Comparison of Two Methods for Determining Item Characteristic Functions and Latent Variable Time-Course for Pharmacometric Item Response Models

Abstract

There are examples in the literature demonstrating different approaches to defining the item characteristic functions (ICF) and characterizing the latent variable time-course within a pharmacometrics item response theory (IRT) framework. One such method estimates both the ICF and latent variable time-course simultaneously, and another method establishes the ICF first then models the latent variable directly. To date, a direct comparison of the “simultaneous” and “sequential” methodologies described in this work has not yet been systematically investigated. Item parameters from a graded response IRT model developed from Parkinson’s Progression Marker Initiative (PPMI) study data were used as simulation parameters. Each method was evaluated under the following conditions: (i) with and without drug effect and (ii) slow progression rate with smaller sample size and rapid progression rate with larger sample size. Overall, the methods performed similarly, with low bias and good precision for key parameters and hypothesis testing for drug effect. The ICF parameters were well determined when the model was correctly specified, with an increase in precision in the scenario with rapid progression. In terms of drug effect, both methods had large estimation bias for the slow progression rate; however, this bias can be considered small relative to overall progression rate. Both methods demonstrated type 1 error control and similar discrimination between model with and without drug effect. The simultaneous method was slightly more precise than the sequential method while the sequential method was more robust towards longitudinal model misspecification and offers practical advantages in model building.