There is currently conflicting evidence from longitudinal follow-up studies concerning the relation between mortality risk and disease risk factor at low levels or the risk factor. This applies to risk factors such as blood pressure, cholesterol, and body-mass index. In some studies, this relation was found to be positive. In others it was negative. This is an issue of importance to clinical and public-health policy, because a negative relation between mortality risk and blood pressure, for instance, implies that anithypertensive medication which lowers blood pressure below a critical threshold could be dangerous. It seemed likely that the conflict could be due to statistical confounding that artifactually elevates mortality risk at low risk-factor levels in survival analyses of longitudinal data. The present paper describes a crude analysis using data from the Framingham Offspring Study to test the idea that such statistical confounding could be caused by the decrease in risk factor with age among subjects near the end of the lifespan (referred to as late-life subjects). The analysis yielded evidence supporting this idea. on the basis of the findings it is hypothesized that: (1). the decrease in risk factor with age during late life causes the late-life bias. This bias distorts a positive relation between mortality risk and risk factor to appear U- or J-shaped in mixed-age adult follow-up cohorts; and (2). removal of the late-life and reverse-causation biases will show that this relation is monotonically positive.