Flexible multivariate joint model of longitudinal intensity and binary process for medical monitoring of frequently collected data.

A frequent problem in longitudinal studies is that data may be assessed at subject-selected, irregularly spaced time-points, resulting in highly unbalanced outcome data, inducing bias, especially if availability of data is directly related to outcome. Our aim was to develop a multivariate joint model in a mixed outcomes framework to minimize irregular sampling bias. We demonstrate using blood glucose monitoring throughout pregnancy and risk of preterm birth among women with type 1 diabetes mellitus. Blood glucose measurements were unequally spaced and intensity of sampling varied between and within individuals over time. Multivariate linear mixed effects submodel for the longitudinal outcome (blood glucose), Poisson model for the intensity of glucose sampling, and logistic regression model for binary process (preterm birth) were specified. Association between models is captured through shared random effects. Markov chain Monte Carlo methods were used to fit the model. The multivariate joint model provided better prediction, compared with a joint model with a multivariate linear mixed effects submodel (ignoring intensity of glucose sampling) and a two-stage model. Most association parameters were significant in the preterm birth outcome model, signifying improvement of predictive ability of the binary endpoint by sharing random effects between glucose monitoring and preterm birth. A simulation study is presented to illustrate the effectiveness of the multivariate joint modeling approach.