Joint modeling with Monolix using IQR Tools
Daniel Kaschek (1), Henning Schmidt (1)
(1) IntiQuan GmbH, Basel, Switzerland
Introduction/Objectives:
Time-to-event (TTE) information is collected in many clinical studies both for the evaluation of safety signals (e.g., time to onset of adverse events) or efficacy (e.g., time of progression-free survival, time to alleviation of symptoms) of a drug. In pharmacometrics, such data are typically analyzed using TTE models. The hazard function of such a model, i.e., the rate of occurrence of an event, usually changes over time. For some diseases, the increasing or decreasing risk of occurrence of the event over time can be well correlated with exposure, an observed biomarker or a readout of disease severity. When individual readout profiles and individual hazard risk are linked, the resulting mixture of a longitudinal and a TTE model is denoted as a joint model. Joint models were used in the past, e.g., for the analysis of a prostate cancer study, to correlate the time to death with prostate-specific antigen (PSA) kinetics [1, 2]. The computational functionality to estimate parameters of joint models was implemented in Monolix [3] and is readily available.
At IntiQuan, we have developed an R framework over the years, the IQR Tools [4], to support the entire pharmacometric workflow from data programming to model development and simulation. The framework interfaces Monolix and NONMEM for parameter estimation. It was our goal to make the joint modeling functionality of Monolix available to users of our framework. The aim of our implementation was to integrate the TTE component of the model development as seamlessly as possible with the longitudinal component, both in terms of dataset requirements and model specification.
Methods:
IQRtools provides a consistent interface to both NONMEM and Monolix. The compatibility with both tools is enabled by a standardized, intuitive, and easy to adopt syntax for structural models, datasets, and the specification of parameters to be estimated. Given the high level of flexibility in the existing syntax, we extended the specification of longitudinal to joint model estimation problems by only a few keywords without changing the overall syntax. Using our extended syntax, joint models were translated into Monolix code and were executed in Monolix. Results from Monolix were imported back in and post-processed to generate diagnostic plots and summary tables.
Results:
We successfully tested our implementation on data from a cancer study. The longitudinal part of the model described the PK of the drug by a compartmental model. Tumor growth was modeled by an exponential process where the growth rate was reduced and eventually compensated by a term proportional to the drug exposure. The time-to-event part of the model described overall survival of the patients by a Weibull distribution. Overall survival and tumor size were linked into a joint model using a typical link function. The joint model was calibrated using data up to a certain data cutoff. Subsequently, the model was simulated to predict the number of individuals alive for different later data cutoff scenarios. The application of the new functionality showed that the transition from the development of a tumor size model (longitudinal model) to a joint survival-tumor size model was hassle-free.
Conclusions:
Joint models allow to integrate individual longitudinal observations (exposure, tumor size, biomarkers) with individual time-to-event information, establishing an individual risk assessment. With our implementation of a joint modeling functionality in IQR Tools, we allow the modeler to easily extend any of the developed longitudinal population models to a joint model, using the familiar syntax. Thereby, IntiQuan has lowered the bar for any modeler to gain access to a great and useful class of models: joint longitudinal time-to-event models.
References:
[1] Desmée S, Mentré F, Veyrat-Follet C, Sébastien B, Guedj J. Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer. BMC Medical Research Methodology. 2017 Dec;17(1):105.
[2] Desmée S, Mentré F, Veyrat-Follet C, Guedj J. Nonlinear mixed-effect models for prostate-specific antigen kinetics and link with survival in the context of metastatic prostate cancer: a comparison by simulation of two-stage and joint approaches. The AAPS journal. 2015 May 1;17(3):691-9.
[3] Lixoft MONOLIX. http://lixoft.com/products/monolix/
[4] IntiQuan R tools (IQRtools). https://iqrtools.intiquan.com/