Chapter 02
Hypothesis Testing
Win ratio statistics, recurrent events, and the design of adequately powered trials.
Chapter overview · Full exposition to follow
2.1 Win Ratio Basics
The two-sample win ratio compares patients across treatment groups using an ordered set of outcome rules. The sample win and loss fractions aggregate the pairwise comparisons; their ratio is the win ratio statistic.
Because each patient contributes to many pairs, the pairwise results are dependent. The slides develop inference using the associated U-statistic structure, including the large-sample behavior of the log win ratio.
Testing and interpretation
A test requires a clearly stated null hypothesis and valid assumptions about observation. The statistic’s interpretation as an effect estimate requires a separate discussion of its target.
2.2 Recurrent Events
When nonfatal events recur, a comparison based only on the first event leaves part of the history unused. The course introduces rules that prioritize survival and then compare recurrent-event frequency and timing.
The HF-ACTION example contrasts recurrent-event win ratio analyses through the WR package. The choice of comparison rule belongs to the endpoint definition and should follow the clinical question.
2.3 Sample Size and Power
Planning a win ratio analysis requires assumptions about the component events and their dependence. The slides use a Gumbel–Hougaard model and pilot information to connect component-specific effects with power and required sample size.
The worked example uses WR::WRSS(). Its inputs and calculations are available in the original chapter code; the full derivation will accompany the later book chapter.