Evaluation of Pharmacostatistical Model Components Using a Nonlinear Mixed-effect Approach

Abstract

A nonlinear mixed-effect population pharmacokinetic (PPK) approach is a pharmacostatistical concept used to study pharmacokinetic (PK) and/or pharmacodynamic (PD) variability at the population level. PPK quantifies the typical PK and/or PD population parameter values (central tendency measures) and the magnitude of variability among individuals (measures of dispersion). Types of data used in PPK are collected from either a well-controlled clinical trial or routine care (observational studies). In terms of samples collected, this method can handle dense and limited (sparse) data given a sufficient number of subjects and assuming the recorded samples were withdrawn at times to allow PK/PD parameter estimation. In a nonlinear mixed-effects modeling (NLMEM) approach of PK and PD data, two levels of random effects are generally modeled: between-subject variability (BSV) and residual unexplained variability (RUV). In the study described in chapter 3, the goal was to investigate the extent to which PK and RUV model misspecification, errors in recording dosing and sampling times, and variability in drug content uniformity contribute to the estimated magnitude of RUV and PK parameter bias. We found the contribution of dose and dosing time misspecifications have negligible effects on RUV but result in higher bias in PK parameter estimates. Inaccurate documentation of sampling time results in biased RUV and increases with the magnitude of perturbations. Combined perturbation scenarios in the studied sources will propagate the variability and accumulate in RUV magnitude and result in bias of PK parameter estimates. This work provides insight into the potential contributions of many factors that comprise RUV and bias in PK parameters.In chapter 4 we describe a study designed to evaluate the impact of deviations in recorded time in NLMEM settings. An assumption that clinical data are recorded without any error is optimistically made. While some study personnel will record the actual times when there is a deviation others record the nominal time. Therefore, we investigate including an additional random effect on the independent variable time and quantitate the bias in estimated parameters; and determine the sensitivity of the magnitude of deviation between actual and recorded times on parameter estimation bias. Hence, we report that adding a random quantity to the recorded time will lead to reducing the bias and imprecision in PK estimates compared to assuming the recorded time is absolute. In chapter 5, we take a closer look at diagnosing pharmacostatistical models. Specifically, both traditional weighted residuals (WRES) and conditional weighted residuals (CWRES) are common metrics to graphically evaluate model acceptability in population analyses. Limited by the lower limit of quantification (LLOQ) of analytical techniques, it is not uncommon to have concentrations reported as below the LLOQ (BLQ) in PK studies. Although various approaches have been proposed to accommodate BLQ data, M3 method currently appears to be the most common. That being said, NONMEM excluded the calculation of all WRES/CWRES for each subject with BLQ data due to a concern that the residuals for that subject might be biased. Our aim was to conduct a simulation study to investigate the extent to which weighted residual calculations in subjects having some BLQ data might be biased when using the M3 method. We conclude that bias in CWRES and WRES can be detected but is small and unlikely to impact decisions made based on weighted residual–based diagnostic plots when the M3 method with MDVRES is performed to accommodate BLQ observations in the scenarios we studied. Another important pharmacostatistical component is the structural PK model, and in chapter 6, we evaluate absorption models. Absorption processes are complex but rarely have sufficient data to capture the parameters of a mechanistic model. Typically, a single absorption model (e.g., first-order, mixed-order, lag, or distributive delay model), is assumed to apply to all individuals with the expectation that random effects will accommodate individual differences. However, distinct absorption profiles may coexist in a given dataset. Thus, we propose that individualized absorption models should be considered when multiple absorption profiles are evident in a population analysis. Machine learning is gaining wider attention in clinical pharmacology and pharmacometrics as computational capacity increases. Methods for machine learning use statistical algorithms and methods that are capable of doing automated learning from existing data to uncover patterns. Therefore, we wish to evaluate an exercise in chapter 7 to train a deep neural network to automatically prespecify absorption models. Finally, the knowledge provided in this thesis will bring us closer to using pharmacometrics methodology to individualize patient care by understanding the sources of variability and embracing the model individualization concept.