A joint latent autoregressive model for patient dropout and longitudinal health-related quality of life subject to informative missingness

In many clinical trials where the endpoint is a time to event, longitudinal measurements are captured on variables that are also thought to influence the underlying data process. For example, there has been considerable interest in the literature in jointly modelling longitudinal Health Related Quality of Life (HRQOL) and patient dropout. To better understand the interrelationship between data processes, a common approach is to posit a joint model for the longitudinal measurements and the survival endpoint in which the components are linked by a random effect. Thus far, joint modelling has focused almost exclusively on models for continuous longitudinal responses where the time to event is modelled via a proportional hazards relationship. In many instances, however, the longitudinal data is not continuous and the assumption of a proportional hazards link is impractical as patients under study in different treatment groups become more homogenous in time. Additionally, the use of a random effect to link model components does not permit sufficiently rich correlation structures that can accommodate important features such as autocorrelation between measurements. A joint proportional odds model for dropout and longitudinal ordinal categorical data model subject to informative missingness is proposed in which model components are linked by a common multivariate Gaussian latent autoregressive effect. A Monte Carlo EM Algorithm is employed to yield maximum likelihood estimates and their asymptotic distributions are derived. Furthermore, one-sided hypothesis testing procedures are presented for the multivariate mean of the latent effects distribution adjusted for the effect of autocorrelation. A data set taken from the literature is used to demonstrate the proposed methodology.