  We consider frequently used scoring rules for right-censored survival
regression models such as time-dependent concordance, survival-CRPS, integrated
Brier score and integrated binomial log-likelihood, and prove that neither of
them is a proper scoring rule. This means that the true survival distribution
may be scored worse than incorrect distributions, leading to inaccurate
estimation. We prove that, in contrast to these scores, the right-censored
log-likelihood is a proper scoring rule, i.e., the highest expected score is
achieved by the true distribution. Despite this, modern feed-forward
neural-network-based survival regression models are unable to train and
validate directly on the right-censored log-likelihood, due to its
intractability, and resort to the aforementioned alternatives, i.e., non-proper
scoring rules. We therefore propose a simple novel survival regression method
capable of directly optimizing log-likelihood using a monotonic restriction on
the time-dependent weights, coined SurvivalMonotonic-net (SuMo-net). SuMo-net
achieves state-of-the-art log-likelihood scores across several datasets with
20--100$\times$ computational speedup on inference over existing
state-of-the-art neural methods, and is readily applicable to datasets with
several million observations.
