Statistical Analysis of Failure Time of the Molar Tooth Using Goodness-of-Fit Technique for Interval Censored Data

The failure time of permanent tooth is of the form of interval censored since the exact time of tooth decay is not available and it is only known that tooth decay occurs between two consecutive visits. There are a few techniques available in the literature for the problem of goodness-of-fit for interval censored data. In this paper, we propose a new goodness-of-fit testing procedure for interval censored data and employ this for the failure time of the first permanent molar tooth (sixth tooth) data.
Two methods of goodness-of-fit for interval censored data that are based on randomly generated data from each interval and averaging over the test statistics or over the p-values are employed for the failure time of the first permanent molar tooth data.
The mean of the failure time of the first permanent molar tooth is found to be at 95 months. The p-values of the two goodness-of-fit testing procedures for the Weibull, log-normal and gamma models are calculated.
By comparing the p-values, the log-normal model is considered as the best model to describe the failure time of the first permanent molar tooth data.