Joint analysis of bivariate longitudinal ordinal outcomes and competing risks survival times with nonparametric distributions for random effects.

We propose a semiparametric joint model for bivariate longitudinal ordinal outcomes and competing risks failure time data. The association between the longitudinal and survival endpoints is captured by latent random effects. This approach generalizes previous joint analysis that considers only one response variable at the longitudinal endpoint. One unique feature of the proposed model is that we relax the commonly used normality assumption for random effects and leave the distribution completely unspecified. We use a modified version of the vertex exchange method in conjunction with an expectation-maximization algorithm to estimate the random effects distribution and model parameters. We show via simulations that robust parameter estimates are obtained from the proposed method under various scenarios. We illustrate the approach using cough severity and frequency data from a scleroderma lung study.