Bayesian joint ordinal and survival modeling for breast cancer risk assessment

Abstract

We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional-odds cumulative logit model. Time-to-event is modeled through a left-truncated proportionalhazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects. General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the assessment of the impact of the baseline covariates and the longitudinal marker on the hazard function. The flexibility provided by the joint model makes possible to dynamically estimate individual event-free probabilities and predict future longitudinal marker values. The model is applied to the assessment of breast cancer risk in women attending a population-based screening program. The longitudinal ordinal marker is mammographic breast density measured with the Breast Imaging Reporting and Data System (BI-RADS) scale in biennial screening exams. ©2016 The Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.

This paper was partially supported by the research grants Combination and Propagation of Uncertainties (ComPro_UN, MTM2013-42323-P), Statistical methods for clinical trials, complex censoring schemes and integrative omics data analysis (MTM2015-64465-C2-1-R), and Women participation in decisions and strategies on early detection of breast cancer (PI14/00113) from the Spanish Ministry of Economy and Competitiveness, ACOMP/2015/202 from the Generalitat Valenciana, and GRBIO-2014-SGR464 and GRAES-2014-SGR978 from the Generalitat de Catalunya.