Use of the Weibull hazard model to estimate age-specific probability of permanent tooth loss

In analysis of the probability of tooth loss with age, the exact time of tooth loss is often unknown, although it is clear whether a tooth remains or has been lost. That is, left censoring is inevitable during data sampling. This may provide a biased estimate if such data are dealt with by the product-limit method, which is a common method of survival analysis. To reduce such a bias in estimating the age-specific probability of tooth loss, we developed a survival analysis method taking left censoring into consideration. Four hundred and forty-six panoramic radiographs obtained in a daily clinical practice were used. The frequency of tooth loss with age was assumed to follow the Weibull hazard model, and a likelihood function taking left censoring into consideration was defined to estimate the probability of tooth loss. The estimate obtained from our method was compared with that from the product-limit method to examine whether the effect of left censoring was reduced. We found that the probability of tooth loss estimated by the product-limit method was biased by left-censored data, and that the bias was reduced when our method was used. A Monte Carlo simulation study, in which the true tooth loss time was given, also showed that our method provided an estimate closer to the true value. Our method is considered to be more accurate in estimating the probability of tooth loss, since it reduces the bias caused by left-censored data.