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A spline for the time
  1. Joel Schwartz
  1. Correspondence to Joel Schwartz, Harvard School of Public Health, 401 Park Drive, P.O. Box 15677, Suite 415L West, Boston 02215, USA; jschwrtz{at}

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‘Nowhere in the Bible does God say the Laws of Nature must be linear’ Enrico Fermi

Indeed, it seems almost necessary that some nonlinearities exist. Most biological processes are under feedback control, for example, which generally implies nonlinearity. The limitation of probabilities to range between zero and one essentially implies S shaped curves. So nonlinear relations seem a fact of life. Of course any continuous curve is well approximated by a straight line within a neighbourhood. Hence, if the effect is not too large, and the range of exposure is likewise limited, linear dose-response relations can be observed even when the underlying phenomenon is not linear.

When epidemiologists primarily dealt with exposure variables such as whether or not one got one's drinking water from the Southwark and Vauxhall water company, such issues hardly mattered. Today, one is more likely to be examining a continuous predictor, such as the role of blood pressure or low-density lipoprotein (LDL) cholesterol in predicting myocardial infarctions (MIs). How should these predictors be handled?

A reasonable first question is does it matter? The answer is clearly yes. Public health interventions must be lined to the shape of the dose-response curve to be effective. For example, figure 1 shows a penalised cubic spline curve I fit to model the difference from expected birth weight in 400 000 live births in Massachusetts versus the number of …

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