When the Loss Stops Tracking the Metric: Value-Monotonicity in Deep Survival Prediction

A validation loss is routinely interpreted as if a lower value implied a better model. Deep survival prediction makes the mismatch stark, since models there are commonly trained with likelihood objectives, evaluated by the concordance index (C-index), and selected on the numerical value of the validation loss. Standard surrogate theory does not justify that interpretation. Fisher consistency constrains the minimizer, not the surrogate value at the intermediate points where early stopping and checkpoint selection occur. We formalize the missing property as value-monotonicity, requiring the loss to fall as the metric rises, to within a stated tolerance, along a training trajectory rather than only at the optimum. We prove that the Cox partial likelihood admits no finite such tolerance on a score class closed under rescaling, because rescaling leaves the C-index unchanged while the likelihood varies without bound, and the discrete-time likelihoods decouple by the same mechanism. The sigmoid concordance loss (SCL), in contrast, approximates one minus the C-index with a two-sided, computable tolerance, so a decrease beyond twice that tolerance certifies a concordance gain. Across eighteen datasets and four modalities the absolute rank correlation between validation SCL and validation C-index averages 0.97 and never falls below 0.91, against 0.37 to 0.46 for the likelihood losses. Replacing C-index-based checkpointing by loss-based checkpointing moves the SCL’s test C-index by at most 0.006, against up to 0.064 for the baselines. The SCL also retains competitive discrimination, with the best mean within-dataset rank, 2.00, among the six losses run on every dataset, although the leading methods are not statistically separated. The contribution is therefore not improved discrimination, but a loss whose numerical value remains interpretable as a proxy for the evaluation metric during training.