A General Framework for Survival Analysis and Multi-State Modelling
- URL: http://arxiv.org/abs/2006.04893v2
- Date: Mon, 15 Feb 2021 17:53:45 GMT
- Title: A General Framework for Survival Analysis and Multi-State Modelling
- Authors: Stefan Groha, Sebastian M Schmon, Alexander Gusev
- Abstract summary: We use neural ordinary differential equations as a flexible and general method for estimating multi-state survival models.
We show that our model exhibits state-of-the-art performance on popular survival data sets and demonstrate its efficacy in a multi-state setting.
- Score: 70.31153478610229
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Survival models are a popular tool for the analysis of time to event data
with applications in medicine, engineering, economics, and many more. Advances
like the Cox proportional hazard model have enabled researchers to better
describe hazard rates for the occurrence of single fatal events, but are unable
to accurately model competing events and transitions. Common phenomena are
often better described through multiple states, for example: the progress of a
disease modeled as healthy, sick and dead instead of healthy and dead, where
the competing nature of death and disease has to be taken into account.
Moreover, Cox models are limited by modeling assumptions, like proportionality
of hazard rates and linear effects. Individual characteristics can vary
significantly between observational units, like patients, resulting in
idiosyncratic hazard rates and different disease trajectories. These
considerations require flexible modeling assumptions. To overcome these issues,
we propose the use of neural ordinary differential equations as a flexible and
general method for estimating multi-state survival models by directly solving
the Kolmogorov forward equations. To quantify the uncertainty in the resulting
individual cause-specific hazard rates, we further introduce a variational
latent variable model and show that this enables meaningful clustering with
respect to multi-state outcomes as well as interpretability regarding covariate
values. We show that our model exhibits state-of-the-art performance on popular
survival data sets and demonstrate its efficacy in a multi-state setting
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