Maximum likelihood estimates for the lifetime of bonded dental prostheses

Clinical studies measuring the lifetime of dental prostheses produce censored data when not all specimens have failed during the course of the study. Such clinical data can be analyzed by the Weibull probability distribution function. Algorithms are presented that provide the maximum likelihood estimates of the distribution's parameters. These parameters are the characteristic lifetime (time to failure for 63% of the specimens of the total sample) and the Weibull or shape parameter. Two iterative methods for solving the maximum likelihood equations are given. These mathematical methods have been applied to the results from a retrospective clinical investigation into the lifetime assessment of resin-bonded prostheses. This study evaluated 164 resin-bonded prostheses (for 146 patients) placed between January, 1980, and May, 1985. To date (April, 1995), 47 prostheses (29%) have failed with a median time in service of 74 months (6.2 yr). For the surviving prostheses, the median time in service is 123 months (10.3 yr) and still increasing. The maximum likelihood estimate of the characteristic lifetime for these restorations is 255 months (21.3 yr). Differences in the characteristic lifetime were observed between prostheses placed anteriorly, 338 months (28 yr), and posteriorly, 207 months (17 yr). Since there are no rigorous confidence intervals for deeply censored samples, only provisional confidence bounds could be determined, which substantiated the observed differences. The Weibull modulus value of 1.5 indicates that the probability of failure for resin-bonded prostheses begins to decrease after 10 years in service.