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Regression analysis of correlated ordinal data using orthogonalized residuals.

ABSTRACT: Semi-parametric regression models for the joint estimation of marginal mean and within-cluster pairwise association parameters are used in a variety of settings for population-averaged modeling of multivariate categorical outcomes. Recently, a formulation of alternating logistic regressions based on orthogonalized, marginal residuals has been introduced for correlated binary data. Unlike the original procedure based on conditional residuals, its covariance estimator is invariant to the ordering of observations within clusters. In this article, the orthogonalized residuals method is extended to model correlated ordinal data with a global odds ratio, and shown in a simulation study to be more efficient and less biased with regards to estimating within-cluster association parameters than an existing extension to ordinal data of alternating logistic regressions based on conditional residuals. Orthogonalized residuals are used to estimate a model for three correlated ordinal outcomes measured repeatedly in a longitudinal clinical trial of an intervention to improve recovery of patients' perception of altered sensation following jaw surgery.

SUBMITTER: Perin J

PROVIDER: S-EPMC4472482 | biostudies-literature | 2014 Dec

REPOSITORIES: biostudies-literature

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Regression analysis of correlated ordinal data using orthogonalized residuals.

Perin J J Preisser J S JS Phillips C C Qaqish B B

Biometrics 20140818 4

Semi-parametric regression models for the joint estimation of marginal mean and within-cluster pairwise association parameters are used in a variety of settings for population-averaged modeling of multivariate categorical outcomes. Recently, a formulation of alternating logistic regressions based on orthogonalized, marginal residuals has been introduced for correlated binary data. Unlike the original procedure based on conditional residuals, its covariance estimator is invariant to the ordering ...[more]

PMID: 25134789

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Project description:Neuroimaging data are increasingly being used to predict potential outcomes or groupings, such as clinical severity, drug dose response, and transitional illness states. In these examples, the variable (target) we want to predict is ordinal in nature. Conventional classification schemes assume that the targets are nominal and hence ignore their ranked nature, whereas parametric and/or non-parametric regression models enforce a metric notion of distance between classes. Here, we propose a novel, alternative multivariate approach that overcomes these limitations - whole brain probabilistic ordinal regression using a Gaussian process framework. We applied this technique to two data sets of pharmacological neuroimaging data from healthy volunteers. The first study was designed to investigate the effect of ketamine on brain activity and its subsequent modulation with two compounds - lamotrigine and risperidone. The second study investigates the effect of scopolamine on cerebral blood flow and its modulation using donepezil. We compared ordinal regression to multi-class classification schemes and metric regression. Considering the modulation of ketamine with lamotrigine, we found that ordinal regression significantly outperformed multi-class classification and metric regression in terms of accuracy and mean absolute error. However, for risperidone ordinal regression significantly outperformed metric regression but performed similarly to multi-class classification both in terms of accuracy and mean absolute error. For the scopolamine data set, ordinal regression was found to outperform both multi-class and metric regression techniques considering the regional cerebral blood flow in the anterior cingulate cortex. Ordinal regression was thus the only method that performed well in all cases. Our results indicate the potential of an ordinal regression approach for neuroimaging data while providing a fully probabilistic framework with elegant approaches for model selection.

Dataset Information

Regression analysis of correlated ordinal data using orthogonalized residuals.

Publications

Regression analysis of correlated ordinal data using orthogonalized residuals.

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