PROC NLIN Example: Parameter Estimation for a Nonlinear Model

The script begins by creating a dataset named 'Enzyme' containing concentration and velocity data. Then, it executes PROC NLIN twice. The first execution uses the Marquardt method to estimate the parameters of a Michaelis-Menten model. The second execution of PROC NLIN uses the Newton method to estimate the parameters of a different exponential model.

Data Analysis

Type : CREATION_INTERNE

The 'Enzyme' data is created directly in the script via a DATA STEP instruction and DATALINES, simulating concentration and velocity observations for an enzymatic reaction.

1 Code Block

DATA STEP Data

Explanation :
This DATA STEP block creates a dataset named 'Enzyme'. It defines two variables, 'Concentration' and 'Velocity', and initializes them with values provided directly in the script via the DATALINES statement. This dataset will be used as input for the NLIN procedures.

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1	DATA Enzyme;
2	INPUT Concentration Velocity;
3	DATALINES;
4	0.26 124.7 0.30 126.9
5	0.48 135.9 0.50 137.6
6	0.54 139.6 0.68 141.1
7	0.82 142.8 1.14 147.6
8	1.28 149.8 1.38 149.4
9	1.80 153.9 2.30 152.5
10	2.44 154.5 2.48 154.7
11	;

2 Code Block

PROC NLIN

Explanation :
This NLIN procedure fits a nonlinear model to the 'Enzyme' data using the Marquardt optimization method. It estimates the parameters 'theta1' and 'theta2' for the Michaelis-Menten model: `Velocity = theta1*Concentration / (theta2 + Concentration)`. The `hougaard` option is used to calculate Hougaard's skewness measures.

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1	PROC NLIN DATA=Enzyme method=marquardt hougaard;
2	parms theta1=155
3	theta2=0 to 0.07 BY 0.01;
4	model Velocity = theta1*Concentration / (theta2 + Concentration);
5	RUN;

3 Code Block

PROC NLIN

Explanation :
This second NLIN procedure fits a different nonlinear model to the same 'Enzyme' data, this time using the Newton optimization method. It estimates the parameters 'x1' and 'x2' for the exponential model: `Velocity = x1 * exp (x2 * Concentration)`. The `listcode` option displays the SAS source code for the model and its derivatives.

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1	PROC NLIN DATA=Enzyme method=newton listcode;
2	parms x1=4 x2=2;
3	model Velocity = x1 * exp (x2 * Concentration);
4	RUN;

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