Easy and reliable maximum a posteriori Bayesian estimation of pharmacokinetic parameters with the open-source R package mapbayr

Abstract

Pharmacokinetic (PK) parameter estimation is a critical and complex step in the model-informed precision dosing (MIPD) approach. The mapbayr package was developed to perform maximum a posteriori Bayesian estimation (MAP-BE) in R from any population PK model coded in mrgsolve. The performances of mapbayr were assessed using two approaches. First, "test" models with different features were coded, for example, first-order and zero-order absorption, lag time, time-varying covariates, Michaelis-Menten elimination, combined and exponential residual error, parent drug and metabolite, and small or large inter-individual variability (IIV). A total of 4000 PK profiles (combining single/multiple dosing and rich/sparse sampling) were simulated from each test model, and MAP-BE of parameters was performed in both mapbayr and NONMEM. Second, a similar procedure was conducted with seven "real" previously published models to compare mapbayr and NONMEM on a PK outcome used in MIPD. For the test models, 98% of mapbayr estimations were identical to those given by NONMEM. Some discordances could be observed when dose-related parameters were estimated or when models with large IIV were used. The exploration of objective function values suggested that mapbayr might outdo NONMEM in specific cases. For the real models, a concordance close to 100% on PK outcomes was observed. The mapbayr package provides a reliable solution to perform MAP-BE of PK parameters in R. It also includes functions dedicated to data formatting and reporting and enables the creation of standalone Shiny web applications dedicated to MIPD, whatever the model or the clinical protocol and without additional software other than R.

FIGURE 1

Workflow of a Shiny web app to perform therapeutic drug monitoring with maximum a posteriori Bayesian estimation performed by mapbayr. Data format, parameter estimation, and estimation report are common whatever the drug and can be assumed by mapbayr functions (in blue). Computation of a specific a posteriori outcome and forecast of a dose adaptation is specific to the drug or protocol (in green). Arguments can be passed through a Shiny app (in red) so that the user enters information through a convenient interface. MAP, maximum a posteriori; PK, pharmacokinetics

FIGURE 2

Performance with 35 test models and four dosing/sampling regimens on parameter estimation. Each line represents 1000 estimations with an associated performance score: excellent if ${\mathrm{\Delta }\widehat{\theta }}_i$ < 0.1%, discordant if ${\mathrm{\Delta }\widehat{\theta }}_i$ > 10%, and acceptable in between. Dashed line indicates 95th percentile

FIGURE 3

OFVs at maximum likelihood for mapbayr and NONMEM. They were aligned on the identity line for the majority of individuals (4000 per run). Discrepancies were in favor of mapbayr for Run 3 (lag time), mainly in favor of NONMEM for Runs 207 (Michaelis–Menten elimination) and 504–513 (large inter‐individual variability), and balanced for Runs 4, 6 (infusion duration), and 911 (ibrutinib). One out‐of‐bound value is omitted in Run 911. OFV, objective function value

FIGURE 4

Performance with seven real models on parameter (left) and specific PK outcome (right) estimation. Dashed line indicates 95th percentile. AUC, area under the curve of concentrations versus time; AUC_τ,SS, AUC at steady state between two doses; C24ss, trough concentration at steady state