The fixed effect estimates were as follows:

Effect |
Estimate |
Empirical SE |
Model-based SE |

Intercept 1 |
-0.32 |
0.56 |
0.52 |

2 |
1.95 |
0.50 |
0.42 |

3 |
4.67 |
0.65 |
0.61 |

Baseline |
-0.078 |
0.01 |
0.01 |

Treatment |
-0.81 |
0.35 |
0.35 |

Visit 1 |
-0.34 |
0.31 |
0.26 |

Visit 2 |
-0.64 |
0.37 |
0.26 |

Visit 3 |
0.29 |
0.36 |
0.25 |

The three intercept terms (arising from the three possible partitions of the four categories) and the visit terms are of little interest. The large size of the baseline term relative to its standard error indicates that the model has benefited from its inclusion. The overall treatment effect is significant (p = 0.02). This differs from the GLMM analysis and appears to indicate that the analysis of the categorised attack rate is more sensitive. This is likely to be because there are three extremely large values (> 60 attacks) in the active treatment group compared with only one in the placebo group. In the GLMM analysis these will have a large effect on the variance of the treatment effects, whereas this does not occur in the categorical analysis since they are grouped with other values above 10. Similarly, they will have a reduced influence on the estimated magnitude of the treatment effect.

The coefficient for the treatment effect is difficult to interpret directly, but by exponentiation we can calculate an odds ratio in an analogous way to Section 3.3.4 where GLMMs were considered. In this case, exp(-0.81) = 0.44 and this is the estimate of the odds ratio for the probability of a 'favourable' outcome on placebo compared with active treatment, whether 'favourable' is defined as 0 attacks, <3 attacks, or <10 attacks. Note that the odds ratio from this model is defined in terms of a 'favourable' outcome, whereas in the GLMM it is in terms of the rate of epilepsy attacks. Note also that it is an inherent assumption of this model that the same odds ratio applies to every partition between the categories. The 95% confidence intervals can be calculated as before from exp(-0.81 ± t57,0.975 x 0.35) = exp(-0.81 ± 2.00 x 0.35) = (0.22, 0.90). (Note that these use a t distribution with the patient DF of 57 as used in the GLMM.)

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