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= Win ratio = The win ratio is a non-parametric statistical analysis technique used to compare composite outcomes in two groups according to a pre-defined outcome hierarchy. Given two groups and a list of outcomes ordered by clinical relevance, the win ratio assesses the set of all possible between-group pairwise comparisons to test the hypothesis that, among pairs untied by this outcome hierarchy, the odds of observing a better outcome in the first group is one.

History
The win ratio was first proposed by Stuart Pocock and colleagues in 2012 [citation needed]. The unmatched approach is an adaption of the Finkelstein-Schoenfeld test proposed by Dianne Finkelstein and David Schoenfeld in 1999.

The net clinical benefit, an absolute measure of treatment effect in the hierarchical outcome paradigm, was proposed independently of the work by Pocock et al. by Marc Buyse in 2010. The win odds FINISH PARAGRAPH.

Method
There are two approaches to a win ratio analysis: the matched approach and the unmatched approach. The matched approach involves the use of a matching algorithm to filter out unfair comparisons between patients with different baseline risks, which can improve statistical power. In practice, however, it is difficult to objectively define the matching process needed in the matched approach, and the unmatched win ratio has proven more favourable. Additionally, having differently-sized groups necessarily leads to patients being omitted from matched analyses, which is not true for the unmatched approach.

In both approaches, an outcome hierarchy must first be defined in descending order of clinical relevance. Each level of the hierarchy must stipulate the conditions under which one observation is considered to have a superior outcome to the other.

The unmatched win ratio
The unmatched approach involves constructing all possible between-group patient pairs. For groups X and Y, with NX and NY patients, respectively, this entails the creation of  patient pairs. Within each pair, patients are initially compared according to the uppermost component of the hierarchy: where one patient is observed to have a better outcome than the other, that patient is declared the "winner" and the pair considered untied. In the event that a pair are not untied, the next outcome in the hierarchy is considered instead, with this process repeated until either the pair is untied or hierarchy is exhausted.

The number of winners belonging to each group is then counted. The win ratio is defined as the ratio of the number of winners in the first group to the number of winners in the second group. P-values, derived from the Finkelstein Schoenfeld test [citation needed], and confidence intervals can be provided to accompany win ratio estimates.

The matched win ratio
The matched win ratio follows similarly, but with comparisons performed only between matched pairs. As a result, for groups X and Y with NX and NY respective patients, the matched win ratio involves just  comparisons, so can be considerably less computationally-intensive.