U-shaped relationship

Encyclopedia of Research Design

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Salkind, Neil J.

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 胆固醇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 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.