Bayesian Semi-parametric Joint Modeling of Item Response Model
Lili Ding, Cincinnati Children's Hospital 
*Bin Huang, Cincinnati Children's Hospital 

Keywords: IRT, PRO, Bayesian, Dirichlet Process, Surrogate Endpoint

Conventional Item Response Theory (IRT) assumes the latent abilities from all individuals following the same standard normal distribution, and that the item parameters are locally independent. However, when applied to public health and medical studies involving patient report outcome (PRO), the uniform normal distribution for the latent trait or symptom often is not appropriate; in addition, how patients answer the question may be different and dependent on their personal characteristics, thus questing the item local independent assumption. Consequently, applying IRT to patient report outcome has post additional challenges. Explanatory item response models (De Boeck and Wilson, 2004) and their generalization proposed modeling patient characteristics in IRT modeling. Other works (Woods 2004, 2006, 2007; Duncan & McEachen 2008) have approached IRT by none parametric modeling of the latent trait/symptom variable. Bayesian IRT has also been under active development (Fox, 2010). In this work, we consider mixture modeling of latent trait/symptom using Bayesian Dirichlet Mixture prior. Our approach could be considered as an extension of the previous literature by considering modeling both patient level and item level parameters, and relaxing the normal assumption for the latent variable.

In health policy research, PRO is often used as an intermediate health outcome, serving as a surrogate endpoint for the clinical endpoint. More accurate and precise measure of PRO is important in obtain a good understanding of the role of PRO, and its relationship with treatment as well as clinical outcome. Here, we propose joint modeling of IRT for latent trait/symptom and mediation modeling, where the mediator variable or surrogate endpoint is a PRO. We compared three different IRT modeling approaches, summary scores from classic IRT, Bayesian parametric IRT and the Bayesian semiparametric IRT. We assessed the estimation of direct and indirect treatment effects explained by the patient report outcome. We illustrate the advantages of Bayesian joint modeling using simulation and case studies.