I have some data which I'm using to predict the potential outcome of a new applicant defaulting on their credit loan.
For Kaplan-Meier, I don't believe there would be a need for splitting the data as the analysis pertains to the observations looked at, solely (correct me if I'm wrong).
But for cox regression, is it needed?
Cox Regression doesn't predict new observations, I don't believe. Does it?
If you are talking about something like train/test splits, that's not required (and typically not a good idea) unless you have at least a few tens of thousands of cases. See this post, for example. That's true for any type of analysis with typical real-world variability. If anything, strict train/test splits are even riskier in survival analysis, where the power is provided mostly by the number of cases with events, typically substantially smaller than the total number of cases. Internal validation via bootstrapping is generally best. The R rms package provides tools for such validation of many types of regression models.
A Cox model can be used for predictions. See this page for an introduction. After the model has been fit and regression coefficients obtained, you back-calculate from the data to estimate the baseline hazard and survival function over time. Then that baseline can be adjusted for any set of covariate values to obtain specific predictions of survival probability over time. The main vignette of the R survival package and the reference manual help pages show how to do this. Be warned that not all software packages allow for predictions if you have covariates whose values change over time. See this page for a brief overview of the associated difficulties.
