Pharmacodynamic Models for Discrete Data

Abstract

Clinical outcomes are often described as events: death, stroke, epileptic seizure, multiple sclerosis lesions, recurrence of cancer, disease progression, pain, infection and bacterial/viral eradication, severe toxic adverse effect, resistance to treatment, etc. They may be quantified as time-to-event, counts of events per time interval (rates), their severity grade, or a combination of these. Such data are discrete and require specific modelling structures and methods. This article references the most common modelling approaches for categorical, count and time-to-event data, and reviews examples of such models applied in the analysis of pharmacodynamic data. Modelling is useful for identification of influential factors related to the clinical outcome, characterization and quantification of their impact, for making better informed predictions and clinical decisions, assessments of efficacy of therapeutic interventions, optimizing the individual treatments and drug development studies.

PharmML in Action: an Interoperable Language for Modeling and Simulation

“…A strength of PharmML is that it can be applied to any kind of deterministic model that can be formulated using algebraic, ordinary, and delayed differential equations, covering most models encountered in PK, PD, PK/PD, or QSP. Discrete data models pose a challenge, as they come in a large variety: PharmML provides a rich vocabulary to cover count, categorical, and time‐to‐event data models, Markovian dependencies, and censoring . Combinations of any number of observations in one model is permitted.…”

“…For this purpose, DDMoRe developed ProbOnto (http://probonto.org), a knowledge base and ontology covering a large family of distributions . ProbOnto now contains over 100 univariate and multivariate probability distributions along with their defining functions and interrelationships, and has proved to be particularly helpful in the encoding of discrete models, abundant in pharmacometrics, such as the zero‐inflated Poisson, zero‐inflated negative binomial, and generalized Poisson models, with various parameterizations …”

“…Discrete data models pose a challenge, as they come in a large variety: PharmML provides a rich vocabulary to cover count, categorical, and time-toevent data models, Markovian dependencies, and censoring. 6,[22][23][24] Combinations of any number of observations in one model is permitted. Modeling individual and population parameters is one of the key ingredients in pharmacometrics.…”

“…26 ProbOnto now contains over 100 univariate and multivariate probability distributions along with their defining functions and interrelationships, and has proved to be particularly helpful in the encoding of discrete models, abundant in pharmacometrics, such as the zero-inflated Poisson, zero-inflated negative binomial, and generalized Poisson models, with various parameterizations. [22][23][24]27 The rest of this section describes the different parts of the PharmML Model Definition. A detailed overview of its structure is provided by Figure S2 in the "Supplementary information -Figures" file.…”

Modeling and Simulation of Count Data

“…Pharmacometrics, 1 while having first been solely applied to continuous data due to its historical ties with pharmacokinetics 2 and its methodological complexities, 3 now commonly includes analysis of discrete type data. 4 This tutorial, intended for pharmacometricians familiar with basic concepts in population modeling, simulation, and model-based drug development, 5 aims at presenting the foundations of count data analyses and builds on a recent tutorial on time to event models. 6 After defining count data and alternative analysis approaches, the main count models will be described with an emphasis on their assumptions, which will be completed by considerations in the context of drug development.…”