Scoring rules in survival analysis

Scoring rules promote rational and good decision making and predictions by models, this is increasingly important for automated procedures of `auto-ML'. The Brier score and Log loss are well-established scoring rules for classification and regression and possess the `strict properness' property that encourages optimal predictions. In this paper we survey proposed scoring rules for survival analysis, establish the first clear definition of `(strict) properness' for survival scoring rules, and determine which losses are proper and improper. We prove that commonly utilised scoring rules that are claimed to be proper are in fact improper. We further prove that under a strict set of assumptions a class of scoring rules is strictly proper for, what we term, `approximate' survival losses. We hope these findings encourage further research into robust validation of survival models and promote honest evaluation.