Question

Assignment 2

 

ü  You are encouraged to work in groups (maximum 3) on homework.

ü  For each part below, please provide the MATLAB code you implemented.

ü  Do not submit the homework solutions from previous years (The data are different).

 

Dose-Response Modeling (100 points)

Suppose that you work for a pharmaceutical company and you are supposed to assess the efficacy and potency of two drugs (Agent A and Agent B) before allowing the agents to proceed to clinical trials. You performed a preliminary experiment to get an overall idea and obtained the following data.

 

 

Dose(mg/kg)	% Response (Agent A)	% Response (Agent B)
1	9	6
10	48	30
60	83	59
100	89	74
200	93	77
450	95	78
600	97	80
850	96	79
1000	98	85

 

You decided to model the dose-response relationship using a three-parameter Hill Model taking a value of 1 for the Hill coefficient as given below.

 

 

 

 

 

a)      Using only one of the MATLAB functions lsqcurvefit and fitnlm perform a nonlinear regression. What are the optimal values for  and  for each drug?

b)      Linearize the Hill Equation using Lineweaver-Burk method. Using the linearized form of the function and the data given above compute the  value and the maximum effect () for each drug. Are the values exactly the same as those you computed in (a). Explain.

c)      Plot separately the fitted curve and the fitted line that you computed in (a) and (b), together with the data used. What do you observe?

d)      Compute  for both (a) and (b). Which fit seems to be better?

e)      Considering the definitions below, compare the efficacy and potency of the drugs. Which one would you prefer and why?

Efficacy: maximum effect that a drug can produce regardless of dose.

Potency: amount of a drug that is needed to produce a given effect (e.g, for instance ).