Abstract : This paper considers the case of two competing, nested, probability predicting models. The nested model contains traditional factors, and the
larger model contains some expensive, or generally hard to obtain, often genetic, relevant markers. The indices used to compare the respective
predictive ability of the two models are the integrated discrimination improvement (IDI) and the Brier's score improvement (BRI). Estimation of the
models and their relative IDI and BRI are conducted on the same sample, and their respective asymptotic properties are proved. The results are
applied to Alzheimer's disease. The authors conduct two different simulations: one to check the behavior of the estimates of IDI and BRI, and the
other parallel to Gu and Pepe's examples. The three city (3C) study is a cohort study conducted in three cities in France (Bordeaux, Dijon and
Montpellier), aiming to estimate the risk of dementia and cognitive impairment attributable to vascular factors.