Rejoinder: Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

Abstract

Few authors would not be pleased when discussants implement their methods or follow-up on their ideas. It is therefore a professional joy to see every discussant doing both! Our heartfelt thanks go to all discussants, and to the Executive Editor, Ed George, for bringing us such joy! Incidentally, the three discussions cover nicely the three main parts of our paper. Zheng and Lo’s discussion centers on our motivating application, namely, designing follow-up strategies in genetic studies, but with the additional consideration of the uncertainty in the measures themselves. Doss’s discussion focuses on the second part of our paper, namely, the likelihood-based relative measure, but with applications to survival analysis where the use of partial likelihood reveals very interesting (and inevitably confusing) complications. Chang, Chen, Chien and Hsing (hereafter C3H) comment on the third part of our paper, the Bayesian mea- sures for small samples, and implement variations that are applied to problems in infectious disease research and isotonic regression. Our responses are organized in the aforementioned order. We very much appreciate all the key messages conveyed by the discussants, though for a few of them we offer alternative explanations. Some questions posed by the discussants make nice Ph.D. or master thesis topics, so we summarize them at the end of this rejoinder.