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. 
- Very low BMD values obtained by extrapolation between
0 and the smallest non null tested dose, 
that correspond to very sensitive items (that we do not want to exclude),
are thresholded at "minBMD", a parameter by default fixed at the smallest non null 
tested dose divided by 100 (considered as a negligible dose).

-- 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}