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4PL model

 
  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.
        and