# An Association Test for Ordinal Outcomes in Clustered Data With Informative Cluster Size

## TL;DR

This paper introduces a new statistical test for analyzing ordinal outcomes in clustered data where cluster size might influence the results.

## Contribution

A novel nonparametric method is proposed to handle ordinal outcomes in clustered data with informative cluster size.

## Key findings

- The new test outperforms existing methods in identifying significant ordinal associations when cluster size is informative.
- The proposed method performs comparably to existing methods when cluster size is not informative.
- The method was successfully applied to real-world cluster-randomized clinical trial data.

## Abstract

In cluster‐correlated data, the number of observations in a cluster can be associated with the outcome from that cluster. This phenomenon is known as informative cluster size which can occur in cluster‐randomized clinical trial data. Several studies have found that ignoring the issue of informative cluster size can produce biased results in the analysis of clustered data. Most of the existing methods for addressing informative cluster size are suited to continuous outcomes. However, ordinal outcomes and covariates are often encountered in clustered data obtained from large clinical studies. The existing methods for ordinal association testing in clustered data can produce suboptimal results in the presence of informative cluster size. In this article, we propose a new nonparametric method for testing marginal association between ordinal variables in clustered data that can account for informative cluster size. Through simulated data analyses, we show that our new test outperforms the existing alternatives in accurately identifying significant marginal ordinal associations in the presence of informative cluster size. Even if the cluster size is not informative, the performance of our method is comparable to the existing methods. Additionally, we demonstrate the usefulness of our proposed method through an application to a real‐world cluster‐randomized clinical trial data.