Bayesian random-effects threshold regression with application to survival data with nonproportional hazards

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Time-to-event data in clinical and epidemiological studies frequently violate Cox regression assumptions due to time-dependent covariates and unmeasured risk factors.
• Existing first hitting time models, while more flexible than Cox regression, do not fully account for unmeasured covariates affecting both initial health status and disease progression rates.

Purpose of the Study:

• To propose a novel Bayesian methodology for survival analysis that incorporates unmeasured covariates.
• To model individual health status as a Wiener process with subject-specific random effects for initial state and drift.

Main Methods:

• Developed a Bayesian framework using a Wiener process to model health status, incorporating subject-specific initial states and drifts.
• Employed Markov chain Monte Carlo (MCMC) with data augmentation for posterior inference, specifically for handling censored observations.
• Applied the methodology to melanoma patient data exhibiting nonproportional hazards.

Main Results:

• The proposed Bayesian model revealed distinct survival probability estimates compared to a model lacking random effects when applied to melanoma data.
• Simulation studies demonstrated that neglecting unmeasured covariates leads to significant inaccuracies in survival probability estimations.
• The method effectively accounts for unmeasured heterogeneity in both the baseline health status and the rate of disease progression.

Conclusions:

• The proposed Bayesian Wiener process model offers a more robust approach to survival analysis when dealing with time-dependent effects and unmeasured covariates.
• Accounting for unmeasured risk factors is crucial for accurate survival probability estimation, particularly in complex disease processes like melanoma.
• This methodology provides a valuable tool for epidemiological and clinical research where standard regression assumptions are often unmet.