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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. [ABSTRACT FROM AUTHOR]

We propose a semiparametric multi-state frailty model to analyze clustered event-history data subject to interval censoring. The proposed model is motivated by an attempt to study the life course of dental caries at the tooth level, taking into account the multiplicity of caries states and the intra-oral clustering of observations made at periodic time points. Of particular interest is the study of the intra-oral distribution of processes leading to carious lesions, and whether this distribution varies with gender. The model assumes, in view of the covariate profile, a proportionality of the transition intensities conditional on subject-level frailties, coupled with a linear spline approximation of the log baseline intensities. The model estimation is conducted using a penalized likelihood where the smoothing parameters are estimated as reciprocal variance components under a mixed-model representation. A Bayesian method is proposed to predict tooth-level caries transition probabilities, which can be used for tailoring tooth-level caries treatment and prevention plans. Intensive simulation studies indicate that the model fitting and prediction perform reasonably well under realistic sample sizes. The practical utility of the methods is illustrated using data from a longitudinal study on oral health among children from low-income families residing in the city of Detroit, Michigan. [ABSTRACT FROM AUTHOR]