Re: Projecting individualized absolute invasive breast cancer risk in African American women.
In their " Discussion, " Gail et al. (1) seem to be saying that a problem with a model's concordance statistic (or area under a receiver operating curve [AUC]) is that it is inherently retrospective, implying that one should therefore not place much stock in it. The concordance statistic from the Gail model is retrospective in the same sense that the Gail model's parameter estimates (which produce the estimated risks) are retrospective; that is, all of these measures derive from existing data on risk factors and outcomes. As is the case with the model's parameter estimates, if the model is applied to a sample or population similar in key respects to that from which it has been derived, we can reasonably expect that the AUC will be generalizable. The key issue about the AUC is not, then, that it is retrospective or at least any more retrospective than parameter estimates. The authors next state that " … if a model includes age only and predicts that every woman in the age range 60-64 years has a 1.7% risk of breast cancer … then the AUC will be 0.50. Some would mistakenly construe this to mean that the model does not perform any better than a coin fl ip in predicting who will or will not get breast cancer. In fact, if one predicted that none of these women would be diagnosed with invasive breast cancer in the next fi ve years, one would predict correctly for 100 – 1.7 = 98.3% of the women. " This latter statement is true, but one does not need to rely on such a statistical model as support for a prediction that no women will get breast cancer during a period of 5 years. One simply needs general population incidence rates to see that only a small minority of women will develop disease over a period of 5 years. In recent years, the Gail model has been promoted as a decision-making aid for women with respect to chemo-prevention of breast cancer. If the goal in providing risk estimates is to help women with such dichotomous decision making about prophylaxis, or even with entrance (or not) into a clinical trial, one cannot imply that a model is doing a good job by giving everyone the same risk estimate. A model that gives each person the same risk estimate has zero discriminatory ability — no individual …