Empirical assessment of gamma generalized linear mixed models for outcomes in oral health research

Objectives. In case of positive and skewed data, the most common approach is to fit a linear model to log-transformed data, with the parameters being eventually evaluated after a back-transformation on the original scale. This method is known to be biased, in particular in repeated measurement studies, with the bias increasing with the heterogeneity in data. An alternative approach based on the Generalized Linear Mixed Model (GLMM) is therefore hereby proposed. Methods. We provide evidence on the performance of the Gamma GLMM model under a variety of data generating mechanisms and compare it to that of the Linear Mixed Effect Model (log-LME) on a log-transformed response. Three case studies from fixed prosthodontics are analyzed and discussed. Results. When the error variance is constant, log-LME and Gamma GLMM produce similar estimates with a negligible relative bias. In presence of heteroscedasticity, the log-LME for a Gamma response provides a substantially biased estimate of the true value, increasing as the error variance increases. Conclusions. No single alternative is best under all the conditions examined in this paper. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either log-LME.