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

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.