Analysing outcome variables with floor effects due to censoring: a simulation study with longitudinal trial data

Abstract

ackground: Randomised controlled trials (RCTs) are the gold standard to estimate treatment effects. When patients receive effective treatment over time they may reach the limit of a certain measurement scale. This phenomenon is known as censoring and lead to skewed distributions of the outcome variable with an excess of either low (floor effect) or high values (ceiling effect). Applying traditional methods such as linear mixed models to analyse this kind of longitudinal RCT data may result in bias of the regression parameters. To deal with floor effects due to censoring,  a tobit mixed model can be used. The objective of this study was to compare the results of longitudinal linear mixed model analyses with longitudinal tobit mixed model analyses.Methods: First, a simulation study was performed in which several situations of RCTs with floor effects were simulated. Second, data from an empirical RCT was analysed with both methods.Results: Although all analyses underestimated the intervention effects, the tobit mixed model performed much better than the linear mixed model in handling floor effects. However, with an increasing number of follow-up measurements in combination with a strong floor effect estimates from the tobit mixed model were also not accurate.Conclusion: tobit mixed model analysis should be used to estimate treatments effects in longitudinal RCTs with floor effects due to censoring.