ORTH.Ord: An R package for analyzing correlated ordinal outcomes using alternating logistic regressions with orthogonalized residuals

Background and objectives: Marginal models with generalized estimating equations (GEE) are usually rec-ommended for analyzing correlated ordinal outcomes which are commonly seen in a longitudinal study or clustered randomized trial (CRT). Within-cluster association is often of interest in longitudinal studies or CRTs, and can be estimated with paired estimating equations. However, the estimators for within -cluster association parameters and variances may be subject to finite-sample biases when the number of clusters is small. The objective of this article is to introduce a newly developed R package ORTH.Ord for analyzing correlated ordinal outcomes using GEE models with finite-sample bias corrections. Methods: The R package ORTH.Ord implements a modified version of alternating logistic regressions with estimation based on orthogonalized residuals (ORTH), which use paired estimating equations to jointly estimate parameters in marginal mean and association models. The within-cluster association between ordinal responses is modeled by global pairwise odds ratios (POR). The R package also provides a finite -sample bias correction to POR parameter estimates based on matrix multiplicative adjusted orthogonal-ized residuals (MMORTH) for correcting estimating equations, and bias-corrected sandwich estimators with different options for covariance estimation.Results: A simulation study shows that MMORTH provides less biased global POR estimates and cover-age of their 95% confidence intervals closer to the nominal level than uncorrected ORTH. An analysis of patient-reported outcomes from an orthognathic surgery clinical trial illustrates features of ORTH.Ord.Conclusions: This article provides an overview of the ORTH method with bias-correction on both esti-mating equations and sandwich estimators for analyzing correlated ordinal data, describes the features of the ORTH.Ord R package, evaluates the performance of the package using a simulation study, and finally illustrates its application in an analysis of a clinical trial.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This article introduces a newly developed R package ORTH.Ord for analyzing correlated ordinal outcomes using GEE models with finite-sample bias corrections. The package implements a modified version of alternating logistic regressions with estimation based on orthogonalized residuals. The simulation study shows that the ORTH method with bias-correction provides less biased estimates and closer coverage to the nominal level.