Analysis of the Barrier stage II colon cancer data – Cox-Snell residuals for various boosting methods. The upper left panel shows the Cox-Snell residuals of a semiparametric Cox model vs. the Nelson-Aalen estimate of their cumulative hazard function. Estimates were obtained from boosting with the negative Cox partial log likelihood. The other panels show the Cox-Snell residuals (together with their cumulative hazard function) obtained from fitting various parametric AFT models to the same data via boosting with the corresponding negative log likelihood loss. Similar to Fig. 1, we see that the line corresponding to the Cox-Snell residuals of the log-logistic model is close to the line through the origin. The Cox model does not seem to fit the data well, indicating that the proportional hazards assumption is violated.
Schmid and Hothorn BMC Bioinformatics 2008 9:269 doi:10.1186/1471-2105-9-269