A comparison of estimators to evaluate the discriminatory power of time-to-event models

Discrimination measures for continuous time-to-event outcomes have become an important tool in medical decision making. The idea behind discrimination measures is to evaluate the performance of a prediction model by measuring its ability to distinguish between observations having an event and those having no event. Researchers proposed a variety of approaches to estimate discrimination measures from a set of right-censored data. These approaches rely on different regularity assumptions that are needed to ensure consistency of the respective estimators. Typical examples of regularity assumptions include the proportional hazards assumption in Cox regression and the random censoring assumption. Because regularity assumptions are often violated in practice, conducting a sensitivity analysis of the estimators is of considerable interest. The aim of the paper is to analyze and to compare the most popular estimators of discrimination measures for event time outcomes. On the basis of the results of an extensive simulation study and the analysis of molecular data, we investigate the behavior of the estimators in situations where the underlying regularity assumptions do not hold. We show that violations of the regularity assumptions may induce a nonignorable bias and may therefore result in biased medical decision making.