A composite endpoint combining multiple outcomes is frequently used for clinical trials. Conventional time-to-first-event analyses have several limitations as the first event analyzed is often a less important, but more frequent outcome. The win ratio (Pocock et al., 2012) addresses these limitations; it considers the clinical importance order and the relative time sequence of the outcomes. In this talk, we consider stratified designs and the stratified win ratio (Dong, Qiu, Wang and Vandemeulebroecke, 2018), constructed similarly to the Mantel-Haenszel stratified odds ratio. As win ratio analyses usually involve many more ties than wins, we present the win odds (Dong et al., 2019), which assigns 50% of ties to the numerator and 50% to the denominator. We illustrate this statistic and compare it with the win ratio using real data from clinical studies.