Bayesian INLA Modeling of Competing Risks in Chronic Kidney Disease with Covariate Measurement Error

Abstract Survival analysis is a crucial statistical tool for evaluating the impact of risk factors on time-to-event outcomes, such as disease progression or death. In clinical monitoring of patients with chronic kidney disease (CKD), subjects are at risk for competing clinical outcomes, such as death or progression to end-stage renal disease, where one event may preclude or alter another from occurring. Standard survival analysis, which treats such events as independent censoring, yields biased estimates. A competing risks framework is therefore essential for valid inference. Time-varying covariates with measurement errors can introduce additional bias if unaccounted for. Furthermore, the demand for scalable and rapid estimation approaches in Bayesian inference for survival data with many features is critical in medical research. This paper proposes an Integrated Nested Laplace Approximation (INLA)-based Bayesian method to model competing risks in CKD while accounting for covariate measurement error. Bayesian cause-specific competing risks models that incorporate a mixed-effects covariate measurement error submodel were proposed. Various nonparametric and parametric baseline hazard distributions were evaluated. The proposed methods were illustrated using both a simulation study and real-world CKD data analysis. The simulation study revealed that the INLA approach provided nearly identical and accurate posterior parameter estimates while being more computationally efficient compared to a Markov-Chain Monte-Carlo (MCMC) approach. The simulation and application studies demonstrate that this study makes noteworthy contributions to the proper and efficient analysis of survival CKD data with competing risks and covariate measurement errors.