Sas code and output

Variables treat = treatment (A,B,C), pat = patient number, dbp = diastolic blood pressure, dbp1 = baseline diastolic blood pressure, visit = visit number.

SAS code is given below for Model 6. Code for the other models is identical except that different REPEATED statements are used. These statements are given after the Model 6 output.

PROC MIXED NOCLPRINT; CLASS pat treat visit; MODEL dbp = dbp1 treat visit treat*visit/ DDFM=KR; REPEATED visit/ SUBJECT=pat TYPE=TOEP GROUP=treat R=1,3,4

RCORR=1,3,4; LSMEANS treat/ DIFF PDIFF CL;

ESTIMATE

'a-

b

v3'

treat

1

-1

0

treat*visit

1

0

0

0

-1

0

0

0

0

0

0

0;

ESTIMATE

'a-

c

v3'

treat

1

0

-1

treat*visit

1

0

0

0

0

0

0

0

-1

0

0

0;

ESTIMATE

>b-

c

v3'

treat

0

1

-1

treat*visit

0

0

0

0

1

0

0

0

-1

0

0

0;

ESTIMATE

'a-

b

v4'

treat

1

-1

0

treat*visit

0

1

0

0

0

-1

0

0

0

0

0

0;

ESTIMATE

'a-

c

v4'

treat

1

0

-1

treat*visit

0

1

0

0

0

0

0

0

0

-1

0

0;

ESTIMATE

>b-

c

v4'

treat

0

1

-1

treat*visit

0

0

0

0

0

1

0

0

0

-1

0

0;

ESTIMATE

'a-

b

v5'

treat

1

-1

0

treat*visit

0

0

1

0

0

0

-1

0

0

0

0

0;

ESTIMATE

'a-

c

v5'

treat

1

0

-1

treat*visit

0

0

1

0

0

0

0

0

0

0

-1

0;

ESTIMATE

>b-

c

v5'

treat

0

1

-1

treat*visit

0

0

0

0

0

0

1

0

0

0

-1

0;

ESTIMATE

'a-

b

v6'

treat

1

-1

0

treat*visit

0

0

0

1

0

0

0

-1

0

0

0

0;

ESTIMATE

'a-

c

v6'

treat

1

0

-1

treat*visit

0

0

0

1

0

0

0

0

0

0

0

-1;

ESTIMATE

>b-

c

v6'

treat

0

1

-1

treat*visit

0

0

0

0

0

0

0

1

0

0

0

-1;

The NOCLPRINT option suppresses the lengthy printing of patient categories. Use of the R and RCORR options displays the covariance parameters in a more meaningful way as matrices. If no subject numbers are specified, matrices for the first patient only will be printed. Here, we have requested matrices for patients 1, 3 and 4 so that a covariance and correlation matrix is printed for a patient on each treatment.

Iteration History

Iteration 0 1 2 3

Evaluations 1 2 1 1

-2 Res Log Like 7794.69107620 7424.25314231 7423.98385033 7423.98024667

Criterion

0.00009243 0.00000131 0.00000000

Convergence criteria met.

Estimated R

Matrix

for

pat 1

Row

Col1

Col2

Col3

Col4

1

76

.1169

52.

7624

46

.4925

35.

3745

2

52

.7624

76.

1169

52

.7624

46.

4925

3

46

.4925

52.

7624

76

.1169

52.

7624

4

35

.3745

46.

4925

52

.7624

76.

1169

Estimated R

Correlation Matrix for

pat 1

Row

Col1

Col2

Col3

Col4

1

1.0000

0.

6932

0.

6108

0.4647

2

0.6932

1.

0000

0.

6932

0.6108

3

0.6108

0.

6932

1.

0000

0.6932

4

0.4647

0.

6108

0.

6932

1.0000

Estimated R

Matrix

for

pat 3

Row

Col1

Col2

Col3

Col4

1

68

.2100

28.

9323

22

.4760

28.

6921

2

28

.9323

68.

2100

28

.9323

22.

4760

3

22

.4760

28.

