U-Shaped Curve

The U-shaped curve usually refers to the nonlinear relationship between two variables, in particular, a dependent and an independent variable. Because many analytic methods assume an underlying linear relationship, systematic deviation from linearity can lead to bias in estimation. Meaningful U-shaped relationships can be found in epidemiology (e.g., between risk factor and disease outcome or mortality), psychology (often age-related developments, such as delinquency or marital happiness), and economics (e.g., short-run cost curves between the variate cost and quantity).

In medicine, U-shaped risk curves have been found for risk factors such as cholesterol level, diastolic blood pressure, work stress, and alcohol use. Of these factors, the alleged U-shape relationship between alcohol use and disease risk has been the most controversial. By the 1920s, a U.S. study by Raymond Pearl already showed a depressed longevity for abstainers. At that time, with alcohol prohibition in effect, this was not a politically correct message. Many years later, better controlled cohort studies looking into what Alvan R. Feinstein in his Science article called the “menace of daily life” have also reported lowest risk estimates for light or moderate drinkers of alcoholic beverages. Heavier drinkers are at highest risk, as could be expected. However, abstainers or non-drinkers in general also are found to have a higher [Page 1587]risk for several negative health outcomes. This effect has been observed for overall mortality and specific categories such as cardiovascular diseases. For the latter, some studies report a J-shape rather than a U-shape, with little increased risk at higher consumption levels. Generally, the risk is estimated to be approximately 20% higher for abstainers, as shown in Figure 1 by Giovanni Corrao and colleagues.

Figure 1 Example of U- or J-Shaped Curve Between Alcohol Intake and Risk for Coronary Heart Disease

Source: Corrao, G., Rubbiati, L., Bagnardi, V., Zambon, A., & Poikolainen, K. (2000). Alcohol and coronary heart disease: A meta-analysis. Addiction, 95, 1505–1523.

During the last 20 years, as results from more and more cohort studies have been accumulating, the J-shaped risk curve has been considered to be the aggregate result of several biological processes underlying the most prevalent of pathologies in the Western world, coronary heart disease. For some diseases or bodily processes, any alcohol has an outright negative effect. Alcohol has been found to raise blood pressure even in small amounts, which in turn is a risk factor for cardiovascular disease. However, alcohol has a proven negative effect on the formation of thrombi or blood clots, which in itself is considered a risk factor for ischemic diseases (heart attack, brain infarctions). A major third process is the positive effect of alcohol use on the high-density cholesterol (HDL) level in the blood, which is considered to be a protective factor in the genesis of arterial plaques, eventually obstructing blood flow to vital tissues of heart or brain. Across the years, several other biological processes and genetic vulnerability factors have been suggested as potential candidates for the explanation of the lower risk for moderate drinkers of alcohol. The message of a potential beneficial health effect of alcohol use has caused considerable debate, as alcohol use at higher intake levels may be considered a serious health hazard. The detrimental effects of alcohol are less disputed, with monotonically increasing risk for outcomes such as injuries, liver functions, liver cirrhosis, and certain forms of cancer (e.g., breast cancer).

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