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#### 16.4.6.1 Mean differences

The point estimate of mean difference for a paired analysis is usually available, since it is the same as for a parallel group analysis (the mean of the differences is equal to the difference in means):

MD = ME – MC.

The standard error of the mean difference is obtained as .

where N is the number of participants in the trial, and SDdiff is the standard deviation of within-participant differences between E and C measurements. As indicated in Section 16.4.4, the standard error can also be obtained directly from a confidence interval for MD, from a paired t-statistic, or from the P value from a paired t-test. The quantities MD and SE(MD) may be entered into RevMan under the generic inverse-variance outcome type.

When the standard error is not available directly and the standard deviation of the differences is not presented, a simple approach is to impute the standard deviation, as is commonly done for other missing standard deviations (see Section 16.1.3). Other studies in the meta-analysis may present standard deviations of differences, and as long as the studies use the same measurement scale, it may be reasonable to borrow these from one study to another. As with all imputations, sensitivity analyses should be undertaken to assess the impact of the imputed data on the findings of the meta-analysis (see Section 16.1 and Chapter 9, Section 9.7).

If no information is available from any study on the standard deviations of the differences, imputation of standard deviations can be achieved by assuming a particular correlation coefficient. The correlation coefficient describes how similar the measurements on interventions E and C are within a participant, and is a number between –1 and 1. It may be expected to lie between 0 and 1 in the context of a cross-over trial, since a higher than average outcome for a participant while on E will tend to be associated with a higher than average outcome while on C. If the correlation coefficient is zero or negative, then there is no statistical benefit of using a cross-over design over using a parallel group design.

A common way of presenting results of a cross-over trial is as if the trial had been a parallel group trial, with standard deviations for each intervention separately (SDE and SDC; see Table 16.4.a). The desired standard deviation of the differences can be estimated using these intervention-specific standard deviations and an imputed correlation coefficient (Corr): .