standard estimation methods fail. References: [1] Davis PJ, Rabinowitz P, Methods of Numerical Integration. Academic Press Inc., San Diego, 1984. [2] PAGE 32 (2024) Abstr 10864 [www.page-meeting.org/?abstract=10864]
[1] Davis PJ, Rabinowitz P, Methods of Numerical Integration. Academic Press Inc., San Diego, 1984. [2] PAGE 32 (2024) Abstr 10864 [www.page-meeting.org/?abstract=10864]
Reference: PAGE 33 (2025) Abstr 11516 [www.page-meeting.org/?abstract=11516]
Poster: Methodology - Estimation Methods