Imputing standard deviations

Missing standard deviations are a common feature of meta-analyses of continuous outcome data. One approach to this problem is to impute standard deviations. Before imputing missing standard deviations however, authors should look carefully for statistics that allow calculation or estimation of the standard deviation (e.g. confidence intervals, standard errors, t values, P values, F values), as discussed in Chapter 7 (Section 7.7.3).


The simplest imputation is of a particular value borrowed from one or more other studies. Furukawa et al. found that imputing standard deviations either from other studies in the same meta-analysis, or from studies in another meta-analysis, yielded approximately correct results in two case studies (Furukawa 2006). If several candidate standard deviations are available, review authors would have to decide whether to use their average, the highest, a ‘reasonably high’ value, or some other strategy. For meta-analyses of mean differences, choosing a higher standard deviation down-weights a study and yields a wider confidence interval. However, for standardized mean difference meta-analyses, choice of an overly large standard deviation will bias the result towards a lack of effect. More complicated alternatives are available for making use of multiple candidate standard deviations. For example, Marinho et al. implemented a linear regression of log(standard deviation) on log(mean), because of a strong linear relationship between the two (Marinho 2003).


All imputation techniques involve making assumptions about unknown statistics, and it is best to avoid using them wherever possible. If the majority of studies in a meta-analysis have missing standard deviations, these values should not be imputed.  However, imputation may be reasonable for a small proportion of studies comprising a small proportion of the data if it enables them to be combined with other studies for which full data are available. Sensitivity analyses should be used to assess the impact of changing the assumptions made.