A mixed effects model for multivariate ordinal response data including correlated discrete failure times with ordinal responses.
The mixed effects model for binary responses due to Conaway (1990, A Random Effects Model for Binary Data) is extended to accommodate ordinal responses in general and discrete time survival data with ordinal responses in particular. Given a multinomial likelihood, cumulative complementary log-log link function, and log-gamma random effects distribution, the resulting marginal likelihood has a closed form. As a result, a Newton-Raphson estimation procedure is feasible without resorting to numerical, approximation-based, or Monte Carlo integration techniques. The parameters in the model have a proportional hazards interpretation in terms of multivariate discrete time data with ordinal responses. Using data from a psychological example, the proposed method is compared with other mixed effects approaches as well as population-averaged models.
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Center for Biostatistics and Epidemiology, Hershey Medical Center, Pennsylvania State University, 17033, USA.
D001699:Biometry; D002648:Child; D002675:Child, Preschool; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D015999:Multivariate Analysis; D016016:Proportional Hazards Models; D011581:Psychological Tests / Q000706:statistics & numerical data; D016019:Survival Analysis