Bayesian survival analysis with missing data using integrated nested laplace approximation

Abstract

Bayesian survival analysis has bene tted from the introduction of Markov Chain Monte Carlo (MCMC) since the 1990s. However, MCMC has high computational cost and requires tuning and convergence checking. These hamper its usefulness. Integrated Nested Laplace Approximation (INLA) is a convenient alternative to MCMC due to its e ciency and straightforward execution to obtain the posterior distributions of relevant survival parameters such as the regression coe cients and Weibull shape parameter. This has been demonstrated in parametric and semi-parametric proportional hazard and piecewise constant hazard models. Nevertheless, it has not been possible until now to use INLA when covariate data are missing since it neither can integrate out missing covariate data nor is it satisfactory to use other subsidiary methods such as multiple imputation to overcome this di culty. We therefore investigate the application of INLA to piecewise exponential constant hazard models when covariate information is missing. We extend and modify the INLA within MCMC method to circumvent the missing covariate data problem in survival cases, assuming that the data are missing at random. We use both hierarchical and autoregressive priors for the baseline log-hazard and covariate e ects and compare the results with those obtained by MCMC. The methods are applied to three di erent data sets; Catheter-related kidney infection, Scotland-Newcastle Lymphoma Group Non Hodgkin Lymphoma, and Malaysian Hospital Universiti Sains Malaysia Advanced Lung Cancer data sets. The priors are constructed based on the information obtained from the meta-analysis of results from previous studies. The results obtained demonstrate that the developed methods are suitable for various survival data sets with reasonable numbers of missing covariate values, making this proposed method a convenient alternative to standard MCMC algorithms for survival analysis.