P

fP11

P12

P13

P14

0

0

P12

P22

P23

P24

0

0

P13

P23

P33

P34

0

0

P14

P24

P34

P44

0

0

0

0

0

0

P55

P12

0

0

0

0

P12

P66

where the Pii are the multinomial 'within-observation' correlation matrices and the Pmn give the correlations between observations on the same patient between visits m and n. The Pmn matrices obtained from Models 1-3 are shown in Table 4.4.

Statistical comparisons between the models using likelihood ratio tests were not readily available because quasi-likelihood values were not produced by the SAS

Model

Parti-1 tion 1

Table 4.4 Pmn correlation submatrices

Parti-

Visit separation = 1 Visit separation = 2 Visit separation = 3 (i.e.P12,P23,P34)_(i.e. Pi3, P24)_(i-e. P14)

Parti-

3 tion 123412341234

3 -0.10 -0.02 0.23 -0.10 -0.03 0.02 0.05 -0.03 -0.18

4 -0.20 -0.12 0.15 0.07 -0.06 -0.02 0.10 0.05 0.02 -0.03-0.07 0.35

macro. On informal examination, the positive diagonal terms in Pii matrix blocks for Models 2 and 3 indicate that the repeated observations on the same patient are correlated. Therefore, Model 1, which has zero correlations and assumes that the observations are independent, should be rejected. The banded pattern (Model 3) does not show marked differences between the correlations depending on visit separation. Therefore, we might choose to base our conclusions on Model 2 with a simpler covariance pattern.

Treatment effect estimates are shown with 'model-based' standard errors in Table 4.5. In Model 1, which naively assumes that the repeated observations are independent, the standard error estimates are noticeably smaller than for Models 2 and 3.

The overall treatment effects in Model 2 were highly significant (p = 0.0007). Cold feet were significantly more likely on treatment B than on treatment A (p = 0.03), and on treatment B than on treatment C (p = 0.0002). The coefficients for the treatment effects are difficult to interpret directly, but, as before, by exponentiation we can calculate odds ratios and 95% confidence intervals (Table 4.6). Confidence intervals are calculated using the 'model-based' standard errors and the z0.975 statistic. The exact DF for t statistics were not available from the SAS macro. However, the patient DF of over 300 can be taken as a conservative estimate and the t statistic is then well approximated by the z0.975 statistic.

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