Guest Editorial

Abstract

The main objective of this journal, Statistical Modelling, deals with original papers which consider statistical modelling as a fundamental tool for statistical learning, both methodological and applied. This special issue, devoted to Bayesian Inference for Joint Models in Survival Analysis, has been entirely inspired by this idea. Survival joint models account for complex structured modelling. Typically, the outcomes of interest are times-to-event which can be jointly analysed with other type of information in order to improve inference and gain a better insight on the scientific question under study. Usually, longitudinal input is modelled jointly with time-to-event data to allow the inclusion of temporal covariates in the survival model, but joint modelling can be extended to deal with other types of data such as spatial observations. In addition, joint models are also suitable for dealing with longitudinal scenarios with non-ignorable missing patterns which can be described in terms of survival tools. Bayesian inference offers a flexible and attractive conceptual framework to joint models of survival data mainly due to its special conception of probability that allows to quantify in probabilistic terms all the sources of uncertainty, observable or not, in the problem under study, and the use of Bayes’ theorem to sequentially update probabilities as more relevant information is obtained. Bayes computation for complex models is not easy. This topic is particularly important in the framework of Bayesian survival joint models because their practical implementation generates new computational scenarios that involve novel questions and challenges. This special issue contains eight articles which include new proposals for model implementation, methodological developments as well as interesting practical applications. Although most of the papers in this issue are methodological, all of them have a special section in which the proposed methodology is applied to a real problem, usually coming from medical contexts. Below, we briefly present the different works in this special issue. The conceptual framework of Beesley and Taylor is multistate models, a class of stochastic processes which account for event history data with individuals who may experience different events in time. This article focuses on model selection, a key topic in multistate models due to the high number of parameters in its specification which are exacerbated by complicated patterns derived from data missingness, the presence of highly correlated predictors, and complex hierarchical parameter relationships. Model selection is based on shrinkage methods that Bayesian methodology addresses through the specification of prior distributions. Horseshoe priors, and spike and slab priors defined in terms of a mixture of two normal distributions and the particular case of a spike with point mass at zero are considered. These proposals are discussed for an illness-and-death model and a generalized multistate cure model for patients treated for prostate cancer and for head and neck cancer, respectively.