Figure 1

Cox-Snell residuals obtained from fitting various survival models to the Barrier data. 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 fitting a Cox proportional hazards model to the Barrier data via maximization of the partial log likelihood. The 14 most differentially expressed genes between the disease and the disease-free group were used as predictor variables. 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 maximum likelihood estimation. Obviously, the lines corresponding to the Cox-Snell residuals of the log-logistic and lognormal models are closest to the line through the origin, indicating that these models fit the data best. By contrast, the Cox model and the Weibull model (which both assume proportional hazards) do not seem to fit the data well, indicating that the proportional hazards assumption is violated.