# Pseudo value-based Deep Neural Networks for Multi-state Survival Analysis

arXiv: https://arxiv.org/abs/2207.05291 · HTML: https://mlsanity.com/paper/2207.05291/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 12 Jul 2022.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [BDNNSurv: Bayesian deep neural networks for survival analysis using pseudo values](https://mlsanity.com/paper/2101.03170/) (2021)
- [A General Framework for Survival Analysis and Multi-State Modelling](https://mlsanity.com/paper/2006.04893/) (2020)

## Built on by (most cited first, 1 of 1)

- [Interpretable Survival Analysis for Heart Failure Risk Prediction](https://mlsanity.com/paper/2310.15472/) (2023)

## Abstract (arXiv)

Multi-state survival analysis (MSA) uses multi-state models for the analysis of time-to-event data. In medical applications, MSA can provide insights about the complex disease progression in patients. A key challenge in MSA is the accurate subject-specific prediction of multi-state model quantities such as transition probability and state occupation probability in the presence of censoring. Traditional multi-state methods such as Aalen-Johansen (AJ) estimators and Cox-based methods are respectively limited by Markov and proportional hazards assumptions and are infeasible for making subject-specific predictions. Neural ordinary differential equations for MSA relax these assumptions but are computationally expensive and do not directly model the transition probabilities. To address these limitations, we propose a new class of pseudo-value-based deep learning models for multi-state survival analysis, where we show that pseudo values - designed to handle censoring - can be a natural replacement for estimating the multi-state model quantities when derived from a consistent estimator. In particular, we provide an algorithm to derive pseudo values from consistent estimators to directly predict the multi-state survival quantities from the subject's covariates. Empirical results on synthetic and real-world datasets show that our proposed models achieve state-of-the-art results under various censoring settings.