Learning Survival Distributions with the Asymmetric Laplace Distribution

Deming Sheng, Ricardo Henao

Abstract:

Probabilistic survival analysis models seek to estimate the distribution of the future occurrence (time) of an event given a set of covariates.
In recent years, these models have preferred nonparametric specifications that avoid directly estimating survival distributions via discretization.
Specifically, they estimate the probability of an individual event at fixed times or the time of an event at fixed probabilities (quantiles), using supervised learning.
Borrowing ideas from the quantile regression literature, we propose a parametric survival analysis method based on the Asymmetric Laplace Distribution (ALD).
This distribution allows for closed-form calculation of popular event summaries such as mean, median, mode, variation, and quantiles.
The model is optimized by maximum likelihood to learn, at the individual level, the parameters (location, scale, and asymmetry) of the ALD distribution.
Extensive results on synthetic and real-world data demonstrate that the proposed method outperforms parametric and nonparametric approaches in terms of accuracy, discrimination and calibration.

Lay Summary:

Predicting how long it will take for something to happen, such as the failure of a machine part or the progression of a disease, is important in many fields including healthcare and engineering. This type of prediction is known as survival analysis. However, making accurate predictions can be challenging, especially when complete information is not available for every case. For example, a patient may not yet have experienced the event being studied by the time data collection ends.

In this work, we introduce a new method based on a statistical distribution called the Asymmetric Laplace Distribution. This distribution provides a flexible way to describe the range and likelihood of possible outcomes for each individual. Unlike many existing approaches that rely on simplifying assumptions or discretizing time, our method models the entire probability distribution directly. As a result, it allows us to compute meaningful summaries, such as the expected time of an event or the uncertainty associated with that prediction.

We evaluated our method on a wide range of simulated and real-world datasets, including several from healthcare applications. Across different settings, it consistently outperformed traditional and modern survival models in terms of accuracy and reliability. Our approach is especially effective when dealing with incomplete data or rare events, making it a valuable tool for personalized risk prediction and decision-making.

Link To Code: https://github.com/demingsheng/ALD

Primary Area: Probabilistic Methods

Keywords: Deep Learning; Survival Analysis; Asymmetric Laplace Distribution; Censored Data

Submission Number: 7409