  We consider the setting of an aggregate data meta-analysis of a continuous
outcome of interest. When the distribution of the outcome is skewed, it is
often the case that some primary studies report the sample mean and standard
deviation of the outcome and other studies report the sample median along with
the first and third quartiles and/or minimum and maximum values. To perform
meta-analysis in this context, a number of approaches have recently been
developed to impute the sample mean and standard deviation from studies
reporting medians. Then, standard meta-analytic approaches with
inverse-variance weighting are applied based on the (imputed) study-specific
sample means and standard deviations. In this paper, we illustrate how this
common practice can severely underestimate the within-study standard errors,
which results in overestimation of between-study heterogeneity in random
effects meta-analyses. We propose a straightforward bootstrap approach to
estimate the standard errors of the imputed sample means. Our simulation study
illustrates how the proposed approach can improve estimation of the
within-study standard errors and between-study heterogeneity. Moreover, we
apply the proposed approach in a meta-analysis to identify risk factors of a
severe course of COVID-19.
