## Fixed versus random effect model

The examples discussed in Section 11.5.7 use the fixed effect model, which is the most straightforward and easiest to understand method of analysis. However, some would argue that a random effect model is a more appropriate way to analyse the data. In the simplest fixed effect model the contribution of each trial to the combined estimate is proportional to the amount of information in it. Weighting each trial by its variance is intuitively appealing. However, in this approach only within-trial variability is considered and no allowance is made for any between-trial variability. Random effect models explicitly allow for between-trial variability by weighting trials using a combination of their own variance and the between-trial variance.

Where there is little between-trial variability, the within-trial variance will dominate and the random effect weighting will tend towards the fixed effect weighting. If, however, there is significant between-trial variability, this will dominate the weighting factor and within-trial variability will contribute little towards the weighting factor. In this way all trials will tend towards contributing equally towards the overall estimate and small trials may unduly influence the results. There are strong proponents of both approaches. Those in favour of the random effect model argue that it formally allows for between-trial variability, and that the fixed effect approach unrealistically assumes a single effect across all trials and thus can give over-precise estimates. Those in favour of the fixed effect approach argue that the random effect model is using a statistical model to address a clinical problem. In particular, it gives no insight into the source of between-trial variability. In practice, it is common to find that the estimates from the two approaches are similar, but in the presence of statistical heterogeneity the confidence interval for the random effects estimate will be much wider than the confidence interval for the fixed effect estimate. Whichever model or approach is adopted, the aim should always be to minimize obvious sources of heterogeneity by carefully specifying questions and not combining obviously heterogeneous trials within a comparison, so that it becomes almost irrelevant which model is used.

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