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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 ...

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