A general multilevel estimation framework: Multivariate joint models and more

A tremendous amount of work has been conducted in the area of joint models in recent years, with new extensions constantly being developed as the methods become more widely accepted and utilised, especially as the availability of software increases. In this talk I will introduce work focused on developing an over-arching general framework, and usable software implementation called megenreg, for estimating many different types of joint models. This will allow the user to fit a model with any number of outcomes, each of which can be of various types (continuous, binary, count, ordinal, survival), with any number of levels, and with any number of random effects at each level. Random effects can then be linked between outcomes in a number of ways. Of course, all of this is nothing new, and can be done (far better) with gsem. My focus, and motivation for writing my own simplified/extended gsem is to extend the modelling capabilities to allow the inclusion of the expected value of an outcome (possibly time-dependent) or its gradient or integral or general function of it, in the linear predictor of another. Furthermore, I develop simple utility functions to allow the user to extend to non-standard distributions in an extremely simple way with a little Mata function, whilst still providing the complex syntax users of gsem will be familiar with. I’ll focus on a special case of the general framework, joint modelling of multivariate longitudinal outcomes and survival, and in particular discuss some of the challenges faced in estimating such complex models, such as high dimensional random effects, and describe how we can relax the normally distributed random effects assumption. I’ll also describe many new methodological extensions, particularly in the field of survival analysis, each of which is simple to implement in megenreg.