# Simultaneous Prediction Intervals for Patient-Specific Survival Curves

## TL;DR

This paper develops methods to quantify uncertainty in patient-specific survival curves generated by individual survival distribution models, enhancing their clinical utility with accurate prediction intervals.

## Contribution

It adapts existing sampling-based methods and introduces new techniques for estimating simultaneous prediction intervals for survival curves, applicable beyond survival analysis.

## Key findings

- Existing method adapted for survival curve intervals
- New methods provide competitive interval estimation performance
- Applicable to any context with tractable sampling of the distribution

## Abstract

Accurate models of patient survival probabilities provide important information to clinicians prescribing care for life-threatening and terminal ailments. A recently developed class of models - known as individual survival distributions (ISDs) - produces patient-specific survival functions that offer greater descriptive power of patient outcomes than was previously possible. Unfortunately, at the time of writing, ISD models almost universally lack uncertainty quantification. In this paper, we demonstrate that an existing method for estimating simultaneous prediction intervals from samples can easily be adapted for patient-specific survival curve analysis and yields accurate results. Furthermore, we introduce both a modification to the existing method and a novel method for estimating simultaneous prediction intervals and show that they offer competitive performance. It is worth emphasizing that these methods are not limited to survival analysis and can be applied in any context in which sampling the distribution of interest is tractable. Code is available at https://github.com/ssokota/spie .