Joint modeling with beta-binomial distribution for patient-reported outcomes and survival data

Abstract

This thesis addresses critical methodological gaps in the joint analysis of patient-reported outcomes (PROs) and survival data. PROs, as discrete bounded measures with inherent overdispersion, require specialized statistical treatment that conventional Gaussian-based joint models fail to provide. We develop novel methodological frameworks that properly account for PRO characteristics through beta-binomial distributions, overcoming limitations of existing approaches. In this work, we propose, explore, and discuss various statistical approaches for joint modeling, from frequentist to bayesian proposals. Our work highlights the advantages of joint models that integrate longitudinal and survival data while emphasizing the importance of choosing appropriate distributions for PRO data. In particular, in this dissertation, we propose three joint models to analyze both, the longitudinal PRO and survival data: a) A frequentist two-stage approach, providing initial practical solutions. In this proposal, the central innovation lies in a joint model based on a two-stage methodology that incorporates the beta-binomial distribution for the longitudinal submodel. This methodology avoids computational complexities while ensuring a distributional fit that considers the natural characteristics of PRO (discrete, bounded and overdispersed). b) A Bayesian one-stage joint model, offering improved estimation. In this proposal, the main objective was to keep the distributional features for PRO data regarding beta-binomial distribution while performing a joint specification approach. The Bayesian formulation of the problem allows us to avoid the computational complexities we found in frequentist approaches. Moreover, we considered the parameters’ posterior estimations to perform dynamic predictions of the survival probabilities, being updated as more longitudinal PRO information is considered. c) A multivariate Bayesian framework, enabling simultaneous analysis of multiple PRO dimensions with survival outcomes. In this proposal, our primary objective was to address the multidimensional structure of questionnaires within the joint modeling framework. However, when dealing with multivariate approaches, it might be necessary to use regularization techniques to avoid possible multicollinearity. Therefore, we explored common regularization techniques in the literature within the joint modeling framework. The proposed methods' performance is evaluated using simulation studies, and comparisons with common approaches in the literature are provided. Additionally, we applied these methods to analyze a study carried out with chronic obstructive pulmonary disease (COPD) patients, where longitudinal tendencies for PRO data collected and their relationship with patients’ mortality are of interest