Correlated probit analysis of repeatedly measured ordinal and continuous outcomes with application to the Health and Retirement Study

Modelling multiple outcomes in repeated measures studies: Comparing aesthetic eyelid surgery techniques

We propose a multivariate regression model to deal with multiple outcomes along with repeated measures in the context of longitudinal data analysis. Our model allows for flexible and interpretable modelling of the covariance structure within outcomes by using a linear combination of known matrices, while the generalized Kronecker product is employed to take into account the correlation between outcomes. We present maximum likelihood estimation along with extensions of the classical multivariate analysis of variance and multiple comparison hypothesis tests to deal with multivariate longitudinal data. The model and the associated multivariate hypothesis test are motivated by a prospective study conducted to compare three aesthetic eyelid surgery techniques, namely blepharoplasty, endoscopic forehead lift and endoscopic forehead lift associated with blepharoplasty. The effect of the techniques was assessed using measurements of a horizontal line through pupil centre and then three vertical lines, which go in direction to lateral canthus, middle pupil and medial canthus to the top of the brow. In this study, 30 female patients were randomly divided into three groups. Preoperative measurements were compared with postoperative measurements taken 30 days, 90 days and 10 years after the surgery. The presented multivariate model provided a better fit than its univariate counterpart. The results showed that the three surgery techniques tend to increase all considered outcomes in a long-term perspective, that is, from preoperative to 10 years postoperative evaluations. The only exception was for the outcome lateral eyebrow, for which the blepharoplasty had no significant effect.