1. Orlistat for Fat Absorption
Nonlinear Regression
Orlistat for Fat Absorption
Zhi, J., Melia, A.T., Guericiolini, R. et al. (1994) “Retrospective Population-Based Analysis of the Dose-Response (Fecal Fat Excretion) Relationship of Orlistat in Normal and Obese Volunteers,” Clinical Pharmacology and Therapeutics, 56:82-85

2. Data Description
163 Patients assigned to one of the following doses (mg/day) of orlistat: 0, 60,120,150,240,300,480,600,1200
Response measured was fecal fat excretion (purpose is to inhibit fat absorption, so higher levels of response are considered favorable)
Plot of raw data displays a generally increasing but nonlinear pattern and large amount of variation across subjects

4. Nonlinear Regression Model
Simple Maximum Effect (Emax) model:
b0 ≡ Mean Response at Dose 0
b1 ≡ Maximal Effect of Orlistat (b0+ b1 = Maximum Mean Response)
b2 ≡ Dose providing 50% of maximal effect (ED50)

5. Nonlinear Least Squares

6. Nonlinear Least Squares

7. Nonlinear Least Squares

8. Estimated Variance-Covariance Matrix

9. Orlistat Example Reasonable Starting Values:
b0: Mean of 0 Dose Group: 5
b1: Difference between highest mean and dose 0 mean: 33-5=28
b2: Dose with mean halfway between 5 and 33: 160
Create Vectors Y and f (b0)
Generate matrix F (b0)
Obtain first “new” estimate of b
Continue to Convergence

10. Orlistat Example – Iteration History (Tolerance = .0001)

12. Variance Estimates/Confidence Intervals
Parameter
Estimate
Std. Error
95% CI b0
6.12
1.08
(3.96 , 8.28) b1
27.62
3.48
(20.66 , 34.58) b2
124.7
47.31
(30.08 , )

13. SAS Code Proc nlin; Parms b0=5 b1=28 b2=160;
Model y = b0 + ((b1*x)/(b2+x));
Der.b0 = 1;
Der.b1 = x/(b2+x);
Der.b2 = -((b1*x)/((b2+x)**2));
Run;