Analysis of Response Profiles of data on Blood Lead Levels

Treatment of Lead Exposed Children (TLC) Trial

The Mixed Procedure

Model Information
Data Set	WORK.TLC
Dependent Variable	y
Covariance Structure	Unstructured
Subject Effect	id
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Between-Within

Class Level Information
Class	Levels	Values
id	100	not printed
group	2	P A
time	4	0 1 4 6

Dimensions
Covariance Parameters	10
Columns in X	15
Columns in Z	0
Subjects	100
Max Obs Per Subject	4
Observations Used	400
Observations Not Used	0
Total Observations	400

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	2626.25517748
1	1	2416.07594087	0.00000000

Convergence criteria met.

Estimated R Matrix for id 1
Row	Col1	Col2	Col3	Col4
1	25.2257	19.1074	19.6995	22.2016
2	19.1074	44.3458	35.5351	29.6750
3	19.6995	35.5351	47.3778	30.6205
4	22.2016	29.6750	30.6205	58.6510

Fit Statistics
-2 Res Log Likelihood	2416.1
AIC (smaller is better)	2436.1
AICC (smaller is better)	2436.7
BIC (smaller is better)	2462.1

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
group	1	98	25.43	25.43	<.0001	<.0001
Time	3	98	184.48	61.49	<.0001	<.0001
group*time	3	98	107.79	35.93	<.0001	<.0001

Note: In the “Solution for Fixed Effects” the default indicator variable coding is not the most natural for a categorical variable denoting the occasions of measurement; for the latter, the “first” level of the factor (the baseline measurement occasions) is a more natural reference group.

Similarly, the placebo group might be regarded as a more natural reference group for treatment comparisons.

Solution for Fixed Effects
Effect	group	time	Estimate	Standard Error	DF	t Value	Pr > |t|
Intercept			20.7620	1.0831	98	19.17	<.0001
Group	P		2.8840	1.5317	98	1.88	0.0627
Group	A		0	.	.	.	.
Time		0	5.7780	0.8885	98	6.50	<.0001
Time		1	-7.2400	0.9343	98	-7.75	<.0001
Time		4	-5.2480	0.9464	98	-5.54	<.0001
Time		6	0	.	.	.	.
Group*time	P	0	-3.1520	1.2566	98	-2.51	0.0138
Group*time	P	1	8.2540	1.3213	98	6.25	<.0001
Group*time	P	4	5.6720	1.3385	98	4.24	<.0001
Group*time	P	6	0	.	.	.	.
Group*time	A	0	0	.	.	.	.
Group*time	A	1	0	.	.	.	.
Group*time	A	4	0	.	.	.	.
Group*time	A	6	0	.	.	.	.

The default coding can be changed with the inclusion of the ORDER=option in the PROC MIXED statement. For example, the ORDER=DATA option forces the levels of all variables included in the CLASS statement to be sorted by their order of appearance in the input data set. Therefore, by previously sorting the data set in descending order of a categorical variable denoting the occasions of measurement, a more natural reference group coding is obtained for that variable (with the lowest, rather than the highest, level of the categorical variable for time used as the reference). This produces the following output for the “Solution for Fixed Effects” :

Solution for Fixed Effects
Effect	group	time	Estimate	Standard Error	DF	t Value	Pr > |t|
Intercept			26.2720	0.7103	98	36.99	<.0001
group	A		0.2680	1.0045	98	0.27	0.7902
group	P		0	.	.	.	.
time		6	-2.6260	0.8885	98	-2.96	0.0039
time		4	-2.2020	0.8149	98	-2.70	0.0081
time		1	-1.6120	0.7919	98	-2.04	0.0445
time		0	0	.	.	.	.
group*time	A	6	-3.1520	1.2566	98	-2.51	0.0138
group*time	A	4	-8.8240	1.1525	98	-7.66	<.0001
group*time	A	1	-11.4060	1.1199	98	-10.18	<.0001
group*time	A	0	0	.	.	.	.
group*time	P	6	0	.	.	.	.
group*time	P	4	0	.	.	.	.
group*time	P	1	0	.	.	.	.
group*time	P	0	0	.	.	.	.

Note: one unappealing consequence of circumventing the default coding of time in this way is that the estimates of the covariance matrix are printed in reverse (or descending) order of time. To avoid potential confusion when extracting the estimates of the covariance matrix, it is advisable to re-run the analysis without the ORDER=DATA option.