Marginal models for longitudinal continuous proportional data.

Continuous proportional data arise when the response of interest is a percentage between zero and one, e.g., the percentage of decrease in renal function at different follow-up times from the baseline. In this paper, we propose methods to directly model the marginal means of the longitudinal proportional responses using the simplex distribution of Barndorff-Nielsen and Jørgensen that takes into account the fact that such responses are percentages restricted between zero and one and may as well have large dispersion. Parameters in such a marginal model are estimated using an extended version of the generalized estimating equations where the score vector is a nonlinear function of the observed response. The method is illustrated with an ophthalmology study on the use of intraocular gas in retinal repair surgeries.