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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. [ABSTRACT FROM AUTHOR]

Principal components analysis (PCA) is a common dimension-reduction tool that transforms a set of variables into a linearly uncorrelated set of variables. Standard PCA estimators involve either the eigendecomposition of the estimated covariance matrix or a singular value decomposition of the centered data. However, for right-censored failure time data, estimating the principal components in this way is not straightforward because not all failure times are observed. Standard estimators for the covariance or correlation matrix should not be used in this case, because they require strong assumptions on the form of the joint distribution and on the marginal distributions beyond the final observation time. We present a novel, nonparametric estimator for the covariance of multivariate right-censored failure time data based on the counting processes and corresponding martingales defined by the failure times. We prove that these estimators are consistent and converge to a Gaussian process when properly standardized. We further show that these covariance estimates can be used to estimate a PCA for the martingales and counting processes for the different failure times. The corresponding estimates of the principal directions are consistent and asymptotically normal. We apply this method to data from a clinical trial of patients with pancreatic cancer, and recover a medically valid low-dimensional representation of adverse events. [ABSTRACT FROM AUTHOR]

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., Competing Interests: 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., (© 2023 Informa UK Limited, trading as Taylor & Francis Group.)