Regression to the mean

Bibliographic information

Kamerman PR, Vollert J. Greater baseline pain inclusion criteria in clinical trials increases regression to the mean effect: a modelling study.

Abstract

We used statistical modelling to assess the effects of pain intensity inclusion thresholds (3/10, 4/10, and 5/10 on an 11-point NRS) on the magnitude of the regression to the mean effect under conditions that were consistent with the sample mean and variance, and inter-measurement correlation observed in clinical trials for the management of chronic pain. All data were modelled on a hypothetical placebo control group. We found a progressive increase in the mean pain intensity as the pain inclusion threshold increased, but this increase was not uniform, having an increasing effect on baseline measurements compared to study endpoint measurements as the threshold was increased. That is, the regression to the mean effect was magnified by increasing inclusion thresholds. Further, the effect increasing pain inclusion thresholds had on the regression to the mean effect was increased by decreasing sample means at baseline and inter-measurement correlations, and increasing sample variance. At its smallest the regression to the mean effect was 0.13/10 (95% CI: 0.03/10 to 0.24/10; threshold: 3/10, baseline mean pain: 6.5/10, standard deviation: 1.6/10, correlation: 0.44) and at its greatest it was 0.78/10 (95% CI: 0.63/10 to 0.94/10; threshold: 5/10, baseline mean pain: 6/10, standard deviation: 1.8/10, correlation: 0.19). We have shown that using pain inclusion thresholds in clinical trials drives progressively larger regression to the mean effects. We believe that a threshold of 3/10, offers the best compromise between maintaining assay sensitivity (the goal of thresholds) and the size of the regression to the mean effect.

Reproducibility

For reproducibility we have built a docker image with the environment used to run the scripts:
kamermanpr/regression-to-the-mean

Using Docker to run the scripts

You need to have docker installed on your computer. To do so, go to docker.com and follow the instructions for installing Docker for your operating system. Once Docker has been installed, follow the steps below, noting that Docker commands are entered in a terminal window (Linux and OSX/macOS) or command prompt window (Windows).

Download the latest image

Enter: docker pull kamermanpr/regression-to-the-mean:v1.6

Run the container

Enter: docker run --name pain_regression -d -p 8787:8787 -e USER=user -e PASSWORD=password kamermanpr/regression-to-the-mean:v1.6

Login to RStudio Server

• Open a web browser window and navigate to: localhost:8787

• Use the following login credentials:

  • Username: user
  • Password: password

Upload repository

• Go to the regression-to-the-mean repository on GitHub and select Code and then Download ZIP.

• In the Files tab on the lower right panel of RStudio, click Upload, located the zip file you downloaded and the click OK. The zip file will be uploaded and will automatically unzip, giving you access to all the content, including the analysis scripts, for the project.

• Please note that because the output file is a PDF, the build will be slow because the required latex packages will need to be downloaded and installed (this is an automatic process, but it is slow).

Shutting down the container

• Once done, log out of RStudio and enter the following into a terminal to stop the Docker container: docker stop pain_regression.

• If you then want to remove the container, enter: docker rm pain_regression.

• If you also want to remove the Docker image you downloaded, enter: docker rmi kamermanpr/pain_regression:v1.6