Abstract
Objective(s): We aim to suitably combine models (already proven to be useful in various medical areas) for numeric, count, binary, ordinal or general multinomial longitudinally measured outcomes. Our complex approach enhances these usually separately fitted models by capturing the relationships among investigated variables.
Software tool for statistical inference for practical use is being developed. Method(s): Linear mixed effect models for numeric variables are viewed in Bayesian framework in order to be merged with models for underlying numeric latent variables for categorical outcomes.
Each level of binary and ordinal variables is considered as the corresponding latent variable falling into certain interval whose bounds are not known in advance. While preserving identifiability of the parameters in our model we allow different sets of regressors across all responses for both fixed and random effects.
Random effects for different variables are distributed from joint normal distribution whose covariance matrix carries the information about relationships among variables. Such model specification allows us to derive full-conditioned distribution of each of the parameters leading to direct use of Gibbs sampling procedure.
A sufficiently long generated Markov Chain with posterior distribution being its stationary and limit distribution serves us for the inference about parameters. Results: In artificial controlled conditions our sampling procedure tends to approximate the true values of model parameters.
Our statistical method is planned to be applied to the well known sequential PBC dataset (Mayo Clinic Primary Biliary Cirrhosis, 1974-84). A suitable joint model for serum bilirubin, stage of edema, presence of hepatomegaly or enlarged liver and blood vessel malformations in the skin will be found.