proportional hazards

copyright john wiley

hazards model

cox proportional

survival functions

time-to-event data

survival models

survival data

Survival analysis (time-to-event analysis) is widely used in economics and finance, engineering, medicine and many other areas. A fundamental problem is to understand the relationship between the covariates and the (distribution of) survival times(times-to-event). Much of the previous work has approached the problem by viewing the survival time as the first hitting time of a stochastic process, assuming a specific form for the underlying stochastic process, using available data to learn the relationship between the covariates and the parameters of the model, and then deducing the relationship between covariates and the distribution of first hitting times (the risk). However, previous models rely on strong parametric assumptions that are often violated. This paper proposes a very different approach to survival analysis, DeepHit, that uses a deep neural network to learn the distribution of survival times directly.DeepHit makes no assumptions about the underlying stochastic process and allows for the possibility that the relationship between covariates and risk(s) changes over time. Most importantly, DeepHit smoothly handles competing risks; i.e. settings in which there is more than one possible event of interest.Comparisons with previous models on the basis of real and synthetic datasets demonstrate that DeepHit achieves large and statistically significant performance improvements over previous state-of-the-art methods.

DeepHit: A Deep Learning Approach to Survival Analysis With Competing Risks