Distributional Regression for Time to Event Data
Final Report Abstract
The main objective of our project “Distributional regression for time-to-event data” was to develop new regression methods to model associations between event times such as survival times and multiple informative variables that allow for a better prediction of the event time. Classically, these models are constructed to predict the mean event time. In our project, however, we aimed to provide a more complete picture in order to predict the complete distribution of event times instead of just the mean. With distributional regression we are able to fit regression models that predict the upper or lower limits of an event time or the mode of the distribution which represents a typical event time. These methods allow us to model the survival time of a colon or lung cancer patient, for example. The main challenge with this type of data was that - luckily - not all of the patients in the data had already died. Hence, their survival time was only partially observed. In the project we had to find ways to include these so called censored observations into the models, since getting rid of them would have resulted in worse predictions. We extended previously established estimation algorithms to incorporate censored observations with either weights or a separate estimation of their further survival. Another main advantage of these models is their flexibility. We can add measurements as explanatory variables and model them to allow very flexible nonlinear associations with the survival time as well as categorical or spatial information and also allow for flexible synergies of multiple explanatory variables. As a result we found that, for example, for colon cancer patients with very short survival times the use of chemotherapy (after surgery) was estimated to have the strongest association with survival. For medium to long survival times the association was much weaker. Further, we aimed to promote the use of Generalised Additive Models for Location, Scale and Shape (GAMLSS) for time-to-event analysis. In a cooperation with colleagues from Bonn and London we prepared a tutorial article for practical use of GAMLSS for survival analysis. The method had been available for some time, thus not in practical use and not properly introduced. We also published a free software package with implementations of our own newly created methods as well as open access articles introducing and evaluating the methods.
Publications
- Analysis of Colorectal Cancer Data using Semiparametric Distributional Regression. GMDS 2019. Dortmund, 09.09.2019
Seipp A
- Outcome-Analyse mithilfe von Quantilregression bei 1028 Patienten mit kolorektalem Karzinom. DGVS Viszeralmedizin 2019. Wiesbaden, 04.10.2019
Weyhe D, Seipp A , Uslar V, Timmer A, Otto-Sobotka F
(See online at https://doi.org/10.1055/s-0039-1695410) - Semiparametric Accelerated Failure Times Quantile and Expectile Regression using Auxiliary Likelihoods. DAGStat 2019. München, 20.03.2019
Otto-Sobotka F
- Weighting Expectile Regression for Survival Analysis with Right-Censoring. DAGStat 2019. München, 20.03.2019
Seipp A
- Mode Regression in Survival Analysis. GMDS 2020. 06.09.2020
Seipp A, Uslar V, Timmer A, Otto-Sobotka F
- Weighted expectile re- gression for right-censored data. Statistics in Medicine. 2021; 40(25): 5501–5520
Seipp A, Uslar V, Weyhe D, Timmer A, Otto-Sobotka F
(See online at https://doi.org/10.1002/sim.9137) - Flexible Semiparametric Mode Regression for Time-to-Event Data. Statistical Methods in Medical Research. 2022; 31(12):2352-2367
Seipp A, Uslar V, Weyhe D, Timmer A, Otto-Sobotka F
(See online at https://doi.org/10.1177/09622802221122406)
