Multilevel modeling of clustered grouped survival data of dental implant failures; a Bayesian approach

In clinical dental studies, each participant has usually several visits, and since the review and ongoing monitoring of the subjects are often expensive or even impossible, so people are examined periodically during regularly pre-scheduled visits. Therefore, discrete or grouped clustered failure time data are collected. We aimed to show the use of Monte Carlo Markov Chain (MCMC) and the non-informative prior in a Bayesian framework in multilevel modeling of clustered grouped survival data.
Methods & Materials: A two-level model with additive variance components model for the random effects was considered. Both the grouped proportional hazards model and logistic regression with logit link function model were used. Using grouped proportional hazards method, we could approximate intracluster correlation of the log failure times. The statistical package OpenBUGS was adopted to estimate the parameter of interest based on the MCMC method. A cohort study was used in which 1011 persons visited at clinic dentistry of Tehran University of Medical Sciences, Iran, between the years 2002 and 2013 for dental implant and 2368 implants were placed for them in total. Clinical status of dental implants was evaluated in three periods after placement, thus clustered grouped failure times of the dental implants were recorded.
The grouped proportional hazards model showed that clustering effect among the log failure times of the different implants from the same person was fairly strong (correlation = 0.99). Complication and biomaterial variables had no effect on the implant failure, and there was no difference in the failure times related to the molar, premolar, canine, primary, and incisor since 95% credible interval (CI) included 0. The CI related to the gender and place of teeth not including 0, so these variables were significant in the model. The estimates of the baseline parameters (γ1, γ2, and γ3) were increasing indicating increasing hazard rates from interval 1-3. Results of logistic regression were similar to grouped proportional hazards model with wider confidence intervals.
The use of MCMC approach and non-informing prior in Bayesian framework to mimic maximum likelihood estimations in a frequentist approach in multilevel modeling of clustered grouped survival data can be easily applied with the use of the software OpenBUGS