Option Option Description Assumed conditions that might lead to deviations from fully informed weighted meta-analyses
1) Complete-case meta-analysis Omits incompletely reported effect sizes due to which grand mean estimates are expected to exhibit lower precision, i.e. larger confidence intervals. Missing values are not MCAR.
2) Unweighted meta-analysis Assigns equal weights to all effect sizes (with reported SSs), disregarding the differences in their precision. Effect sizes are related to effect size precision.
3) Sample-size-weighted meta-analysis Calculates approximate effect size weights (eqn 1). Not applicable for Hedges’ d, whose calculation is based on SSs (see Supplement S3). Effect sizes are related to the unaccounted SDs in the log response ratio and Hedges’ d.
Imputation of missing values Imputation of missing values Imputation of missing values
4) Mean value imputation Fills missing values with the mean of the reported ones and thereby keeps the weights of the completely reported effect sizes. Missing values are outside the range of the reported values and/or not MCAR.
5) Median value imputation Fills missing values with the median of the reported ones and might be more suitable than mean value imputation if SDs or SSs follow a skewed distribution. Missing values are outside the range of the reported values and/or not MCAR.
Multivariate imputation by chained equations (with the R-package used) Multivariate imputation by chained equations (with the R-package used)
The following imputation techniques are applied multiple times to yield separate imputed data sets with separate grand mean estimates which are pooled to obtain meta-analysis estimates that incorporate the uncertainty in the imputed values (illustrated in Fig. 2). Thereby, SDs and SSs with missing values were treated as dependent variables. SDs and SSs with complete data as well as mean values and correlation coefficients were treated as predictor variables.
The following imputation techniques are applied multiple times to yield separate imputed data sets with separate grand mean estimates which are pooled to obtain meta-analysis estimates that incorporate the uncertainty in the imputed values (illustrated in Fig. 2). Thereby, SDs and SSs with missing values were treated as dependent variables. SDs and SSs with complete data as well as mean values and correlation coefficients were treated as predictor variables.
6) mice: Random sample Fills missing values via randomly selecting one of the reported ones. Missing values are outside the range of the reported values and/or not MCAR.
7) mice: Linear regression Fills missing values with predictions that are obtained from linear models. Missing values are MNAR.
8) mice: Predictive mean matching Estimates linear models and fills missing values with those reported values that are closest to the predictions. Imputed values are thereby restricted to a subset of the reported ones. Missing values are outside the range of the reported values and/or MNAR.
9) mice: Classification and regression trees Implements a machine-learning algorithm that seeks cutting points in the set of supplied predictor variables in order to divide the meta-analysis dataset into homogenous subsamples. Fills missing values with random samples from the reported values that are assigned to the same subgroup as the predictions ones. Like predictive mean matching, imputed values are thereby restricted to a subset of the reported ones. Missing values are outside the range of the reported values and/or MNAR