Non-monotonic dose-response curves


 
 
Dose response curves can come in several types.

 
  Linear, in which a unit increase in the dose produces a unit increase in the response. Linearity may be seen over a limited range of the response curve.
 
 

Non-linear, in which the shape of the relationship is curved.

 
  There are several types of non-linear relationships. Most non-linear curves are assumed to be monotonic. In monotonic curves, the direction of change does not reverse.
 
The curve is either increasing (or flat) or decreasing (or flat) across the full range of responses. It never increases then decreases.

 
Sometimes nonlinearity involves a threshold: beneath that level, there is no response.
 

 

Recently published results indicate that for endocrine disrupting chemicals, at least under certain conditions, there may be no threshold. In other words, any EDC contamination will change the response.

 
 

 
Sometimes nonlinearity involves an asymptote: once the dose reaches an asymptote, no additional amount has an effect on the response.

 
 

 
A non-monotonic dose-response curve is by definition a type of non-linear curve.
 

The crucial point is that the slope of the curve reverses sign somewhere along the curve. In other words, at some point it is increasing while at another it is decreasing.

Two simple non-monotonic patterns seen in dose-response curves are "U-shaped" and "inverted U-shaped" curves.