JdS2012


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Résumé de communication



Résumé 267 :

Cherry-picking: multiple testing for exploratory research
Goeman, Jelle ; Solari, Aldo
Leids Universitair Medisch Centrum

Exploratory research, e.g. in genomics, is often aimed at selecting promising findings to be probed further in later experiments. The selection process may result in false positive and false negative findings, and may be formulated as a multiple hypothesis testing problem. Theory for multiple hypothesis testing, however, generally assumes a confirmatory point of view. Exploratory research is different from confirmatory research in the sense that the process is more flexible, allowing more user input, and that crucial decisions are made post hoc, after seeing the data. Motivated by the practice of exploratory research, we formulate an approach to multiple testing that reverses the conventional roles of the user and the multiple testing procedure. Traditionally, the user chooses the error criterion, and the procedure the resulting rejected set. Instead, we propose to let the user choose the rejected set freely, and to let the multiple testing procedure return a confidence statement on the number of false rejections incurred. In our approach, such confidence statements are simultaneous for all choices of the rejected set, so that post hoc selection of the rejected set does not compromise their validity. The proposed reversal of roles requires nothing more than a review of the familiar closed testing procedure, but with a focus on the non-consonant rejections that this procedure makes. We suggest several shortcuts to avoid the computational problems associated with closed testing.