Regression to the mean: Error reduction versus blood pressure normalization by sports training

We previously investigated 463 young people, aged 20.6+ 0.05 years, who enrolled in a one-year sports training programme (Chen et al., 2010). They were dichotomized into two groups: hypertensive (systolic blood pressure4 140 mmHg, n1⁄4 69) and normotensive (n1⁄4 394), based on clinical hypertensive criteria. In this cohort, we found that the blood pressure lowering effect of sports training was confined to the hypertensive group, which may account for the overall limited reduction in blood pressure observed in many previous intervention studies using subclinical participants. Atkinson and Taylor (2011) raise an important issue: to what extent was this finding influenced by the statistical artifact termed ‘‘regression to the mean’’. Regression to the mean can be caused by inherent error of measurement so that individuals who are initially measured to have extreme blood pressure are likely to record at follow up values that are closer to the population mean. As suggested by Atkinson and Taylor (2011), the ideal way to resolve this ambiguity is to include an additional control group that does not receive the intervention between baseline and followup measurements. Atkinson and Taylor also offered another tactic to decrease the effect of regression to the mean due to inherent error by taking several measurements of the outcome at baseline (Atkinson & Taylor, 2011; Barnett, van der Pols, & Donson, 2004). In longitudinal studies, error reduction after repeated measurements and true sample value normalizations after an intervention can co-exist. This is especially common in studies that involve beneficial interventions in complex regulatory systems aimed at reducing entropy (which occurs in most healthy living organisms). For example, linedrawing precision and motor control skills, composed of many loops of negative-feedback regulatory mechanisms, are generally improved over time by task-specific training or during maturation of the nervous system. In the metabolic systems that many exercise scientists are interested in, an asymmetric distribution of many metabolic outcome measures is commonly observed. For example, humans tend to maintain fasting blood glucose concentration in the range 70–90 mg dL, while extremely high glucose values are more common than extremely low glucose values as we age (Yashin et al., 2009), due to deterioration in the insulin signalling system (Lai, Chen, Chen, & Kuo, 2009). Lifestyle interventions are beneficial to individuals with high blood glucose concentrations, but are ineffective for those individuals who are within the normal glucose range (Schäfer et al., 2007). It is thus imperative to develop a statistical method to distinguish whether regression of metabolic measures to the population mean in a longitudinal study is contributed to by error reduction after the second measurement or true sample value normalization after the intervention. In interventional studies of the metabolic system, one way to measure the magnitude of regression to the mean caused by inherent error of measurement is to examine the symmetry of the regression trend over time on extreme samples (such as mean changes of the upper and lower 15% of samples) of initial measurements. In general, inherent error of measurement is less likely to have a preferential distribution towards over-estimation than under-estimation, and vice versa. Therefore, if we assume that inherent measurement error is the only contributor to regression to the mean over time, the absolute slope of sample value regression to the population mean from upper and lower extremes of initial measurement should be roughly equal. This means that the expected symmetry ratio of regression to the mean (SRTM) should be approximately equal to 1. The mathematical model for SRTM is detailed in the Appendix. In the example of our previous study (Chen et al., 2010), the absolute regression slopes of blood pressure to the mean form the high and low extremes (upper 15% and lower 15%) of the first measurement were 14.7+ 1.3 mmHg per year and 4.2+ 1.1 mmHg per year (P50.0001), which produced a symmetry ratio of *3.5. This result demonstrates that the regression trend of blood pressure values over a one-year training period is asymmetric, and is contributed, for the most part, by the interventional effect. Frequency distribution curves of samples at baseline and follow-up provide further detail in Figure 1. We concur with Atkinson and Taylor (2011) that regression to the mean, to some extent, may account Journal of Sports Sciences, March 15th 2011; 29(6): 645–647