Comparison of Cox Model Methods in A Low-dimensional Setting with Few Events

Francisco M. Ojeda, Christian Müller, Daniela Börnigen, David-Alexandre Trégouët, Arne Schillert, Matthias Heinig, Tanja Zeller, Renate B. Schnabel

Prognostic models based on survival data frequently make use of the Cox proportional hazards model. Developing reliable Cox models with few events relative to the number of predictors can be challenging, even in low-dimensional datasets, with a much larger number of observations than variables. In such a setting we examined the performance of methods used to estimate a Cox model, including (i) full model using all available predictors and estimated by standard techniques, (ii) backward elimination (BE), (iii) ridge regression, (iv) least absolute shrinkage and selection operator (lasso), and (v) elastic net. Based on a prospective cohort of patients with manifest coronary artery disease (CAD), we performed a simulation study to compare the predictive accuracy, calibration, and discrimination of these approaches. Candidate predictors for incident cardiovascular events we used included clinical variables, biomarkers, and a selection of genetic variants associated with CAD. The penalized methods, i.e., ridge, lasso, and elastic net, showed a comparable performance, in terms of predictive accuracy, calibration, and discrimination, and outperformed BE and the full model. Excessive shrinkage was observed in some cases for the penalized methods, mostly on the simulation scenarios having the lowest ratio of number of events to the number of variables. We conclude that in similar settings, these three penalized methods can be used interchangeably. The full model and backward elimination are not recommended in rare event scenarios.