Continuous bounded outcome data are unlikely to meet the usual assumptions for mixed-effects models of normally distributed and independent subject-specific and residual random effects. Additionally, overly complicated model structures might be necessary to account adequately for non-drug (time-dependent) and drug treatment effects. A transformation strategy with a likelihood component for censoring is developed to promote the simplicity of model structures and to improve the plausibility of assumptions on the random effects. The approach is motivated by Health Assessment Questionnaire Disability Index (HAQ-DI) data from a study in subjects with rheumatoid arthritis and is evaluated using a simulation study. Copyright © 2011 John Wiley & Sons, Ltd.