Christopher L. Blizzard, Stephen J. Quinn, Jana D. Canary, David W. Hosmer
Department of Public Health, University of Massachusetts, Amherst, USA.
Flinders Clinical Effectiveness, Flinders University, Adelaide, Australia.
Menzies Research Institute Tasmania, University of Tasmania, Hobart, Australia.
DOI: 10.4236/ojs.2013.34A003   PDF    HTML     5,013 Downloads   8,438 Views   Citations

Abstract

The adjacent-categories, continuation-ratio and proportional odds logit-link regression models provide useful extensions of the multinomial logistic model to ordinal response data. We propose fitting these models with a logarithmic link to allow estimation of different forms of the risk ratio. Each of the resulting ordinal response log-link models is a constrained version of the log multinomial model, the log-link counterpart of the multinomial logistic model. These models can be estimated using software that allows the user to specify the log likelihood as the objective function to be maximized and to impose constraints on the parameter estimates. In example data with a dichotomous covariate, the unconstrained models produced valid coefficient estimates and standard errors, and the constrained models produced plausible results. Models with a single continuous covariate performed well in data simulations, with low bias and mean squared error on average and appropriate confidence interval coverage in admissible solutions. In an application to real data, practical aspects of the fitting of the models are investigated. We conclude that it is feasible to obtain adjusted estimates of the risk ratio for ordinal outcome data.

Keywords

Ordinal; Risk Ratio; Multinomial Likelihood; Logarithmic Link; Log Multinomial Regression; Adjacent Categories; Continuation-Ratio; Proportional Odds; Ordinal Logistic Regression

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Conflicts of Interest

The authors declare no conflicts of interest.

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