# Applications of survival analysis and learning curves methods in neurosurgical stroke data and simulations to account for provider heterogeneity

## TL;DR

This paper explores how survival analysis and learning curves can improve understanding of surgical outcomes for hemorrhagic stroke patients by accounting for provider differences and learning effects.

## Contribution

The study introduces novel applications of Cox frailty models and random survival forests to account for provider heterogeneity in neurosurgical stroke data.

## Key findings

- Age was a significant predictor of time from procedure to death in an adjusted Cox model.
- Smoking became the main statistically significant predictor in frailty models with restricted mean survival time.
- Random survival forests showed the best fit for real data compared to other methods.

## Abstract

We used a unique application of Cox frailty models as well as random survival forests (RSF) to capture unexplained heterogeneity amongst providers (Int Neuro. Article 102149, 2025), along with using restricted mean survival time as an alternative survival time measure. Hemorrhagic stroke accounts for approximately 10–20% of all strokes annually and some patients with it may benefit from a surgical intervention, a placement of an external ventricular drain (EVD) catheter to manage post-procedure complications. In order to model post-surgical outcomes, we first employed frailty models or RSFs to capture heterogeneity between providers and account for unmeasured covariates (Int Neuro. Article 102149, 2025). Additionally, we had modeled learning curves among operators to guide and improve surgical learning in which we utilized our database of EVD procedures for hemorrhagic stroke interventions from 2019 to 2022, which revealed age was a significant predictor (p < 0.015) of time from procedure to death in an adjusted Cox model. In our novel modeling with frailty models along with restricted mean survival time, smoking became the main statistically significant predictor (Int Neuro. Article 102149, 2025), while RSFs showed the best fit in the real data as compared to the other methods. In this further exploration, simulations indicated that the exponential shape performed best while visually the logarithmic function performed best, aligning with prior research (Stat Med. 37:4185-4199, 2018), (Stat Med. 36:2764-2785PMC6463283, 2017), (J Med Stat Inform. 6, 2018).