Extended multivariate generalised linear and non-linear mixed effects models


There has recently been a tremendous amount of work in the area of joint models. New extensions are constantly being developed as methods become more widely accepted and used, especially as the availability of software increases. In this talk, I will introduce work focused on developing an overarching 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 or extended gsem is to extend the modeling capabilities to allow inclusion of the expected value of an outcome (possibly time-dependent) or its gradient, integral, or general function in the linear predictor of another. Furthermore, I develop simple utility functions to allow the user to extend to nonstandard distributions in an extremely simple way with a short Mata function, while still providing the complex syntax that users of gsem will be familiar with. I will focus on a special case of the general framework and joint modeling of multivariate longitudinal outcomes and survival. I will particularly discuss some challenges faced in fitting such complex models, such as high dimensional random effects, and describe how we can relax the normally distributed random effects assumption. I will also describe many new methodological extensions, particularly in the field of survival analysis, each of which is simple to implement in megenreg.

London, United Kingdom