Random-effect models for ordinal responses: application to self-reported disability among older persons

Abstract

Longitudinal studies with ordinal repeated outcomes are now widespread in epidemiology and clinical research. The statistical analysis of these studies combines two difficulties: the choice of the best ordinal model and taking into account correlations for within-subject responses. Random-effect models are of particular value in this context and we propose here a fitting strategy. The various ordinal models extended to the case of repeated responses are detailed. We explain how the choice of model constrains the random effect structure. Model selection criteria and goodness-of-fit measures are also presented. These issues are dealt with by using an example of self-reported disability in older women assessed annually over a period of seven years. The proportionality of the odds ratios was validated for the covariables "age" and "gait speed". In contrast the impact of the covariable "pain" differs according to the levels of disability. The restricted partial proportional odds model was found to have a goodness of fit equivalent to the full generalized ordered logit model while the stereotype model appeared to give poorer fit. The random-effects models presented in this paper allow taking into account the ordinal nature of the outcome in longitudinal studies. Furthermore the impact of the risk factors can be modeled according to the response levels. This approach can be useful for a better understanding of complex processes of evolution.