Bridging data exploration and modeling in event-history analysis: the supervised-component Cox regression

In event-history analysis with many possibly collinear regressors, Cox’s proportional hazard model, like all generalized linear models, can fail to be identified. Dimension-reduction and regularization are therefore needed. Penalty-based methods such as the ridge and the least absolute shrinkage and selection operator (LASSO) provide a regularized linear predictor, but fail to highlight the predictive structures. This is the gap filled by the supervised-component Cox regression (SCCoxR). Its principle is to compute a sequence of orthogonal explanatory components, which both rely on the strong correlation structures of regressors and optimize the goodness-of-fit of the model. One of its parameters tunes the balance between component strength and goodness of fit, thus bridging the gap between classical Cox regression with Cox regression on principal components. A second parameter allows the focus on subsets of highly correlated explanatory variables. A third parameter tunes the regularization of the model coefficients, leading to more robust estimates. Simulations show how to tune the parameters. The method is applied to the case study of polygamy in Dakar, Senegal.