An automated pipeline to generate initial estimates for population Pharmacokinetic base models

Abstract

Nonlinear mixed-effects models rely on adequate initial parameter estimates for efficient parameter optimization. Poor initial estimates can result in failed model convergence or termination with incorrect parameter estimates. Non-compartmental analysis (NCA) and other manual methods have typically been used to derive initial estimates for pharmacokinetic (PK) parameters. However, NCA struggles with sparse data and recent advances in automated modeling increasingly emphasize the need for initial estimates that require no user input. This study aimed to develop an integrated pipeline for the computation of initial estimates applicable to various data types and model structures. The designed pipeline incorporated a custom-designed algorithm that leveraged data-driven methods to generate initial estimates for both structural and statistical parameters in population pharmacokinetic (PopPK) base models. The pipeline's performance was evaluated across twenty-one simulated datasets and thirteen real-life datasets. The results suggested that this pipeline performed well in all test cases. Initial estimates recommended by the pipeline resulted in final parameter estimates closely aligned with pre-set true values in simulated datasets or with literature references in the case of real-life data. This study provides an efficient and reliable tool for delivering PK initial estimates for population pharmacokinetic modeling in both rich and sparse data scenarios. An open-source R package has been created.

Keywords: Automated modeling; Initial estimates; Population pharmacokinetics; Sparse data.

Fig. 1

Workflow diagram of the automated pipeline for generating initial estimates of commonly used PK parameters. The workflow consists of three main parts: the first focuses on computing one-compartment parameters, including clearance (CL), volume of distribution (V_d), and absorption rate constant (K_a) (the top panel); the second part concentrates on extended structural parameters of multi-compartment and Michaelis-Menton elimination models (the middle panel). These include: V_c (central volume of distribution), V_p (volume of distribution of peripheral compartment), Q (inter-compartmental clearance), V_p2 (volume of distribution of the second peripheral compartment), Q₂ (the second inter-compartmental clearance), maximum elimination rate (V_max), and Michaelis constant (K_m); The final part (the bottom panel) handles statistical model components, including σ_add (standard deviation of additive residual error model), σ_prop (standard deviation of proportional residual error model), and ω² (variance of IIV). The rRMSE refers to the relative root mean square error

Fig. 2

Example simulation outputs from a parameter sweep exploring different K_m/C_max ratios (A) and V_c/V_p ratios (B). Panel A shows simulation results using K_m/C_max ratios ranging from 4:1 to 1:20, modeled using a one-compartment model with Michaelis-Menten elimination. Panel B presents outputs for V_c/V_p ratios ranging from 10:1 to 1:10, simulated in a two-compartment model. The dose event was set as a single intravenous administration of 100 mg. Input parameters included CL = 4 L/h and V_c = 70 L, with C_max = 100 ng/mL. In this example, C was set as 10% of C_max for V_max calculation in Panel A, and Q was set equal to CL in Panel B. Other values were also examined during the actual parameter sweeping, including V_max calculated at 5%, 10%, 25%, 50%, and 75% of C_max, and Q scaled to 0.25-, 0.5-, 1- and 2-fold of CL

Fig. 3

Initial and final estimate deviations [%] from true values used in the simulation across simulated datasets. Each subplot corresponds to one PK parameter: (A) CL, clearance, (B) V_c (1CMPT), the central volume of distribution in a one-compartment model, (C) V_max, the maximum metabolic rate, (D) K_m, the Michaelis-Menten constant, (E) V_c (2CMPT), the central volume in a two-compartment model, and (F) V_p, the peripheral volume of distribution. (G) K_a absorption rate constant, (H) standard deviations of proportional residual error model. Bars represent the percentage deviations of parameter estimates from their true values, with blue bars indicating the initial estimate deviations (before model fitting), orange bars showing the final deviations after fitting with the SAEM algorithm, and green bars showing the final deviations after fitting with the FOCEI algorithm. A dashed black horizontal Line at 20% denotes a reference threshold

Fig. 4

Comparison of re-estimated clearance (top) and volume of distribution (bottom) in simulated datasets across different strategies of setting initial estimates run by SAEM. This figure containes re-estimation of clearance and volume of distribution using five different initial estimate strategies, represented by distinct colors. inits = 1 sets all initial estimates to 1, while inits = nls, inits = nlm, and inits = nlminb used parameter estimates from respective algorithms as initial values. inits = pipeline referred to pipeline-specific recommendations. To address excessively large initial estimates, the y-axis was capped at 2-fold of the true values. Bars exceeding this limit were truncated at the 2-fold value and annotated with “>2-fold” to indicate their magnitude