Learning Survival Distributions with the Asymmetric Laplace Distribution
This work addresses survival analysis for event prediction, offering a novel parametric approach that improves performance, though it is incremental as it builds on quantile regression ideas.
The authors tackled the problem of probabilistic survival analysis by proposing a parametric method based on the Asymmetric Laplace Distribution, which outperformed existing parametric and nonparametric approaches in accuracy, discrimination, and calibration on synthetic and real-world data.
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.