The two types of benchmark doses (BMD-zSD and BMD-xfold) proposed by 
the EFSA (2017) are computed for each responsive item using 
the best fit dose-reponse model previously obtained (see Larras et al. 2018 
for details).

- the BMD-xfold considers a x-fold change of the control response which makes 
it equivalent to a x% inhibition/enhancement concentration. The so-called 
BMD-xfold is calculated as the concentration corresponding to a Benchmark 
Response (BMR-xfold) defined as follows: BMR-xfold = y0 +/- y0*x/100, where y0 
is the mean control response and x is the percentage of change (x fixed at 10 
by default). The BMD-xfold is thus hazardously sensitive to the signal level : 
if the control response is low so will be the x-fold change.

- the BMD-zSD detects the concentration leading to a level of change compared 
to the control response that takes data variability of the modelled curve into 
account. It is calculated as the concentration corresponding to a Benchmark
Response (BMR-zSD) defined as follows: BMR-zSD = y0 +/- z*SD, where y0 is the 
mean control response, and SD is the residual standard deviation of the 
considered CRC and z is the factor of SD (z fixed at 1 by default).

We recommend the latter approach (BMD-zSD).

In cases where the BMD cannot be reached due to the asymptote at high doses, 
NaN is returned. In cases where the BMD is not reached at the highest tested 
dose, NA is returned.

-- REFERENCES --

EFSA Scientific Committee, Hardy A, Benford D, Halldorsson T, Jeger MJ, Knutsen KH,
... & Schlatter JR  (2017). Update: use of the benchmark dose approach in risk assessment.
EFSA Journal, 15(1), e04658.

Larras F, Billoir E, Baillard V, Siberchicot A, Scholz S, Wubet T, Tarkka M,
Schmitt-Jansen M and Delignette-Muller ML (2018). DRomics: a turnkey tool to support 
the use of the dose-response framework for omics data in ecological risk assessment. 
Environmental science & technology.\doi{10.1021/acs.est.8b04752}