Individual Survival Distributions: A More Effective Tool for Survival Prediction

Abstract

An accurate model of a patient’s individual survival distribution can help determine the appropriate treatment for terminal patients. Unfortunately, risk scores (e.g., from Cox Proportional Hazard models) do not provide survival probabilities, single-time probability models (e.g., the Gail model, predicting 5 year probability) only provides a probability for a single time point, and standard Kaplan-Meier survival curves provide only population averages for a large class of patients meaning they are not specific to individual patients. This motivates an alternative class of tools that can learn a model which provides an individual survival distribution which gives survival probabilities across all times. This work motivates such "individual survival distribution" (ISD) models, explains how they differ from standard models, and gives examples of common ISD models. It then discusses ways to evaluate such models and introduces a new approach, “D-Calibration”, which determines whether a model’s probability estimates are meaningful. We also discuss how these evaluation measures differ, and use them to evaluate many ISD prediction tools (both standard and state of the art) over a range of survival datasets. We further compare ISD models to common risk (non-ISD) models to demonstrate the superiority of our ISD class of models.