Biostatistical approaches for modeling U-shaped dose-response curves and study design considerations in assessing the biological effects of low doses

The demonstration of hormetic effects is rendered difficult for a number of reasons: The spontaneous rate must be large enough for a difference to be detectable. In contrast with detrimental effects, there is a limited range of doses over which beneficial effects are likely to be found. Publication bias hampers publication of low-dose beneficial effects and discourages research in the area. Some scientists actually believe that hormetic effects are contary to reason. All these factors contribute to lessen the chances of detecting hormetic effects through synthesis of the scientific literature. The extra statistical power obtained from mathematical modeling is not available for hormetic studies when appropriate models are not available. Even a simple statistical device such as a test for linear trend does not work well for U-shaped data. The first part of this two-part chapter deals with the probabilities of determining qualitatively what kinds of health effects may result from exposures to substances, and the second part with characterizing quantitative relationships between such health effects and exposures. The health effects may be beneficial in some situations, and detrimental in others