Joint Modelling Approaches to Survival Analysis via Likelihood-Based Boosting Techniques

Joint models are a powerful class of statistical models which apply to any data where event times are recorded alongside a longitudinal outcome by connecting longitudinal and time-to-event data within a joint likelihood allowing for quantification of the association between the two outcomes without possible bias. In order to make joint models feasible for regularization and variable selection, a statistical boosting algorithm has been proposed, which fits joint models using component-wise gradient boosting techniques. However, these methods have well-known limitations, i.e., they provide no balanced updating procedure for random effects in longitudinal analysis and tend to return biased effect estimation for time-dependent covariates in survival analysis. In this manuscript, we adapt likelihood-based boosting techniques to the framework of joint models and propose a novel algorithm in order to improve inference where gradient boosting has said limitations. The algorithm represents a novel boosting approach allowing for time-dependent covariates in survival analysis and in addition offers variable selection for joint models, which is evaluated via simulations and real world application modelling CD4 cell counts of patients infected with human immunodeficiency virus (HIV). Overall, the method stands out with respect to variable selection properties and represents an accessible way to boosting for time-dependent covariates in survival analysis, which lays a foundation for all kinds of possible extensions.