Bayesian hierarchical modeling of operating room times for surgeries with few or no historic data

In this work it is proposed a modeling for operating room times based on a Bayesian Hierarchical structure. Specifically, it is employed a Bayesian generalized linear mixed model with an additional hierarchical level on the random effects. This configuration allows the estimation of operating room times (ORT) with few or no historical observations, without requiring a prior surgeon’s estimate. In addition to the widely used lognormal distribution, it is also studied the gamma distribution to model the operating room times. For the scale parameters related to the random effects (surgeon and surgical group), which are important quantities in this type of modeling, different kinds of prior distributions such as Half-Cauchy, Sbeta2, and uniform are studied. A Bayesian version of the classical ANOVA is implemented to identify relevant predictors for the operating room times. We find that lognormal models outperform the gamma models in estimating upper prediction bounds (UB). Especially, the best ORT predictions for cases with few or no historical data (i.e., between 0 and 3 historical cases) are obtained with the Y ∼ l o g n o r m , SBeta 2 model. With a deviation of less than 1% with respect to the nominal coverage of the upper bound predictions UB80% and UB90% and an average absolute percentage error of 38.5% in the point estimate.