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Title

metaan-- Module for performing fixed- or random-effects meta-analyses

Syntax

metaanvarname1varname2[if] [in] [,options]where

varvame1the study effect sizes.

varvame2the study effect variation, with standard error used as default.

optionsDescription ------------------------------------------------------------------------- OptionsfeFixed-effect modeldlDerSimonian-Laird random-effects modelmlMaximum likelihood random-effects modelremlRestricted maximum likelihood random-effects modelplProfile likelihood random-effects modelpePermutations random-effects modelvarcVariances provided instead of the standard errors/deviationslabel(varname)Study label variable(s)forestForest plotforestw(#)Forest plot with adjusted weight ratiosplplot(string)Likelihood plot for the mu or tau^2 estimate in the maximum-likelihood models (ml, pl, reml)

DescriptionThe

metaancommand performs a meta-analysis on a set of studies and calculates the overall effect and a confidence interval for the effect. The command also displays various heterogeneity measures: Cochrane's Q, I-squared (0-100% with larger scores indicating heterogenity) , H-squared (zero in the case of homogeneity) and the between-study variance estimate. Cochrane's Q is the same across all methods, but the between-study variance estimate (and hence I-squared and H-squared) can vary between thedlandmlmethods. Only one method option must be selected. For calculating the effects and variance of the effects, for a group of studies, from various statistical parameters please see metaeff.

Options+-------+ ----+ Model +------------------------------------------------------------

feFixed-model that assumes there is no heterogeneity between the studies. The model assumes that within-study variances may differ, but that there is homogeneity of effect size across allstudies. Often the homogeneity assumption is unlikely and variation in the true effect across studies is to be expected. Therefore, caution is required when using this model. Reported heterogeneity measures are estimated using thedlmodel.

dlDerSimonian-Laird, the most commonly used random-effects model. Models heterogeneity between the studies i.e. assumes that the true effect can be different for each study. The method assumes that the individual study true effects are distributed with a variance tau^2, around an "overall" true effect, but makes no assumptions about the form of the distribution of either the within- or between-study effects. Reported heterogeneity measures are estimated using thedlmodel.

mlMaximum likelihood random-effects model. Makes the additional assumption (necessary to derive the log-likelihood function, and also true forremlandplbelow) that both the within-study and between-study effects have Normal distributions. It solves the log-likelihood function iteratively to produce an estimate of the between-study variance. However, the method does not always converge while in some cases the between-study variance estimate is negative and set to zero (in which case the model is reduced to thefemodel). Estimates are reported as missing in the event of non-convergence. Reported heterogeneity measures are estimated using themlmodel.

remlRestricted maximum-likelihood random-effects model. Similar method tomland using the same assumptions. The log-likelihood function is maximized iteratively to provide estimates as inml. However, underremlonly the part of the likelihood function which is location invariant is maximized (i.e. maximizing the portion of the likelihood that does not involve mu, if estimating tau^2, and vice versa). The method does not always converge while in some cases the between-study variance estimate is negative and set to zero (in which case the model is reduced to thefemodel). Estimates are reported as missing in the event of non-convergence. Reported heterogeneity measures are estimated using theremlmodel.

plProfile likelihood random-effects model. Profile likelihood uses the same likelihood function asml, but takes into account the uncertainty associated with the between-study variance estimate when calculating an overall effect, by using nested iterations to converge to an maximum. The confidence intervals provided by the method are asymmetric and hence so is the the diamond in the forest plot. However, the method does not always converge. Values that were not computed are reported as missing. Reported heterogeneity measures are estimated using themlmodel (the effect and tau^2 estimates are the same, only the confidence interevals are re-estimated) but also provides a confidence interval for the between-study variance estimate.

pePermutations random-effects model. A non-parametric random-effects method, which can be described in three steps. First, in line with a Null hypothesis that all true study effects are zero and observed effects are due to random variation, a dataset of all possible combinations of observed study outcomes is created by permuting the sign of each observed effect. Then thedlmethod is used to compute an overall effect for each combination. Finally, the resulting distribution of overall effect sizes is used to derive a confidence interval for the observed overall effect. The confidence interval provided by the method is asymmetric and hence so is the diamond in the forest plot. Reported heterogeneity measures are estimated using thedlmodel.+----------------------+ ----+ Variable information +---------------------------------------------

varcInforms the program that the study effect variation variable (varname2) holds variance values. If this option is omitted the program assumes the variable contains standard error values (the default)

label(varname)Selects labels for the studies. Up to two variables can be selected and converted to strings. If two variables are selected they will be separated by a comma. Usually, the author names and the year of study are selected as labels. The final string is truncated to 20 characters.+-------+ ----+ Graph +------------------------------------------------------------

Only one graph output is allowed in each execution

forestRequests a forest plot. The weights from the specified analysis are used for plotting symbol sizes ({opth pe} uses {opth dl} weights).

forestw(#)Requests a forest plot with adjusted weight ratios for better display. The value can be in the [1,50] range. For example if the largest to smallest weight ratio is 60 and the graph looks awkward the user can use this command to improve the appearance, by requesting the weight to be rescaled to a largest/smallest weight ratio of 30. It should be noted that only the weight squares in the plot are affected and not the model. The confidence intervals in the plot are unaffected.

plplot(string)Requests a plot of the likelihood function for the mu or tau^2 estimates of theml,plorremlmodels. Optionplplot(mu)fixes mu to its model estimate, in the likelihood function, and creates a two way plot of tau^2 vs the likelihood function. Optionplplot(tsq)fixes tau^2 to its model estimate, in the likelihood function, and creates a two way plot of mu vs the likelihood function.

RemarksFor a detailed description of the methods see Brockwell & Gorndon (methods

fe,dl,pl,ml) and Follmann & Proschan (pe). Method performance investigated by Kontopantelis & Reeves and Brockwell & Gorndon.

Examples

. metaan eff SEeff, ml

. metaan eff SEeff, pl forest

. metaan eff effvar, varc pe

. metaan eff effvar, varc fe forestw(20)

AuthorsEvangelos Kontopantelis, National Primary Care Research and Development Centre,

University of Manchester, e.kontopantelis@manchester.ac.uk

David Reeves, Health Sciences Primary Care Research Group, University of Manchester

ReferencesBrockwell, S.E. and Gordon I.R. 2001.

A Comparison of StatisticalMethods for Meta-Analysis. Statistics in Medicine.Follmann, D.A. and Proschan M.A. 1999.

Valid Inference in Random EffectsMeta-Analysis. Biometrics.Higgins, J.P. and Thompson S.G. 2002.

Quantifying Heterogeneity in aMeta-Analysis. Statistics in Medicine.Mittlbock, M. and Heinzl H. 2006.

A Simulation Study ComparingProperties of Heterogeneity Measures in Meta-Analyses. Statistics in Medicine.Kontopantelis, E. and Reeves D. 2009.

A Meta-Analysis add-in forMicrosoft Excel. Journal of Statistical Software.Kontopantelis, E. and Reeves D. 2009.

The Robustness of StatisticalMethods for Meta-Analysis when Study Effects are Non-NormallyDistributed: A Simulation Study. Submitted.

Also seeSTB: STB-44 sbe24

help for metaeff, metan7 (if installed)

metannt (if installed), meta (if installed)

metacum (if installed), metareg (if installed)

metabias (if installed), metatrim (if installed)

metainf (if installed), galbr (if installed)

metafunnel (if installed)