A multivariate discrete failure time model for the analysis of infant motor development

We develop a multivariate discrete failure time model for the analysis of infant motor development. We use the model to jointly evaluate the time (in months) to achievement of three well-established motor milestones: sitting up, crawling, and walking. The model includes a subject-specific latent factor that reflects underlying heterogeneity in the population and accounts for within-subject dependence across the milestones. The factor loadings and covariate effects are allowed to vary flexibly across milestones, and the milestones are permitted to have unique at-risk intervals corresponding to different developmental windows. We adopt a Bayesian inferential approach and develop a convenient data-augmented Gibbs sampler for posterior computation. We conduct simulation studies to illustrate key features of the model and use the model to analyze data from the Nurture study, a birth cohort examining infant health and development during the first year of life.