Note a minimum of 5 dose points is required to fit a 4PL model.
and
where y is the response and x is the log (dose), for the reference standard and the test sample respectively.
is proportional to the slope at the midpoint.
If > 0: is the left asymptote
is the right asymptote
If < 0: is the right asymptote
is the left asymptote
is the log (dose) corresponding to the midpoint between and
ε is an error term with distribution N(0,1) so σi ε is the error with distribution N(0, σi2), for i = Ref or Test.
QuBAS allows the user to select the ‘orientation’ of the model by choosing whether the left asymptote should be A or D. The four possible situations are:
A Left upper A left lower A right upper A right lower
For the parallel fit, = , = and the variance, σ2, is common to all dose groups.