Adapting and evaluating deep-pseudo neural network for survival data with time-varying covariates

Albert Whata, Justine B. Nasejje, Najmeh Nakhaei Rad, Tshilidzi Mulaudzi and Ding-Geng Chen

Journal of Applied Statistics, 2025, vol. 52, issue 10, 1847-1870

Abstract: The Extended Cox model provides an alternative to the proportional hazard Cox model for modelling data including time-varying covariates. Incorporating time-varying covariates is particularly beneficial when dealing with survival data, as it can improve the precision of survival function estimation. Deep learning methods, in particular, the Deep-pseudo survival neural network (DSNN) model have demonstrated a high potential for accurately predicting right-censored survival data when dealing with time-invariant variables. The DSNN's ability to discretise survival times makes it a natural choice for extending its application to scenarios involving time-varying covariates. This study adapts the DSNN to predict survival probabilities for data with time-varying covariates. To demonstrate this, we considered two scenarios: significant and non-significant time-varying covariates. For significant covariates, the Brier scores were below 0.25 at all considered specific time points, while, in the non-significant case, the Brier scores were above 0.25. The results illustrate that the DSNN performed comparably to the extended Cox, the Dynamic-DeepHit and mulitivariate joint models and on the simulated data. A real-world data application further confirms the predictive potential of the DSNN model in modelling survival data with time-varying covariates.

Date: 2025
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DOI: 10.1080/02664763.2024.2444649

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