Random Coefficients Model with PROC MIXED

The script begins by creating a dataset named 'rc' via a DATA step with in-line data (datalines). This data simulates a pharmaceutical stability study with batches (Batch) and measurements (Y) taken at different months (Month). Subsequently, two MIXED procedures are executed. The first fits a linear regression model with random coefficients (intercept and 'Month' slope) for each batch. The second explores a model variation by including an additional class variable 'Monthc'.

Data Analysis

Type : CREATION_INTERNE

The data is generated directly within the script using a DATA step and DATALINES statement. The 'rc' dataset is created in memory for the SAS session.

1 Code Block

DATA STEP Data

Explanation :
This DATA block creates the 'rc' table. It reads the 'Batch' and 'Month' variables, then uses a 'do' loop to read up to 6 'Y' values for each initial record. For each 'Y' value read, a new observation is generated. The 'Monthc' variable is created as a copy of 'Month'. Data is provided in-line via 'datalines'.

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1	DATA rc;
2	INPUT Batch Month @;
3	Monthc = Month;
4	DO i = 1 to 6;
5	INPUT Y @;
6	OUTPUT;
7	END;
8	DATALINES;
9	1 0 101.2 103.3 103.3 102.1 104.4 102.4
10	1 1 98.8 99.4 99.7 99.5 . .
11	1 3 98.4 99.0 97.3 99.8 . .
12	1 6 101.5 100.2 101.7 102.7 . .
13	1 9 96.3 97.2 97.2 96.3 . .
14	1 12 97.3 97.9 96.8 97.7 97.7 96.7
15	2 0 102.6 102.7 102.4 102.1 102.9 102.6
16	2 1 99.1 99.0 99.9 100.6 . .
17	2 3 105.7 103.3 103.4 104.0 . .
18	2 6 101.3 101.5 100.9 101.4 . .
19	2 9 94.1 96.5 97.2 95.6 . .
20	2 12 93.1 92.8 95.4 92.2 92.2 93.0
21	3 0 105.1 103.9 106.1 104.1 103.7 104.6
22	3 1 102.2 102.0 100.8 99.8 . .
23	3 3 101.2 101.8 100.8 102.6 . .
24	3 6 101.1 102.0 100.1 100.2 . .
25	3 9 100.9 99.5 102.2 100.8 . .
26	3 12 97.8 98.3 96.9 98.4 96.9 96.5
27	;
28

2 Code Block

PROC MIXED

Explanation :
This procedure fits a mixed model to the 'rc' data. 'Batch' is defined as a classification variable. The 'model' statement specifies 'Y' as the dependent variable and 'Month' as a fixed effect. The 'random' statement defines random intercept ('Int') and slope ('Month') for each 'Batch' level, with an unstructured covariance structure ('type=un'). The 's' option requests the display of solutions for fixed and random effects.

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1	PROC MIXED DATA=rc;
2	class Batch;
3	model Y = Month / s;
4	random Int Month / type=un sub=Batch s;
5	RUN;

3 Code Block

PROC MIXED

Explanation :
A second PROC MIXED analysis is performed, adding 'Monthc' to the list of classification variables. The fixed model remains the same. The 'random' statement is modified to include 'Monthc' as a random effect in addition to the intercept and 'Month', still grouped by 'Batch'. This allows exploring a different random model structure.

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1	PROC MIXED DATA=rc;
2	class Batch Monthc;
3	model Y = Month / s;
4	random Int Month Monthc / sub=Batch s;
5	RUN;

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