Multilevel Modelling of Caries Clinical Trial Data

Caries data follows a naturally hierarchical structure, with surfaces clustered within teeth, clustered within individuals. Caries increment analysis aggregates data by individual, losing tooth and surface specific information. Multilevel modelling allows analysis of data at surface level without aggregating. Objectives: To investigate the potential of multilevel modelling to increase efficiency in caries clinical trials, by reducing the number of participants required to detect an intervention effect. Methods: A simulation study is conducted to investigate the performance of multilevel modelling methods and standard caries increment analysis. Data sets are simulated from a three level binomial distribution based on analysis of a caries clinical trial in Scottish adolescents, with varying sample sizes, treatment effects and random tooth level effects, to compare the power of multilevel models and traditional analysis. 40500 data sets were simulated using the MLwiN syntax language, 1500 for each of 27 combinations of parameters. Parameter values were chosen based on trials reported in Cochrane reviews of topical fluorides. Results: Observed power for the caries increment method was very similar to that of the multilevel models, with more variation in the smaller data sets (50 per group). For simulated data sets with a prevented fraction of 25%, and a tooth level random effect with variance 1, observed power was 43% for caries increment (CI) versus 39% for multilevel modelling (MLM) with 50 participants per group, 80% (CI) versus 81% (MLM) for 150 per group, and both methods showed 98% power for 300 per group. Conclusions: This study has shown little difference between the observed power of multilevel models and traditional DFS increment analysis. This work indicates that the advantages of multilevel modelling in dental caries clinical trials may lie in greater understanding of the data structure and within mouth patterns of caries development, rather than reduction of required sample size.