  The Cox proportional hazards model is ubiquitous in the analysis of
time-to-event data. However, when the data dimension p is comparable to the
sample size $N$, maximum likelihood estimates for its regression parameters are
known to be biased or break down entirely due to overfitting. This prompted the
introduction of the so-called regularized Cox model. In this paper we use the
replica method from statistical physics to investigate the relationship between
the true and inferred regression parameters in regularized multivariate Cox
regression with L2 regularization, in the regime where both p and N are large
but with p/N ~ O(1). We thereby generalize a recent study from maximum
likelihood to maximum a posteriori inference. We also establish a relationship
between the optimal regularization parameter and p/N, allowing for
straightforward overfitting corrections in time-to-event analysis.
