Parametric and nonparametric methods for confidence intervals and sample size planning for win probability in parallel-group randomized trials with Likert item and Likert scale data

Data on the Likert scale are ubiquitous in medical research, including randomized trials. Statistical analysis of such data may be conducted using the means of raw scores or the rank information of the scores. In the context of parallel-group randomized trials, we quantify treatment effects by the probability that a subject in the treatment group has a better score than (or a win over) a subject in the control group. Asymptotic parametric and nonparametric confidence intervals for this win probability and associated sample size formulas are derived for studies with only follow-up scores, and those with both baseline and follow-up measurements. We assessed the performance of both the parametric and nonparametric approaches using simulation studies based on real studies with Likert item and Likert scale data. The simulation results demonstrate that even without baseline adjustment, the parametric methods did not perform well, in terms of bias, interval coverage percentage, balance of tail error, and assurance of achieving a pre-specified precision. In contrast, the nonparametric approach performed very well for both the unadjusted and adjusted win probability. We illustrate the methods with two examples: one using Likert item data and the other using Like scale data. We conclude that non-parametric methods are preferable for two-group randomization trials with Likert data. Illustrative SAS code for the nonparametric approach using existing procedures is provided.