Joint analysis of nonlinear longitudinal and time-to-event dataapplication to predicting pregnancy outcomes

Resumen

Nonlinear mixed effects models are statistical models containing both xed and random effects. They are particularly useful in settings where repeated measurements are made on the same statistical units (longitudinal data), or where measurements are made on clusters of related statistical units. Observations in the same unit/cluster cannot be considered independent and mixed effects models constitute a convenient tool for modeling unit/cluster dependence. Nonlinear mixed effects models are commonly used in longitudinal data analysis since they can cope with missing observations and unbalanced data, and take into account individual variations from a common pattern. A commonly encountered complication in the analysis of longitudinal data is the variable length of follow-up due to interval censoring. This can be further exacerbated by the possible dependency between the time-to-event data and the longitudinal measurements. This paper proposes a combination of a nonlinear mixed effects model for the longitudinal measurements and a parametric model for the time-to-event data. The dependency is handled via latent variables, which are naturally incorporated. Estimation procedures based on the Stochastic Aproximation of the EM algorithm (SAEM) are proposed.