Kaplan-Meier plots as feature selection method?

Question

Can Kaplan-Meier plots be used for feature selection when building a multivariable survival model (e.g. Cox PH)? Would a visual assessment (no separation/crossing curves) suffice or would it have to be based on something more formal like log-rank test?

I'm in a situation where I have access to very large amounts of clinical data and I know that most of it has some relevance in predicting my outcome of interest. I will be using PCA to remove collinearity and reduce the number of features—but am limited in the model I can use to an extension of the Cox proportional hazards model (my outcome is interval-censored...). Can I use the outputs of a Kaplan Meier plot to decide if a variable is worth including or not?

Or is it just as misguided as when multiple regression models are built using features that give p values < 0.05 in univariate models?

Answer 1

If you have large amounts of survival data, in the sense of having a large number of events, then you should include as many features as is reasonable without overfitting. You usually can estimate 1 coefficient per 15 or so events in the data set, but some features (e.g., continuous predictors, those involved in interactions) might require more than 1 coefficient for proper modeling.

The large model has the best chance of making sure that you are adjusting properly for outcome-associated variables that might not be of primary interest, and to avoid the omitted-variable bias that can occur in a survival model if any outcome-associated variable isn't included in the model.

In that context, pre-selection of individual features based on Kaplan-Meier curves isn't a good idea.

I'd recommend careful study of Frank Harrell's Regression Modeling Strategies, which covers these issues both in the general context of regression and specifically for survival models.

Briefly, the idea is to decide first how many coefficients you can try to estimate without overfitting, based on your number of events. That's how many "degrees of freedom" you have to spend on your model. Then decide, based on subject-matter understanding, which predictors need the most flexibility in fitting and which might be combined together in what he calls "data reduction." Spend those "degrees of freedom" accordingly in setting up the model structure. Then run the full model, perhaps with some later simplification.