4 (based on lowest level of article analyzed in meta-analysis/systematic review).

No abstract

The random effects model in meta-analysis is a standard statistical tool often used to analyze the effect sizes of the quantity of interest if there is heterogeneity between studies. In the special case considered here, meta-analytic data contain only the sample means in two treatment arms and the sample sizes, but no sample standard deviation. The statistical comparison between two arms for this case is not possible within the existing meta-analytic inference framework. Therefore, the main objective of this paper is to estimate the overall mean difference and associated variances, the between-study variance and the within-study variance, as specified as the important elements in the random effects model. These estimators are obtained using maximum likelihood estimation. The standard errors of the estimators and a quantification of the degree of heterogeneity are also investigated. A measure of heterogeneity is suggested which adjusts the original suggested measure of Higgins' I for within study sample size. The performance of the proposed estimators is evaluated using simulations. It can be concluded that all estimated means converged to their associated true parameter values, and its standard errors tended to be small if the number of the studies involved in the meta-analysis was large. The proposed estimators could be favorably applied in a meta-analysis on comparing two surgeries for asymptomatic congenital lung malformations in young children.

Statistical inference for analyzing the results from several independent studies on the same quantity of interest has been investigated frequently in recent decades. Typically, any meta-analytic inference requires that the quantity of interest is available from each study together with an estimate of its variability. The current work is motivated by a meta-analysis on comparing two treatments (thoracoscopic and open) of congenital lung malformations in young children. Quantities of interest include continuous end-points such as length of operation or number of chest tube days. As studies only report mean values (and no standard errors or confidence intervals), the question arises how meta-analytic inference can be developed. We suggest two methods to estimate study-specific variances in such a meta-analysis, where only sample means and sample sizes are available in the treatment arms. A general likelihood ratio test is derived for testing equality of variances in two groups. By means of simulation studies, the bias and estimated standard error of the overall mean difference from both methodologies are evaluated and compared with two existing approaches: complete study analysis only and partial variance information. The performance of the test is evaluated in terms of type I error. Additionally, we illustrate these methods in the meta-analysis on comparing thoracoscopic and open surgery for congenital lung malformations and in a meta-analysis on the change in renal function after kidney donation.

No abstract