Section: New Results

Survival Analysis with Complex Covariates: A Model-based Clustering Preprocessing Step

Participants : Christophe Biernacki, Vincent Vandewalle.

Many covariates are now available through sensors in the industrial context, and are expected to be related to the survival analysis target. Such covariates are often complex, what has to be understood as a possible mix between continuous, categorical, even functional over time, variables with the possibility to contain missing or uncertain values. A natural question in survival analysis is to design in both flexible and easy way an hazard function related to these potentially complex covariates, while preserving the opportunity to benefit from classical hazard functions.

In the context of a bilateral contract with Alstom company on the survival analysis topic, we have been invited to give a tutorial in the IEEE PHM International Conference on Prognostics and Health Management in US [22] . In this tutorial, we have described how to decompose the unknown targeted hazard function into two complementary parts. The first one can be any classical user hazard function conditional on a latent categorical variable. The second one is the distribution of this latent variable conditionally to the complex covariates. The way to combine both parts is to sum their product over the latent variable (marginal distribution), leading to the final targeted hazard function. The key to perform this approach is to focus on the latent variable definition which can be obtained with a model-based clustering approach dedicated to complex covariates. Beyond a selected review of recent methodologies dedicated to clustering, we have described in depth some related software to perform previous clustering methods. Some case studies have been also provided in an industrial context. At the end of the talk the practitioner is thus able to perform such clustering method to use it finally with its own hazard function.