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Title: Joint modelling of longitudinal and discrete time-to-event data Authors:  Jessica Barrett - MRC Biostatistics Unit (United Kingdom) [presenting]
Peter Diggle - Lancaster University and University of Liverpool (United Kingdom)
Robin Henderson - Newcastle University (United Kingdom)
David Taylor-Robinson - University of Liverpool (United Kingdom)
Abstract: Maximum likelihood estimation of joint models with shared latent random effects typically involves numerical integration of the likelihood over the random effects distribution or use of an expectation-maximisation algorithm. We present an estimation method for joint modelling of a longitudinal outcome and a discrete time-to-event outcome. By writing the joint likelihood in the form of a skew-normal distribution, we are able to analytically integrate over the random effects distribution and express it as a multivariate normal cumulative distribution function. This method allows more efficient estimation of joint models with more complex random effects structures, including higher-dimensional random effects. We illustrate our methods with an application to data from the UK Cystic Fibrosis Registry.