Missing data commonly occur in health-related quality of life data in clinical trial studies because these data are reported by patients. Mixed effects models are frequently chosen for the primary analysis of clinical trial studies. However, mixed effects models require data missing at random. Pattern mixture models and selection models are two methods for handling nonignorable missing data. Each method is built on specific assumptions on the mechanism of missing data. We are interested in the magnitude of the bias and the robustness of mixed effects models, pattern mixture models, and selection models under various missing mechanisms. Simulations were performed that focused on the treatment effect, which is the primary interest of clinical trial studies. Simulation data were generated from 10 missing mechanisms that may occur in clinical trial studies. Both the point estimate and the variance of the estimate were calculated for each model. These analyses are the first we know to systematically evaluate and compare the mixed effects models, pattern mixture models, and selection models using simulation data.