In many medical studies, researchers widely use composite or long ordinal scores, that is, scores that have a large number of categories and a natural ordering often resulting from the sum of a number of short ordinal scores, to assess function or quality of life. Typically, we analyse these using unjustified assumptions of normality for the outcome measure, which are unlikely to be even approximately true. Scores of this type are better analysed using methods reserved for more conventional (short) ordinal scores, such as the proportional-odds model. We can avoid the need for a large number of cut-point parameters that define the divisions between the score categories for long ordinal scores in the proportional-odds model by the inclusion of orthogonal polynomial contrasts. We introduce the repeated measures proportional-odds logistic regression model and describe for long ordinal outcomes modifications to the generalized estimating equation methodology used for parameter estimation. We introduce data from a trial assessing two surgical interventions, briefly describe and re-analyse these using the new model and compare inferences from the new analysis with previously published results for the primary outcome measure (hip function at 12 months postoperatively). We use a simulation study to illustrate how this model also has more general application for conventional short ordinal scores, to select amongst competing models of varying complexity for the cut-point parameters.