Joint analysis of multivariate interval-censored survival data and a time-dependent covariate

We develop a joint modeling method for multivariate interval-censored survival data and a time-dependent covariate that is intermittently measured with error. The joint model is estimated using nonparametric maximum likelihood estimation, which is carried out via an expectation-maximization algorithm, and the inference for finite-dimensional parameters is performed using bootstrap. We also develop a similar joint modeling method for univariate interval-censored survival data and a time-dependent covariate, which excels the existing methods in terms of model flexibility and interpretation. Simulation studies show that the model fitting and inference approaches perform very well under realistic sample sizes. We apply the method to a longitudinal study of dental caries in African-American children from low-income families in the city of Detroit, Michigan.