Advanced Statistical Inference in Joint Models for Longitudinal and Time to Event Data

• Applicant: Professorin Dr. Elisabeth Bergherr
• Subject Area: Epidemiology and Medical Biometry/Statistics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 426493614

Joint models for longitudinal and time-to-event data have gained a lot of attention in the last few years, both in the statistical and the biomedical community, as they address a data structure very common in the life sciences. In many clinical studies or disease registries, longitudinal outcomes such as diagnostic measurements are recorded alongside event times such as death, two processes which are oftentimes linked to each other and modelling them jointly avoids the bias introduced by independent modelling. Even though extensive research has been done on this topic in the last two decades, most approaches fail to incorporate advanced models in the longitudinal part of the joint model and hardly any suggestions on variable selection have been made. The goal of this project is to use knowledge from the framework of statistical learning to close this gap. The focus in extending the modeling of the longitudinal outcome will be on distributional regression. This can be used to capture properties of the longitudinal outcome that go beyond the mean and for example measure the impact of the variance of a continuous outcome on the event-time. For this purpose, recent developments in the field of statistical learning "gradient boosting" will be extended. This framework also offers variable selection and shrinkage methods even in settings with more covariates than observations. Variable selection in a joint model involves the additional task of allocating covariates to the correct part of the model i.e. the detection if the variable has an impact on the longitudinal outcome, the survival part or both of them. This allocation principle was already implemented in simpler model classes in the first round of this project, but shall be adapted to the aforementioned distributional regression. Further extensions of the model itself, like extensions towards spatial modelling, are planned and make a good model selection strategy necessary. Therefore this project also aims at adapting and testing model selection tools from the broad field of statistical learning such as probing or stability selection to the gradient boosted joint model. The developed inference framework will be implemented and made publicly available in open-source R packages. The methods will be developed with a special focus on cystic fibrosis, where the lung function measurements is the longitudinal outcome and lung infection or death is the event, in cooperation with the Deutsche Mukoviszidose-Register (German cystic fibrosis registry). The methods will however be implemented in a generic way, making it possible to apply them to further practical research problems.

• DFG Programme: Research Grants