Figure 2.

Cox-Snell residuals obtained from fitting various survival models to the esophageal cancer data.

The panels indicate the Cox-Snell residuals (together with their cumulative hazard function) obtained from fitting different parametric AFT models to the same data via maximum likelihood estimation. Obviously, the lines related to the Cox-Snell residuals of the log-normal and log-logistic models with gamma frailty are nearest to the line through the origin, indicating that these models fit the data best. In addition, the Cox model does not appear to fit the data well; it means that the proportional hazards assumption is violated. These results are consistent with our finding based on Akaike's Information Criterion