When centre and centre-treatment effects are fitted as random, allowance is made for variability in the magnitude of the treatment effects between centres. However, deciding whether centre and centre-treatment effects should be fixed or random is often the subject of debate. In practice, the choice will depend on whether treatment estimates are to relate only to the set of centres used in the study or, more widely, to the circumstances and locations of which the trial centres can be regarded as a sample. In the former case, local treatment estimates for the sampled set of individual centres are obtained by fitting centre and centre-treatment effects as fixed. To obtain global treatment estimates, centre and centre-treatment effects should be fitted as random. When this is done the standard error of treatment differences is increased to reflect the heterogeneity of the treatment effects across centres.
If the centre-treatment term is omitted, there is a choice of whether to fit centre effects as fixed or random. Taking centre effects as random can increase the accuracy of treatment estimates, since information from the centre error stratum is used in addition to that from the residual stratum. Thus, it is nearly always beneficial to fit centres as random, regardless of whether a local or global interpretation is required. The amount of extra information will depend on the degree of treatment imbalance within the centres and the relative sizes of the variance components.
In the analysis of multi-centre trials it is important to check whether results from any particular centre are outlying. If this occurs it may be an indication that a centre has not followed the protocol correctly. In the fixed effects model, spurious outlying estimates caused by random variation may occur, particularly in small centres. In contrast, the shrunken estimates of centre and centre-treatment effects obtained by the random effects model do not have this problem.
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