Analyzing the emergence times of permanent teeth: an example of modeling the covariance matrix with interval-censored data

Based on a data set obtained in a large dental longitudinal study, conducted in Flanders (Belgium), the joint emergence distribution of seven teeth was modeled as a function of gender and caries experience on primary teeth. Besides establishing the marginal dependence of emergence on the covariates, there was also interest in examining the impact of the covariates on the association among emergence times. This allows the establishment of the preferred rankings of emergence and their dependence on covariates. To this end, the covariance matrix was modeled as a function of covariates. Modeling the covariance matrix in this way needs to ensure the positive definiteness of the covariance matrix and it is preferable that the regression parameters of the model are interpretable. The modified Cholesky decomposition of the covariance matrix, as suggested by Pourahmadi, splits up the covariance matrix into two parts where the parameters can be interpreted, given a natural ranking of the responses. This approach was used here taking into account that the emergence times are interval-censored. Hence, we opted for a Bayesian implementation of the data augmentation algorithm.