Fit A Five-Parameter Logistic Function

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Fit A Five-Parameter Logistic Function

In their paper "A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies," James H. Ricketts and Geoffrey A. Head develop a 5-parameter logistic (sigmoidal) function to model heart rate as a function of blood pressure. They call this model "Baro5".

The five parameters that define the function are:
P1 = asymptotic minimum
P2 = asymptotic maximum
P3 = slope parameter
P4 = value at inflection point
p5 = slope parameter

Here are the NLREG statements to fit this function:

Title "Five-parameter Logistic Function (Baro5)";
Variables BP, HR;
Parameters p1=50, p2=200, p3=-0.5, p4=85, p5=-0.5;
Double c, f, g, h;
c = 2*p3*p5/abs(p3+p5);
f = 1/(1+exp(-c*(p4-BP)));
g = exp(p3*(p4-BP));
h = exp(p5*(p4-BP));
Function HR = p1+(p2/(1+f*g+(1-f)*h));
Plot xvar=BP, xlabel="Blood Pressure", ylabel="Heart Rate";
Data;
[ data goes here ]

Here is a plot generated by NLREG showing the Baro5 function fitted to a a set of values.