Best (but oft-forgotten) practices: identifying and accounting for regression to the mean in nutrition and obesity research

Abstract

Background: Regression to the mean (RTM) is a statistical phenomenon where initial measurements of a variable in a nonrandom sample at the extreme ends of a distribution tend to be closer to the mean upon a second measurement. Unfortunately, failing to account for the effects of RTM can lead to incorrect conclusions on the observed mean difference between the 2 repeated measurements in a nonrandom sample that is preferentially selected for deviating from the population mean of the measured variable in a particular direction. Study designs that are susceptible to misattributing RTM as intervention effects have been prevalent in nutrition and obesity research. This field often conducts secondary analyses of existing intervention data or evaluates intervention effects in those most at risk (i.e., those with observations at the extreme ends of a distribution).

Objectives: To provide best practices to avoid unsubstantiated conclusions as a result of ignoring RTM in nutrition and obesity research.

Methods: We outlined best practices for identifying whether RTM is likely to be leading to biased inferences, using a flowchart that is available as a web-based app at https://dustyturner.shinyapps.io/DecisionTreeMeanRegression/. We also provided multiple methods to quantify the degree of RTM.

Results: Investigators can adjust analyses to include the RTM effect, thereby plausibly removing its biasing influence on estimating the true intervention effect.

Conclusions: The identification of RTM and implementation of proper statistical practices will help advance the field by improving scientific rigor and the accuracy of conclusions. This trial was registered at clinicaltrials.gov as NCT00427193.

Keywords: nutrition and obesity research; regression to the mean; statistical errors; treatment effect; unsupported conclusions.

Published by Oxford University Press on behalf of the American Society for Nutrition 2019.

Figures

FIGURE 1

Distribution of control population weights in the Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy Phase 2 (CALERIE 2) study at baseline, with second measurements at baseline, 1 y, and 2 y. The control participants in the first baseline measurement were color coded by location: blue for 1 SD above the mean, red for 1 SD below the mean, and green for within 1 SD of the mean. The location of participants in subsequent measurements can be tracked. We found that the blue-coded participants moved down toward the mean, and the red-coded participants moved up toward the mean, visually demonstrating the effect of regression to the mean.

FIGURE 2

(A) Decision tree for assessing whether RTM leads to unsubstantiated conclusions above intervention effects. (B) The path is highlighted in the decision tree that follows the analysis performed in reference . RTM, regression to the mean.

FIGURE 3

The graph shows the fathers’ heights (cm) on the ordinate and the sons’ heights on the abscissa from Galton's study (7). The tallest fathers had shorter sons and, likewise, the shortest sons had taller fathers. The deviation of the line of regression from the line of identity reflects the degree of regression to the mean (RTM).