Repeated Measures Regression in Laboratory, Clinical and Environmental Research: Common Misconceptions in the Matter of Different Within- and Between-Subject Slopes

Abstract

When using repeated measures linear regression models to make causal inference in laboratory, clinical and environmental research, it is typically assumed that the within-subject association of differences (or changes) in predictor variable values across replicates is the same as the between-subject association of differences in those predictor variable values. However, this is often false. For example, with body weight as the predictor variable and blood cholesterol (which increases with higher body fat) as the outcome: (i) a 10-lb. weight increase in the same adult affects more greatly an increase in cholesterol in that adult than does (ii) one adult weighing 10 lbs. more than a second indicate higher cholesterol in the heavier adult. A 10-lb. weight gain in the first adult more likely reflects a build-up of body fat in that person, while a second person being 10 lbs. heavier than the first could be influenced by other factors, such as the second person being taller. Hence, to make causal inferences, different within- and between-subject slopes should be separately modeled. A related misconception commonly made using generalized estimation equations (GEE) and mixed models on repeated measures (i.e., for fitting cross-sectional regression) is that the working correlation structure only influences variance of the parameter estimates. However, only independence working correlation guarantees that the modeled parameters have interpretability. We illustrate this with an example where changing the working correlation from independence to equicorrelation qualitatively biases parameters of GEE models and show that this happens because within- and between-subject slopes for the outcomes regressed on the predictor variables differ. We then systematically describe several common mechanisms that cause within- and between-subject slopes to differ: change effects, lag/reverse-lag and spillover causality, shared within-subject measurement bias or confounding, and predictor variable measurement error. The misconceptions we describe should be better publicized. Repeated measures analyses should compare within- and between-subject slopes of predictors and when they do differ, investigate the causal reasons for this.