Example Covariance Pattern Models For Count Data

This was a placebo-controlled trial of an anti-convulsant treatment for epilepsy involving 59 patients. The data are taken from Thall and Vail (1990). The number

Figure 6.2 Histograms of the number of epilepsy episodes by treatment group.

of epileptic seizures was counted over an eight-week period prior to treatment and then over four two-week periods following treatment. None of the patients dropped out of the study. A histogram of the number of epileptic episodes is shown in Figure 6.2 by treatment group. These show that many patients have few seizures, while a few have a large number. This distribution indicates that a Poisson error and a log link function may be appropriate. However, it is possible that the small number of very large frequencies will produce outlying residuals. Note that here an offset variable (see Section 3.1.2) is not needed because the trial periods are strictly two weeks long (it does not matter that the baseline period is longer - this is taken into account by the baseline effect estimate).

6.4.1 Analysis models

Models with several different covariance patterns are fitted. Baseline, treatment, visit and treatment-visit are fitted as fixed in all the models. Models 1-5 were fitted initially. The pattern for Model 6 was suggested by the results from these models.

Model

Covariance pattern

1

Compound symmetry

2

Separate compound symmetry for each treatment group

3

First-order autoregressive

4

Toeplitz

5

General

6

Separate general pattern for each treatment group

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