Abstract

The win ratio, initially developed for time-to-event data, can be ex

tended to any data type equipped with a partial order. We study this extension

in both nonparametric inference and semiparametric regression. We begin by

formulating the win ratio as an estimand of contrast between two populations

with partially ordered responses, showing that it reduces to the familiar odds

ratio in the case of binary data. For hypothesis testing, we prove that the empirical two-sample win ratio is consistent against stochastically ordered distributions

and efficient against proportional odds alternatives under a total order. In regression, we model the conditional win ratio multiplicatively against covariates,

extending logistic regression from binary to partially ordered responses.

This

model is implied by a generalized continuation-ratio logit model but requires

fewer assumptions on the relationship between response levels. To make inference, we construct a class of weighted U-statistic estimating equations and derive

pseudo-efficient weights to improve efficiency.

Simulation studies demonstrate

that the proposed procedures perform well in both testing and regression under

finite samples. As illustrations, we analyze bivariate radiologic assessments in

a recent liver disease study and subject smoking status in a youth tobacco use

study, treating them both as partially ordered outcomes. The proposed methodology is implemented in the R package poset, publicly available on GitHub at

work (CRAN).

Information

Preprint No.SS-2023-0321
Manuscript IDSS-2023-0321
Complete AuthorsLu Mao
Corresponding AuthorsLu Mao
Emailslmao@biostat.wisc.edu

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Acknowledgments

This research was supported by the U.S. National Institutes of Health grant

R01HL149875 and National Science Foundation grant DMS-2015526.

Supplementary Materials

includes technical results and additional numerical

studies. An R-package poset that implements the proposed methodology

is available on GitHub at https://lmaowisc.github.io/poset as well as

the Comprehensive R Archive Network (CRAN), both with a tutorial based

on the liver study in Section 5.1.

Supplementary materials are available for download.