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Estimation in meta-analyses of mean difference and standardized mean difference.

ABSTRACT: Methods for random-effects meta-analysis require an estimate of the between-study variance, ?² . The performance of estimators of ?² (measured by bias and coverage) affects their usefulness in assessing heterogeneity of study-level effects and also the performance of related estimators of the overall effect. However, as we show, the performance of the methods varies widely among effect measures. For the effect measures mean difference (MD) and standardized MD (SMD), we use improved effect-measure-specific approximations to the expected value of Q for both MD and SMD to introduce two new methods of point estimation of ?² for MD (Welch-type and corrected DerSimonian-Laird) and one WT interval method. We also introduce one point estimator and one interval estimator for ?² in SMD. Extensive simulations compare our methods with four point estimators of ?² (the popular methods of DerSimonian-Laird, restricted maximum likelihood, and Mandel and Paule, and the less-familiar method of Jackson) and four interval estimators for ?² (profile likelihood, Q-profile, Biggerstaff and Jackson, and Jackson). We also study related point and interval estimators of the overall effect, including an estimator whose weights use only study-level sample sizes. We provide measure-specific recommendations from our comprehensive simulation study and discuss an example.

SUBMITTER: Bakbergenuly I

PROVIDER: S-EPMC6916299 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature

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Estimation in meta-analyses of mean difference and standardized mean difference.

Bakbergenuly Ilyas I Hoaglin David C DC Kulinskaya Elena E

Statistics in medicine 20191111 2

Methods for random-effects meta-analysis require an estimate of the between-study variance, τ<sup>2</sup> . The performance of estimators of τ<sup>2</sup> (measured by bias and coverage) affects their usefulness in assessing heterogeneity of study-level effects and also the performance of related estimators of the overall effect. However, as we show, the performance of the methods varies widely among effect measures. For the effect measures mean difference (MD) and standardized MD (SMD), we use ...[more]

PMID: 31709582

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Project description:BackgroundAdvantages of meta-analysis depend on the assumptions underlying the statistical procedures used being met. One of the main assumptions that is usually taken for granted is the normality underlying the population of true effects in a random-effects model, even though the available evidence suggests that this assumption is often not met. This paper examines how 21 frequentist and 24 Bayesian methods, including several novel procedures, for computing a point estimate of the heterogeneity parameter ([Formula: see text]) perform when the distribution of random effects departs from normality compared to normal scenarios in meta-analysis of standardized mean differences.MethodsA Monte Carlo simulation was carried out using the R software, generating data for meta-analyses using the standardized mean difference. The simulation factors were the number and average sample size of primary studies, the amount of heterogeneity, as well as the shape of the random-effects distribution. The point estimators were compared in terms of absolute bias and variance, although results regarding mean squared error were also discussed.ResultsAlthough not all the estimators were affected to the same extent, there was a general tendency to obtain lower and more variable [Formula: see text] estimates as the random-effects distribution departed from normality. However, the estimators ranking in terms of their absolute bias and variance did not change: Those estimators that obtained lower bias also showed greater variance. Finally, a large number and sample size of primary studies acted as a bias-protective factor against a lack of normality for several procedures, whereas only a high number of studies was a variance-protective factor for most of the estimators analyzed.ConclusionsAlthough the estimation and inference of the combined effect have proven to be sufficiently robust, our work highlights the role that the deviation from normality may be playing in the meta-analytic conclusions from the simulation results and the numerical examples included in this work. With the aim to exercise caution in the interpretation of the results obtained from random-effects models, the tau2() R function is made available for obtaining the range of [Formula: see text] values computed from the 45 estimators analyzed in this work, as well as to assess how the pooled effect, its confidence and prediction intervals vary according to the estimator chosen.

Dataset Information

Estimation in meta-analyses of mean difference and standardized mean difference.

Publications

Estimation in meta-analyses of mean difference and standardized mean difference.

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