9323

68

.2100

28.

9323

4

28

.6921

22.

4760

28

.9323

68.

2100

Estimated R Correlation Matrix for pat 3

Row Col1 Col2 Col3 Col4

1 1.0000 0.4242 0.3295 0.4206

2 0.4242 1.0000 0.4242 0.3295

3 0.3295 0.4242 1.0000 0.4242

4 0.4206 0.3295 0.4242 1.0000

Estimated R Matrix for pat 4

Row Col1 Col2 Col3 Col4

1 84.9809 49.5186 41.0737 42.2137

2 49.5186 84.9809 49.5186 41.0737

3 41.0737 49.5186 84.9809 49.5186

4 42.2137 41.0737 49.5186 84.9809

Estimated R Correlation Matrix for pat 4

Row Col1 Col2 Col3 Col4

1 1.0000 0.5827 0.4833 0.4967

2 0.5827 1.0000 0.5827 0.4833

3 0.4833 0.5827 1.0000 0.5827

4 0.4967 0.4833 0.5827 1.0000

Covariance Parameter Estimates

Cov Parm Subject Group Estimate

Variance

pat

treat

A

84.

. 9809

TOEP(2)

pat

treat

A

49.

5186

TOEP(3)

pat

treat

A

41.

0737

TOEP(4)

pat

treat

A

42.

2137

Variance

pat

treat

B

68.

2100

TOEP(2)

pat

treat

B

28.

9323

TOEP(3)

pat

treat

B

22.

4760

TOEP(4)

pat

treat

B

28.

6921

Variance

pat

treat

C

76.

1169

TOEP(2)

pat

treat

C

52.

7624

TOEP(3)

pat

treat

C

46.

4925

TOEP(4)

pat

treat

C

35.

-2 Res Log Likelihood 7424.0

AIC (smaller is better) 7448.0

AICC (smaller is better) 7448.3

BIC (smaller is better) 7491.9

Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq

Type III Tests of Fixed Effects

Num

Den

Effect

DF

DF

F Value

Pr > F

dbp1

1

285

28.73

<.0001

treat

2

187

4.04

0.0192

visit

3

437

12.41

<.0001

treat*visit

6

356

1.73

0.1130

Estimates

Standard

Label

Estimate

Error

DF

t Value

Pr

> |t|

a-b,

, v3

1

.3578

1

.2598

426

1.

08

0.

2817

a-c,

, v3

3

.4212

1

.2866

367

2.

66

0.

0082

b-c,

, v3

2

.0634

1

.2426

390

1.

66

0.

0976

a-b,

, v4

0

.5557

1

.2789

439

0.

43

0.

6641

a-c,

v4

1

.8917

1

.3002

377

1.

45

0.

1465

b-c,

v4

1

.3360

1

.2481

393

1.

07

0.

2851

a-b,

v5

3

.0026

1

.3081

456

2.

30

0.

0222

a-c,

v5

4

.7694

1

.3221

390

3.

61

0.

0003

b-c,

v5

1

.7668

1

.2592

400

1.

40

0.

1614

a-b,

v6

0.

08613

1

.3316

470

0.

06

0.

9485

a-c,

v6

2

.0957

1

.3397

399

1.

56

0.

1185

b-c,

v6

2

.0096

1

.2745

410

1.

58

0.

1156

Least Squares Means

Effect treat treat treat

Least Squares Means treat Estimate

92.7437 91.4931 89.6992

Standard Error

0.7595 0.6404 0.7631

93.3

122.11 142.87 117.55

treat treat treat

Effect treat treat treat

Least Squares Means treat Lower

91.2361 90.2215 88.1840

Upper

94.2513 92.7648 91.2144

Differences of Least Squares Means

Effect treat treat Estimate

1.2506 3.0445 1.7939

Standard Error

0.9945 1.0759 0.9975

186 191 181

0.2102 0.0052 0.0738

Effect treat treat treat

Differences of Least Squares Means treat treat Lower

Upper

3.2126 5.1667 3.7623

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