## Model

SAS code

PROC GENMOD; CLASS centre treat;

MODEL cf/one=cf1 treat/ DIST=B COVB TYPE3 WALD;

The GENMOD Procedure Model Information

Data Set WORK.B

Distribution Binomial

Response Variable (Events) cf

Response Variable (Trials) one

Number of Observations Read 283

Number of Observations Used 283

Number of Events 41

Number of Trials 283

Class centre treat

Class Level Information

Levels Values

Parameter Information Parameter Effect treat

Prm1 Prm2 Prm3 Prm4 Prm5

Intercept cf1

treat treat treat

Criteria For Assessing Goodness Of Fit

Criterion

DF

Value

Value/DF

Deviance

279

178.1744

0.

6386

Scaled Deviance

279

178.1744

0.

6386

Pearson Chi-Square

279

282.4176

1.

0122

Scaled Pearson X2

279

282.4176

1.

0122

Log Likelihood

-89.0872

The deviance and Pearson chi-square are measures of model fit and have similar roles to the residual sum of squares in normal data models. The Pearson chi-square is the sum of squared Pearson residuals (see above) and the deviance is calculated as 2 log(Ly/Lm). Ly is the maximum likelihood achievable if all available DF were used (usually this is obtained when u = y,) and Lm is the likelihood for the model fitted.

Estimated Covariance Matrix

Prm1 Prm2 Prm3 Prm4

Prm1 0.26581 -0.06973 -0.24923 -0.25407

Prm2 -0.06973 0.23598 0.01363 0.03002

Prm3 -0.24923 0.01363 0.35992 0.24694

Prm4 -0.25407 0.03002 0.24694 0.32686

TheCOVBoptionhascausedthecovariancematrixforthefixedeffects(intercept, cf1, treat A and treat B)tobeprinted.

Analysis Of Parameter Estimates

Standard Wald 95% Chi-

 Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 -3. 3532 0.5156 -4. 3637 -2. 3427 42. 30 < .0001 cf1 1 2. 9697 0.4858 2. 0176 3. 9218 37. 37 < .0001 treat A 1 0. 9361 0.5999 -0. 2397 2. 1120 2. 43 0 .1187 treat B 1 1. 7043 0.5717 0. 5837 2. 8248 8. 89 0 .0029 treat C 0 0. 0000 0.0000 0. 0000 0. 0000 Scale 0 1. 0000 0.0000 1. 0000 1. 0000

NOTE: The scale parameter was held fixed.

Wald Statistics For Type 3 Analysis Chi-

Source DF Square Pr > ChiSq cf1 1 37.37 <.0001

treat 2 9.60 0.0082

Contrast Estimate Results

Standard Chi-

Label Estimate Error Alpha Confidence Limits Square Pr > ChiSq

Asymptotic chi-squared tests are performed for each fixed effects parameter. These tests should be interpreted cautiously in small datasets.