SAS macros for point and interval estimation of area under the receiver operating characteristic curve for non-proportional and proportional hazards Weibull models

Aims and objectives  For prediction of risk of cardiovascular end points using survival models the proportional hazards assumption is often not met. Thus, non-proportional hazards models are more appropriate for developing risk prediction equations in such situations. However, computer program for evaluating the prediction performance of such models has been rarely addressed. We therefore developed SAS macro programs for evaluating the discriminative ability of a non-proportional hazards Weibull model developed by Anderson (1991) and that of a proportional hazards Weibull model using the area under receiver operating characteristic (ROC) curve.

Method  Two SAS macro programs for non-proportional hazards Weibull model using Proc NLIN and Proc NLP respectively and model validation using area under ROC curve (with its confidence limits) were written with SAS IML language. A similar SAS macro for proportional hazards Weibull model was also written.

Results  The computer program was applied to data on coronary heart disease incidence for a Framingham population cohort. The five risk factors considered were current smoking, age, blood pressure, cholesterol and obesity. The predictive ability of the non-proportional hazard Weibull model was slightly higher than that of its proportional hazard counterpart. An advantage of SAS Proc NLP in terms of the example provided here is that it provides significance level for the parameter estimates whereas Proc NLIN does not.

Conclusion  The program is very useful for evaluating the predictive performance of non-proportional and proportional hazards Weibull models.