The goal of this article is to propose a new direct method that provides straightforward inference for AUC(t) and IAUC. Our method directly models AUC(t) as a function of time t using a flexible and yet parsimonious parametric model, namely, the fractional polynomials model proposed by Royston and Altman (1994).

For the purpose of estimating the time‐dependent AUC and IAUC, the “indirect” methods have some drawbacks. For example, most ROC‐estimation procedures rely on strong parametric assumptions such as proportional hazards, which may lead to potential bias due to the misspecification of the time‐to‐event model. In addition, because these methods are “indirect,” they are not particularly efficient and require unnecessary intensive computation.

Heagerty and Zheng (2005) showed that IAUC is equivalent to the global concordance summary with a proper weight function.