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Janet Gray, Ph.D.
Janet Gray, Ph.D.

As author of our 2008 and 2010 State of the Evidence reports, Dr. Gray drives the science behind all our work.

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Non-monotonic Curves

In chemical safety testing, traditional toxicology and regulatory science assumes that higher doses will have a greater effect on health than low doses and that, in simple terms, the relationships will be fairly linear.

Using this logic, risk assessors test chemicals at high doses and statistically estimate the effects at low doses.


A linear dose-response relationship is a consistent straight line.

According to these models, whether truly linear or not, higher doses have greater effects, and the dose-response curve has a consistent slope, whether positive (left) or negative (right).

Yet this assumption of a consistent slope (positive or negative), called monotonicity, is inappropriate when studying endocrine disrupting compounds (EDCs). Instead, non-monotonicity, or changes in slope directions on dose-response curves might best be used as models for dose-response curves when studying EDCs. The examples below illustrate some of the different kinds of non-monotonic relationships between exposures and health effects.

A recent extensive review of the literature on EDCs (Vandenberg et al., 2012) concluded that non-monotonic dose-response curves “are not the exception, but should be expected and [are] perhaps even common” (p. 27).


Not all relationships between exposures and responses are linear.

Why does this matter? If dose-response curves are non-monotonic, meaning that the slopes of the dose-response curve can change over the range of doses of exposures, then it is not possible to predict low-dose effects by calculations based on higher-dose effects, as is the common practice at present. It also means that doses below those often studied in traditional toxicology studies cannot be assumed to be safe or to have no effect on the body (Vandenberg et al., 2012). 

This issue is critical in addressing the growing evidence showing low-dose effects of EDCs, especially at developmentally sensitive times. While non-monotonicity does not necessarily mean that biological responses occur at low doses, it does require valid experimentation to test whether such responses do occur (Vandenberg et al., 2012). Additionally, the finding of non-monotonic responses to environmental exposures has serious repercussions for current chemicals testing policy and practice.