Approximate Bayesian inference for joint partially linear modeling of longitudinal measurements and spatial time-to-event data

TL;DR

This paper presents a new Bayesian hierarchical model that jointly analyzes longitudinal measurements and spatial survival data, effectively capturing spatial effects and nonlinear time influences, with demonstrated success in simulations and real HIV/AIDS data.

Contribution

It introduces a novel approximate Bayesian joint model incorporating spatial autoregressive effects and nonlinear longitudinal influences, advancing analysis of spatially dependent longitudinal and survival data.

Findings

Model accurately captures spatial effects and nonlinear time influences.

Simulation studies confirm the model's effectiveness.

Application to HIV/AIDS data demonstrates practical utility.

Abstract

The integration of longitudinal measurements and survival time in statistical modeling offers a powerful framework for capturing the interplay between these two essential outcomes, particularly when they exhibit associations. However, in scenarios where spatial dependencies among entities are present due to geographic regions, traditional approaches may fall short. In response, this paper introduces a novel approximate Bayesian hierarchical model tailored for jointly analyzing longitudinal and spatial survival outcomes. The model leverages a conditional autoregressive structure to incorporate spatial effects, while simultaneously employing a joint partially linear model to capture the nonlinear influence of time on longitudinal responses. Through extensive simulation studies, the efficacy of the proposed method is rigorously evaluated. Furthermore, its practical utility is demonstrated through an application to real-world HIV/AIDS data sourced from various Brazilian states, showcasing its adaptability and relevance in epidemiological research.