Alternating logistic regressions with improved finite sample properties

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 recommended 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 orthogonalized 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 coverage 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 estimating 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.

Marginal modeling of cluster-period means and intraclass correlations in stepped wedge designs with binary outcomes

Stepped wedge cluster randomized trials (SW-CRTs) with binary outcomes are increasingly used in prevention and implementation studies. Marginal models represent a flexible tool for analyzing SW-CRTs with population-averaged interpretations, but the joint estimation of the mean and intraclass correlation coefficients (ICCs) can be computationally intensive due to large cluster-period sizes. Motivated by the need for marginal inference in SW-CRTs, we propose a simple and efficient estimating equations approach to analyze cluster-period means. We show that the quasi-score for the marginal mean defined from individual-level observations can be reformulated as the quasi-score for the same marginal mean defined from the cluster-period means. An additional mapping of the individual-level ICCs into correlations for the cluster-period means further provides a rigorous justification for the cluster-period approach. The proposed approach addresses a long-recognized computational burden associated with estimating equations defined based on individual-level observations, and enables fast point and interval estimation of the intervention effect and correlations. We further propose matrix-adjusted estimating equations to improve the finite-sample inference for ICCs. By providing a valid approach to estimate ICCs within the class of generalized linear models for correlated binary outcomes, this article operationalizes key recommendations from the CONSORT extension to SW-CRTs, including the reporting of ICCs.