A Bayesian Approach to Item Response Theory Modeling for Exposure-Response Relationships in Stan
Authors: Chen Po-Wei , Pourzanjani Arya , Modi Saurabh , Lin Chih-Wei 
Published: February 2025

Objectives: In recent years, exploring insights of Patient Reported Outcome (PRO) data has drawn interest in the drug development community. Item Response Theory (IRT) modeling is a mathematical framework commonly used to characterize such composite data. Techniques for modeling PRO data to characterize exposure response (ER) using IRT models have been developed in R/NONMEM [1] and Monolix [2]. Bayesian approaches can offer certain advantages such as uncertainty quantification and model flexibility, that can be useful in an IRT modeling. We explore a Bayesian approach to IRT modeling in Stan and compare to the approaches developed in R/NONMEM [3] and Monolix [4] by implementing a drug exposure driven IRT model for the Migraine-Specific Quality-of-Life Questionnaire (MSQ), a self-administered, migraine-specific form that is composed of a 14-item instrument assessment of quality of life evaluating the effect of migraine on daily functioning [5]. Methods: Stan is an open-source software for Bayesian statistical inference [6]. To develop the Bayesian IRT modeling platform in Stan, 4 MSQ datasets with sample sizes of 100, 200, 400 and 800 subjects, were simulated. In each dataset, the placebo group and 3 active treatment sets were assigned 1:1:1:1 to four groups (placebo, 15 mg QM, 50 mg QM and 150 mg QM), and data was simulated over a period of 6 months. Steady state trough exposures simulated by a target mediated drug disposition model were adopted as the PK metrics. The data were used to characterize: 1) the item-specific parameters describing the probabilities of patients’ responses at baseline. 2) an exposure-dependent Emax model describing the change of item responses longitudinally. A total of 88 parameters, including the item specific parameters and the longitudinal Emax parameters, were estimated simultaneously. Finally, a comparative study, including parameter estimates and simulations of item response were performed to compare with the R/NONMEM and Monolix approaches. The Bayesian IRT model was able to describe baseline and longitudinal MSQ data on an item and total score level, as well as the ER relationships between drug concentration and item/total scores. The estimated parameters, as the means of posterior distributions, are comparable to the parameter estimates from the R/NONMEM and Monolix. Item and treatment level diagnostic simulations were performed and visualized, yielding the similar results for the Stan, R/NONMEM and Monolix approaches. Conclusions: This analysis illustrated how IRT can be implemented to describe the ER relationship using a Bayesian approach in an open-source Stan framework. The performance of the modeling was validated by comparing with the established modeling frameworks.Citations: [1] Ueckert, S. Modeling composite assessment data using item response theory. CPT:PSP. 2018;7(4): 205-218. [2] Savic, RM, Mentré, F, Lavielle, M. Implementation and Evaluation of the SAEM Algorithm for Longitudinal ordered categorical data with an illustration in pharmacokinetics-pharmacodynamics. AAPS J. 2011; 13(1): 44-53. [3] Chen PW, Karlsson MO, Ueckert, S et al. Evaluation of Migraine-Specific Questionnaire (MSQ) to Inform Migraine Drug Development Using Item Response Theory Modeling. ACoP poster, 2021. [4] Chen PW, Chauvin J, Cellière G et al. An Integrated Workflow of Item Response Theory Modeling in Monolix. AcoP poster, 2023. [5] Martin, BC, Pathak, DS, Sharfman, MI, et al. Validity and reliability of the migraine-specific quality of life questionnaire (MSQ version 2.1). Headache. 2000; 40(3): 204-215. [6] Carpenter, B, Gelman A, Hoffman MD et al. Stan: A probabilistic programming language. Journal of statistical software, 2017, 76.