Are you regressing to the mean?** #StatSpeak #MSBlog #MSResearch**

*"To understand research outputs and the research process you need to have an understanding of statistics and how we use them. Today we discuss the concept of regression to the mean. Regression means a return to a former state. So if you are having a relapse the likelihood is you will return to a former state of being in remission rather than going onto have another relapse. This is a big problem in clinical trials as we select study subjects based on recent MS activity (relapses or active MRI scans) in the hope that will continue to be more active. What we always see is a return to a state with less activity; i.e. fewer relapse or fewer MRI new lesions. This is why when we do power calculations we need to assume that regression to the mean will occur." *

The following is typical statistician speak:

In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement and, paradoxically, if it is extreme on its second measurement, it will tend to have been closer to the average on its first. To avoid making incorrect inferences, regression toward the mean must be considered when designing scientific experiments and interpreting data, as people more likely to volunteer for trials may be doing worse at the time of volunteering.

*"Another real life example is if two very tall people who have children, the children will be on average relatively shorter than them due to regression to the mean. Please note this is an average effect and does not apply to all individuals; hence you will have many exceptions to this rule. You may be interested to know that the natalizumab in SPMS trial (ASCEND TRIAL) has selected SPMSers based on recent evidence of progression. Regression to the mean would indicate that they are less likely to progress in the trial compared to their clinical course before the trial. Let's hope the statisticians who designed this trial included regression to the mean in their power calculations. It would be a travesty if the ASCEND trial showed a trend, but was not positive as it was underpowered due to a failure to include regression to the mean in the initial power calculations?" *

*"In our PROXIMUS trial we are selecting SPMSers based on a raised spinal fluid neurofilament level. We have made an assumption that levels will drop by 30% in the placebo arm due to regression to the mean. Why 30%? Thirty percent is a typical figure for regression to the mean in relation to other MS activity markers. Let's hope we are correct; we may me not."*

Stellmann et al. Regression to the Mean and Predictors of MRI Disease Activity in RRMS Placebo Cohorts - Is There a Place for Baseline-to-Treatment Studies in MS? PLoS One. 2015;10(2):e0116559.

**BACKGROUND**: Gadolinium-enhancing (GD+) lesions and T2 lesions are MRI outcomes for phase-2 treatment trials in RRMS. Little is known about predictors of lesion development and regression-to-the-mean, which is an important aspect in early baseline-to-treatment trials.

**OBJECTIVES**: To quantify regression-to-the-mean and identify predictors of MRI lesion development in placebo cohorts.

**METHODS**: 21 Phase-2 and Phase-3 trials were identified by a systematic literature research. Meta-analyses were performed to estimate development of T2 and GD+ after 6 months (phase-2) or 2 years (phase-3).

**RESULTS**: The mean number of GD+-lesions per scan was similar after 6 months (1.19, 95%CI: 0.87-1.51) and 2 years (1.19, 95%CI: 1.00-1.39). 39% of the patients were without new T2-lesion after 6 month and 19% after 2 years (95%CI: 12-25%). Mean number of baseline GD+-lesions was the best predictor for new lesions after 6 months.

**CONCLUSION**: Baseline GD-enhancing lesions predict evolution of Gd- and T2 lesions after 6 months and might be used to control for regression to the mean effects. Overall, proof-of-concept studies with a baseline to treatment design have to face a regression to 1.2 GD+lesions per scan within 6 months.