Survival modeling using deep learning, machine learning and statistical
  methods: A comparative analysis for predicting mortality after hospital
  admission
Ziwen Wang Jin Wee Lee Tanujit Chakraborty Yilin Ning Mingxuan Liu Feng Xie Marcus Eng Hock Ong Nan Liu
Survival analysis is essential for studying time-to-event outcomes and
providing a dynamic understanding of the probability of an event occurring over
time. Various survival analysis techniques, from traditional statistical models
to state-of-the-art machine learning algorithms, support healthcare
intervention and policy decisions. However, there remains ongoing discussion
about their comparative performance. We conducted a comparative study of
several survival analysis methods, including Cox proportional hazards (CoxPH),
stepwise CoxPH, elastic net penalized Cox model, Random Survival Forests (RSF),
Gradient Boosting machine (GBM) learning, AutoScore-Survival, DeepSurv,
time-dependent Cox model based on neural network (CoxTime), and DeepHit
survival neural network. We applied the concordance index (C-index) for model
goodness-of-fit, and integral Brier scores (IBS) for calibration, and
considered the model interpretability. As a case study, we performed a
retrospective analysis of patients admitted through the emergency department of
a tertiary hospital from 2017 to 2019, predicting 90-day all-cause mortality
based on patient demographics, clinicopathological features, and historical
data. The results of the C-index indicate that deep learning achieved
comparable performance, with DeepSurv producing the best discrimination
(DeepSurv: 0.893; CoxTime: 0.892; DeepHit: 0.891). The calibration of DeepSurv
(IBS: 0.041) performed the best, followed by RSF (IBS: 0.042) and GBM (IBS:
0.0421), all using the full variables. Moreover, AutoScore-Survival, using a
minimal variable subset, is easy to interpret, and can achieve good
discrimination and calibration (C-index: 0.867; IBS: 0.044). While all models
were satisfactory, DeepSurv exhibited the best discrimination and calibration.
In addition, AutoScore-Survival offers a more parsimonious model and excellent
interpretability.