Weight Set Decomposition for Weighted Rank Aggregation: An interpretable and visual decision support tool

The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking and then ordered. This paper describes a new tool for visualizing and displaying ranking information for the weighted rank aggregation method. Traditionally, the aim of rank aggregation is to summarize the information from the input rankings and provide one final ranking that hopefully represents a more accurate or truthful result than any one input ranking. While such an aggregated ranking is, and clearly has been, useful to many applications, it also obscures information. In this paper, we show the wealth of information that is available for the weighted rank aggregation problem due to its structure. We apply weight set decomposition to the set of convex multipliers, study the properties useful for understanding this decomposition, and visualize the indifference regions. This methodology reveals information--that is otherwise collapsed by the aggregated ranking--into a useful, interpretable, and intuitive decision support tool. Included are multiple illustrative examples, along with heuristic and exact algorithms for computing the weight set decomposition.

Theoretical Issues for Global Cumulative Treatment Analysis (GCTA)

Adaptive trials are now mainstream science. Recently, researchers have taken the adaptive trial concept to its natural conclusion, proposing what we call "Global Cumulative Treatment Analysis" (GCTA). Similar to the adaptive trial, decision making and data collection and analysis in the GCTA are continuous and integrated, and treatments are ranked in accord with the statistics of this information, combined with what offers the most information gain. Where GCTA differs from an adaptive trial, or, for that matter, from any trial design, is that all patients are implicitly participants in the GCTA process, regardless of whether they are formally enrolled in a trial. This paper discusses some of the theoretical and practical issues that arise in the design of a GCTA, along with some preliminary thoughts on how they might be approached.