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

Abstract

Background: 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 leads 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 these kind of longitudinal RCT data may result in bias of the regression coefficients. 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: A simulation study was performed in which several situations of RCTs with floor effects were simulated. From the simulated datasets, which were set up to estimate the interaction between treatment and time, the regression coefficient for this interaction and for the overall treatment effect were estimated. Additionally, data from an empirical RCT were analysed with both methods. Results: Regarding the interaction between treatment and time, the results of the tobit mixed model analysis were the same as the true values in all conditions, while the linear mixed model analysis revealed highly underestimated regression coefficients. However, the overall treatment effect with an increasing number of follow-up measurements in combination with a strong floor effect showed that the 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.