Estimating intracluster correlation for ordinal data

Abstract

In this paper, we consider the estimation of intracluster correlation for ordinal data. We focus on pure-tone audiometry hearing threshold data, where thresholds are measured in 5 decibel increments. We estimate the intracluster correlation for tests from iPhone-based hearing assessment applications as a measure of test/retest reliability. We present a method to estimate the intracluster correlation using mixed effects cumulative logistic and probit models, which assume the outcome data are ordinal. This contrasts with using a mixed effects linear model which assumes that the outcome data are continuous. In simulation studies, we show that using a mixed effects linear model to estimate the intracluster correlation for ordinal data results in a negative finite sample bias, while using mixed effects cumulative logistic or probit models reduces this bias. The estimated intracluster correlation for the iPhone-based hearing assessment application is higher when using the mixed effects cumulative logistic and probit models compared to using a mixed effects linear model. When data are ordinal, using mixed effects cumulative logistic or probit models reduces the bias of intracluster correlation estimates relative to using a mixed effects linear model.

Keywords:

• Test/retest reliability
• reliability and validity
• pure-tone audiometry
• intracluster correlation
• ordinal data

Disclosure statement

SGC serves as a consultant to Decibel Therapeutics. GCC is an employee of OM1, has equity in Allena Pharmaceuticals, and receives royalties from UpToDate for being an author and Section Editor. All other authors have no competing interests to report.

Data availability statement

The Nurses' Health Study (NHS) II supports transparency and has data sharing mechanisms clearly in place, which have been approved by their IRB. Further details can be found at http://www.nurseshealthstudy.org/researchers and http://www.nurseshealthstudy.org/contact. Further questions about the data can be addressed to [email protected]. The CHEARS study can be contacted at [email protected].

Relevant code can be found at https://github.com/blangworthy/ICCordinal

Additional information

Funding

This work was supported by the National Institute Health [grant numbers R01 DC017717 and U01 DC010811].