Biomedical Data Science Department, Geisel School of Medicine - USA
Comparing the behavior of two or more populations with respect to a particular outcome is a common problem in many research fields. The usual approach of performing a hypothesis test, computing the related p-value, and taking the corresponding decision has derived in an over-simplification of the underlying problem which is one of the starting points for the so-called replication crisis. Reporting statistics which provide adequate measures of the size of the observed difference is always advisable. Besides, the correct interpretation of these measures is fundamental for having an adequate knowledge of the real state of the art of the considered topic. In this work, we discuss different measures for summarizing the differences between two populations in both the complete and the right-censored scenarios. The common link of these measures is the well-known area under the receiver-operating characteristic, ROC, curve. We study the behavior of both parametric and non-parametric estimators though Monte Carlo simulations and in different real-world problems. In addition, we discuss the implication of these measures based on both the study design and the employed estimator. Measures based on the area under the ROC curve provide a useful and easy to interpret metric which can facilitate the description of the observed difference between populations although, the causal interpretation of these measures is still a challenging problem which depends on strong assumptions.