Beta Survival Models

Survival modeling is an important area of study, and has been used widely in many applications including clinical research, online advertising, manufacturing, etc. There are many methods to consider when analyzing survival problems, however these techniques generally focus on either estimating the uncertainty of different risk factors (cox-proportional hazards, etc), or predicting the time to event in a non-parametric way (e.g. tree based methods), or forecasting the survival beyond an observed horizon (parametric techniques such as exponential). In this work, we introduce efficient estimation methods for linear, tree, and neural network versions of the Beta-Logistic model - a classical extension of the logistic function into the discrete survival setting. The Beta-Logistic allows for recovery of the underlying beta distribution as well as having the advantages of non-linear or tree based techniques while still allowing for projecting beyond an observed horizon. Empirical results using simulated data as well as large-scale data-sets across three use-cases (online conversions, retention modeling in a subscription service, and survival of democracies and dictatorships), demonstrate the competitiveness of the method at these tasks. The simplicity of the method and its ability to capture skew in the data makes it a viable alternative to standard techniques particularly when we are interested in forecasting time to event beyond our observed horizon and when the underlying probabilities are heterogeneous.