#### 9.4.5.3 Meta-analysis of skewed data

Analyses based on means are appropriate for data that are at least approximately normally distributed, and for data from very large trials. If the true distribution of outcomes is asymmetrical then the data are said to be skewed. Skew can sometimes be diagnosed from the means and standard deviations of the outcomes. A rough check is available, but it is only valid if a lowest or highest possible value for an outcome is known to exist. Thus the check may be used for outcomes such as weight, volume and blood concentrations, which have lowest possible values of 0, or for scale outcomes with minimum or maximum scores, but it may not be appropriate for change from baseline measures. The check involves calculating the observed mean minus the lowest possible value (or the highest possible value minus the observed mean), and dividing this by the standard deviation. A ratio less than 2 suggests skew (Altman 1996). If the ratio is less than 1 there is strong evidence of a skewed distribution.

Transformation of the original outcome data may substantially reduce skew. Reports of trials may present results on a transformed scale, usually a log scale. Collection of appropriate data summaries from the trialists, or acquisition of individual patient data, is currently the approach of choice. Appropriate data summaries and analysis strategies for the individual patient data will depend on the situation. Consultation with a knowledgeable statistician is advised.

Where data have been analysed on a log scale, results are commonly presented as geometric means and ratios of geometric means. A meta-analysis may be then performed on the scale of the log-transformed data; an example of the calculation of the required means and standard deviation is given in Chapter 7 (Section 7.7.3.4). This approach depends on being able to obtain transformed data for all studies; methods for transforming from one scale to the other are available (Higgins 2008a). Log-transformed and untransformed data can not be mixed in a meta-analysis.