Magnitude of the regression to the mean within one-year intra-individual changes in serum lipid levels among Japanese male workers

Assessing regression to the mean effects in health care initiatives

Background

Interventions targeting individuals classified as “high-risk” have become common-place in health care. High-risk may represent outlier values on utilization, cost, or clinical measures. Typically, such individuals are invited to participate in an intervention intended to reduce their level of risk, and after a period of time, a follow-up measurement is taken. However, individuals initially identified by their outlier values will likely have lower values on re-measurement in the absence of an intervention. This statistical phenomenon is known as “regression to the mean” (RTM) and often leads to an inaccurate conclusion that the intervention caused the effect. Concerns about RTM are rarely raised in connection with most health care interventions, and it is uncommon to find evaluators who estimate its effect. This may be due to lack of awareness, cognitive biases that may cause people to systematically misinterpret RTM effects by creating (erroneous) explanations to account for it, or by design.

Methods

In this paper, the author fully describes the RTM phenomenon, and tests the accuracy of the traditional approach in calculating RTM assuming normality, using normally distributed data from a Monte Carlo simulation and skewed data from a control group in a pre-post evaluation of a health intervention. Confidence intervals are generated around the traditional RTM calculation to provide more insight into the potential magnitude of the bias introduced by RTM. Finally, suggestions are offered for designing interventions and evaluations to mitigate the effects of RTM.

Results

On multivariate normal data, the calculated RTM estimates are identical to true estimates. As expected, when using skewed data the calculated method underestimated the true RTM effect. Confidence intervals provide helpful guidance on the magnitude of the RTM effect.

Conclusion

Decision-makers should always consider RTM to be a viable explanation of the observed change in an outcome in a pre-post study, and evaluators of health care initiatives should always take the appropriate steps to estimate the magnitude of the effect and control for it when possible. Regardless of the cause, failure to address RTM may result in wasteful pursuit of ineffective interventions, both at the organizational level and at the policy level.

Regression to the mean. A threat to exercise science?

Regression to the mean (RTM) can bias any investigation where the response to treatment is classified relative to initial values for a given variable without the use of an appropriate control group. The phenomenon and resulting errors of interpretation have been recognised by clinicians in a number of disciplines. The causes of RTM include both intra-individual variance and measurement error. The magnitude of RTM can be estimated quite simply, given a knowledge of intra- and inter-individual variance. RTM can be avoided by using a fully controlled experimental design. Difficulties can also be minimised by making duplicate measurements prior to the experimental manipulation, the first measurement serving for classification, and the second (with randomly distributed variance) allowing an assessment of the response to treatment. Less satisfactorily, surrogate measurements (for example, plasma volume for maximal oxygen intake [VO2(max)]) can assess the bias introduced by an initial non-random sorting of study participants. The impact of RTM on the design and interpretation of investigations has as yet received little consideration by exercise scientists and sports physicians. The response to training is often related to initial measurements of a dependent variable such as heart size, ST segmental depression, fitness or level of physical activity. In particular, analyses of this type have been adduced to support the belief that the response to aerobic training is inversely related to an individual's VO2(max). In fact, RTM may account for a major part of this apparent relationship.

Effect of five-year supplementation of vitamin C on serum vitamin C concentration and consumption of vegetables and fruits in middle-aged Japanese: a randomized controlled trial

OBJECTIVE

This study was aimed at evaluating the effect of long-term vitamin C supplementation on serum and dietary vitamin C and identifying the factors associated with change in serum concentration.

METHODS

A total of 439 subjects with atrophic gastritis initially participated in a randomized clinical trial using vitamin C and beta-carotene to prevent gastric cancer. We originally randomized the participants into four treatment groups using a 2x2 factorial design, whereby 0 or 15 mg/day beta-carotene and 50 or 500 mg/day vitamin C were administered in a double-blind manner. The beta-carotene component was terminated early after a mean treatment duration of four months. Before and upon early termination of beta-carotene supplementation, 134 subjects dropped out this trial, while 120 and 124 subjects took the vitamin C supplement at either 50 mg or 500 mg daily for five years.

RESULTS

Changes in serum vitamin C were significantly higher in the high-dose group (38.5% increase, 95% CI = 27.0-49.9) than in the low-dose group (13.0% increase, 5.1-20.9) or in the dropout group (3.3% increase, -2.1-8.6) after five-year supplementation. The serum vitamin C at baseline was negatively associated with changes in serum vitamin C (p < 0.0001), while high-dose (p < 0.0001) and low-dose (p < 0.05) supplementation and female gender (p < 0.001) were positively associated. Dietary intake of vitamin C in the supplementation group was almost identical before and after five-year supplementation of vitamin C (2.31 mg/day decrease, 95% CI = -15.3-10.7), while a 17.7 mg/day decrease (95% CI = -44.2-8.86) was observed in the drop-out group.

CONCLUSION

Five-year vitamin C supplementation induces a remarkable increase in serum vitamin C concentration, and our intervention program appears to have no effect on dietary vitamin C intake.