### 16.4.5 Methods for incorporating cross-over trials into a meta-analysis

Unfortunately, the reporting of cross-over trials has been very variable, and the data required to include a paired analysis in a meta-analysis are often not published. A common situation is that means and standard deviations (or standard errors) are available only for measurements on E and C separately. A simple approach to incorporating cross-over trials in a meta-analysis is thus to take all measurements from intervention E periods and all measurements from intervention C periods and analyse these as if the trial were a parallel group trial of E versus C. This approach gives rise to a unit-of-analysis error (see Chapter 9, Section 9.3) and should be avoided unless it can be demonstrated that the results approximate those from a paired analysis, as described in Section 16.4.4. The reason for this is that confidence intervals are likely to be too wide, and the trial will receive too little weight, with the possible consequence of disguising clinically important heterogeneity. Nevertheless, this incorrect analysis is conservative, in that studies are under-weighted rather than over-weighted. While some argue against the inclusion of cross-over trials in this way, the unit-of-analysis error might be regarded as less serious than some other types of unit-of-analysis error.

A second approach to incorporating cross-over trials is to include only data from the first period. This might be appropriate if carry-over is thought to be a problem, or if a cross-over design is considered inappropriate for other reasons. However, it is possible that available data from first periods constitute a biased subset of all first period data. This is because reporting of first period data may be dependent on the trialists having found statistically significant carry-over.

A third approach to incorporating inappropriately reported cross-over trials is to attempt to approximate a paired analysis, by imputing missing standard deviations. We address this approach in detail in Section 16.4.6.

Cross-over trials with dichotomous outcomes require more complicated methods and consultation with a statistician is recommended (Elbourne 2002).