Hybrid Bayesian Estimation in the additive hazards model

TL;DR

This work introduces a hybrid Bayesian framework for the semiparametric Additive Hazards Model under right-censoring by recasting the baseline hazard as piecewise-constant and expressing the likelihood as a mixture of Gamma distributions. It couples Lin and Ying's estimating equations for the Euclidean parameter $\\boldsymbol{\\beta}$ with informative priors (a truncated normal on $\\boldsymbol{\\beta}$ and a Gamma Process prior on the baseline hazard $\\Lambda_0$) to yield closed-form posterior estimators, avoiding full posterior sampling. The method disentangles estimation of $\\boldsymbol{\\beta}$ from the baseline hazard and provides a practical two-step procedure demonstrated through simulations and a real dataset (Welsh Nickels miners), showing convergence to Lin and Ying's results as priors flatten or sample sizes increase. The approach offers a computationally efficient route for Bayesian survival analysis in the additive hazards setting and has potential extensions to time-varying effects or frailty models.

Abstract

Hereby we propose a Bayesian method of estimation for the semiparametric Additive Hazards Model (AHM) from Survival Analysis under right-censoring. With this aim, we review the AHM revisiting the likelihood function, so as to comment on the challenges posed by Bayesian estimation from the full likelihood. Through an algorithmic reformulation of that likelihood, we present an alternative method based on a hybrid Bayesian treatment that exploits Lin and Ying (1994) estimating equation approach and which chooses tractable priors for the parameters. We obtain the estimators from the posterior distributions in closed form, we perform a small simulation experiment, and lastly, we illustrate our method with the classical Nickels Miners dataset and a brief simulation experiment.