Some diagnostic methods for Cox regression models through hazard smoothing

In this paper some graphical methods are proposed for evaluating the fit of Cox regression models in survival analysis. The simplest procedure proposed is to estimate the baseline hazard separately within subgroups by applying kernel-based smoothing to standard cumulative hazard estimates. The different estimates should be the same, to within sampling variability, when the model is correct. A modification of this procedure gives a direct way of calculating smooth estimates of hazard ratios over time. A further modification gives estimates of ratios as a function of a continuous covariate and time. The methods are applied to data taken from a clinical trial of adjuvant therapy for breast cancer.