The recording of multiple interval-censored failure times is common in dental research. Modeling multilevel data has been a difficult task. This paper aims to use the Bayesian approach to analyze a set of multilevel clustered interval-censored data from a clinical study to investigate the effectiveness of silver diamine fluoride and sodium fluoride varnish in arresting active dentin caries in Chinese pre-school children. The time to arrest dentin caries on a surface was measured. A three-level random-effects Weibull regression model was used. Analysis was performed with WinBUGS. Results revealed a strong positive correlation (0.596) among the caries lesions' arrest times on different surfaces from the same child. The software WinBUGS made the above complicated estimation simple. In conclusion, the annual application of silver diamine fluoride on caries lesions, and caries removal before the application, were found to shorten the arrest time.