Discrete data

Andrew Hooker, Mats Karlsson, Maria Kjellsson, Elodie Plan,
Sebastian Ueckert

For many diseases, the primary outcome is of discrete nature: stage category, symptom severity, number of events, or occurrence of events. In pharmacometrics we distinguish (non-)ordered categorical data, count data, and (repeated) time-to-event data. Models handling this type of data are based on probabilities and, even if they have been around for ~20 years in pharmacometrics, are still not widely used and subject to important innovations. In this project, we aim to study and develop new methodologies for discrete data, in order to better describe disease progression, characterize exposure-response with a higher power, as well as simulate clinical trials in a more realistic manner.

Our recent focus has been on score-based clinical outcomes, for which we introduced the item response theory approach as well as bounded integer models. While the former allows to describe disease assessments with unique details, the latter is a more parsimonious modeling approach with excellent statistical properties. In our work, we continue to investigate the statistical properties of these complementing techniques and develop tools and techniques to simplify their application. Another current area of research is the application of hidden Markov models in NONMEM, which we use, for example, for the detection of anti-drug antibodies. 

In the past, we have analyzed sleep stages in patients with insomnia using Markov models and modeled pain scores rated on a Likert scale by neuropathic patients by including features for under-dispersion and serial correlation to count models. We also used daily numbers of seizures in the investigation of over-dispersion or Markov patterns in count data, and introduced repeated time-to-categorical event model to simultaneous characterize the drug effect on severity and time to acid reflux events.

Methodology-wise, we have compared parametric time-to-event models to semi-parametric Cox proportional hazard models, developed an approach to simulate large scale unbiased repeated time-to-event data, and studied methods such as dynamic inter-occasion variability or stochastic differential equations to handle within-subject variability in count models.

We also explored the performance of estimation methods available for discrete models and studied how the Laplace approximation behaves in situations with non-even distributions of ordered categories as well as for different Poisson-type models. In another study, we compared the accuracy of parameter estimation with SAEM and importance sampling to the one of Laplace in repeated time-to-event models where the frequency of individuals with events was low. We have also conducted a study investigating all methods available in NONMEM 7 for all types of discrete models.