Abstract
In event-history analysis with numerous and collinear regressors, Cox's proportional hazard model, as all generalized linear models, encounters crippling instability problems. Dimension-reduction and regularization are therefore needed. Penalty-based methods such as ridge and least absolute shrinkage and selection operator (LASSO) provide a regularized linear predic-tor, but do not enable exploratory analysis of predictive structures. A new and flexible component-based technique is proposed here, as an alternative: Supervised-Component Cox Regression (SCCoxR). Its principle is to calculate a sequence of uncorrelated explanatory components which both lean on 1 the strong correlation structures of regressors, and optimize the goodness-of-fit of the model. The flexibility of the method comes from three tuning-parameters. The first one allows to tune the balance between component-strength and goodness-of-fit, thus bridging classical Cox Regression with Cox regression on principal components. The second one tunes the focus on more or less local explanatory variable-bundles. The third one tunes the regularization of the model coefficients, hence the robustness of the output estimated formula of the hazard. Supervised-component Cox regression is demonstrated on simulated data, with intent to give the user some hints on the tuning process, and then used to explore and model the entrance of men into polygamy in Dakar.