In Model C we took account of the fact that there may be an underlying difference in DBP between the centres. We did so in such a way that the effect of a patient being in a particular centre would be additive to the effect of treatment. Another possibility is that the response of patients to treatments may vary between the centres. That is, the effects of centre and treatment are non-additive, or that there is an interaction. For example, in any multi-centre trial, if some centres tended to have more severely ill patients, it is plausible that the reaction of these patients to the treatments would differ from that of patients at other centres who are less severely ill. We can take this possibility into account in the model by allowing the treatment effects to vary between the centres. This is achieved by adding a centre-treatment interaction to Model C. It causes a separate set of treatment effects to be fitted for each centre.
DBPi = ¡1 + b ■ pre + tk + Cj + (ct)jk + et, where
(ct)jk = the kth treatment effect at the jth centre.
Throughout this book we will refer to such interactions using the notation 'centre-treatment'. When Model D is fitted, the first question of interest is whether the centre-treatment effect is statistically significant. If the interaction term is significant, then we have evidence that the treatment effect differs between the centres. It will then be inadvisable to report the overall treatment effect across the centres. Results will need to be reported for each centre. If the interaction is not significant, centre-treatment may be removed from the model and the results from Model C reported. Further discussion on centre-treatment interactions appears in Chapter 5.
As we will see in more detail in Section 2.5, the centre-treatment effect is nonsignificant for our data (p = 0.19) and the results of Model C can be presented. Centre effects are statistically significant in Model C (p = 0.004), so this model will be preferred to Model B.
From our data, b is estimated as 0.22 with a standard error of 0.11. Thus, if the baseline DBPs of two patients receiving the same treatment differ by 10 mmHg, we can expect that their final DBPs will differ by only 2.2 mmHg (0.22 x 10), as illustrated in Figure 1.1. The relationship is therefore weak and hence we can anticipate that the analysis of covariance approach will be preferable to a simple analysis of change in DBP. In fact, the statistical significance of the treatment differences is p = 0.054 using the analysis of covariance, compared with p = 0.072 for the analysis of change.
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