Fixed and random-effects meta-analysis, with graphics -----------------------------------------------------
^meta^ { theta | exp(theta) } { se_theta | var_theta | ll ul [cl] } [^if^ exp] [^in^ range] [^,^ ^v^ar ^ci^ ^ef^orm ^pr^int ^eb^aye > s ^l^evel^(^#^)^ ^gr^aph^(f^|^r^|^e)^ ^id(^strvar^)^ ^fm^ult^(^#^)^ ^boxy^sca^(^ > #^)^ ^boxsh^ad^(^#^)^ ^cl^ine ^ltr^unc^(^#^)^ ^rtr^unc^(^#^)^]
Description -----------
^meta^ provides pooled estimates, confidence limits, and a test that the true pooled effect is zero, obtained from fixed and random effects meta-analysis, a test for heterogeneity between studies and an estimator of between studies variance, and, optionally, plots the individual and pooled estimates.
The user provides the effect estimate as ^theta^ (i.e., a log risk ratio, log odds ratio, or other measure of effect). Likewise, the user supplies a measure of theta's variability (i.e., its standard error, ^se_theta^, or its variance, ^var_theta^. Alternatively, the user provides ^exp(theta)^ (i.e., a risk ratio or odds ratio) and its confidence interval, ^(ll, ul)^).
If you have a dataset which contains data for all studies, then the @byvar@ command (STB-27) can be used to derive the effect estimates and standard errors for the individual studies. For example:
. ^sort study^ . ^byvar study, coef(group) se(group) generate:^ . ^quietly poisson cases group, e(pyrs)^ . ^sort study^ . ^qui by study: keep if _n==1^ . ^rename _C_1 logrr^ . ^rename _S_1 se^ . ^meta logrr se^
Alternatively, the @collapse@ or @for@ commands may be useful.
Options -------
^var^ means the user has specified a variable containing the variance of the effect estimate. If this option is not included, the command assumes the standard error has been specified.
^ci^ means the user has specified the lower and upper confidence limits of the effect estimate, which is assumed to be on the ratio scale (e.g. odds ratio or risk ratio).
^eform^ requests that the output is exponentiated. This is useful for effect measures such as log odds ratios which are derived from generalized linear models. If the ^eform^ and ^graph^ options are used, then the graph output is exponentiated, with a log scale for the x axis. If either the ^print^ or the ^ebayes^ option are used together with the ^eform^ option, the resulting empirical Bayes estimates are exponentiated.
^print^ requests that the weights used in the fixed and random effects estimation are listed for each study, together with the individual study estimates and confidence intervals. The studies are labelled by name if the ^id^ option is specified, or by number otherwise. If the ^ebayes^ option is specified, the study estimates and confidence intervals are empirical Bayes.
^ebayes^ creates two new variables in the dataset: ^ebest^ contains empirical Bayes estimate for each study, and ^ebse^ the corresponding standard errors. Any existing variables called ^ebest^ or ^ebse^ are overwritten. Empirical Bay > es estimates are calculated by shrinking the study-specific estimates towards the overall random effects estimate by a factor which depends on the relative magnitude of the estimated within and between study variances.
^level(^#^)^ specifies the level for the confidence intervals (default 95).
Options for graphing results ----------------------------
^graph(f^|^r^|^e)^ requests a graph. The options ^graph(f)^ or ^graph(r)^ request that the combined estimate in the graph is derived using fixed or random effects meta-analysis. The option ^graph(e)^ requests that empirical Bayes estimates of the individual study estimates be plotted. In this case, the combined estimate is the random-effects estimate, and the ^print^ and ^ebayes^ options are also automatically requested.
Graph options are allowed, except for ^ylabel()^, ^symbol()^, ^xlog^, ^ytick^ and ^gap^.
^id(^strvar^)^ is a character variable which is used to label the studies. If the data contains a labelled numeric variable then the @decode@ command can be used to create a character variable
^fmult(^#^)^ is a number greater than zero which can be used to scale the font size for the study labels. The font size is automatically reduced if the maximum label length is greater than 8, or the number of studies is greater than 20. However it may be possible to increase it somewhat over the default size.
^boxysca(^#^)^ provides a number ^#^ between zero and 1 which can be used to reduce the vertical length of the boxes. This is used to make boxes square if a vertical magnification of more than 100 has been used to increase the length of the graph. The default is 1.
^boxshad(^#^)^ provides an integer ^#^ between 0 and 4 which gives the box shad > ing (0 most, 4 no shading). The default is 0.
^cline^ asks that a vertical dotted line be drawn at the combined estimate.
^ltrunc(^#^)^ truncates the left side of the graph at ^#^. This is used to trun > cate very wide confidence intervals. However ^#^ must be less than each of the individual study estimates.
^rtrunc(^#^)^ truncates the right side of the graph at ^#^, and must be greater > than each of the individual study estimates.
Required input variables ------------------------
^theta^ the effect estimate ^se_theta^ the corresponding standard error
or
^theta^ the effect estimate ^var_theta^ the corresponding variance
or
^exp(theta)^ the risk (or odds) ratio ^ll^ the lower limit of the risk ratio's confidence interval ^ul^ the upper limit of the risk ratio's confidence interval [^cl^] optional (see below)
Optional input variable -----------------------
^cl^ contains the confidence level of the confidence interval defined by ^ll^ and ^ul^. If ^cl^ is not provided, the procedure assumes that each confidence interval is at the 95% confidence level. ^cl^ allows the user to provide the confidence level, by study, when the confidence interval is not at the default level. ^cl^ can be specified with or without a decimal point. For example, .90 and 90 are equivalent and may be mixed (i.e., 90, .95, 80, .90 etc.).
Examples --------
. ^meta logor selogor, eform gr(f) cline xline(1) id(trialnam) xlab^ . ^meta meandiff vardiff, var gr(r) eb print^ . ^meta rr ll ul, ci gr(e)^
Authors -------
Stephen Sharp London School of Hygiene and Tropical Medicine, UK email: stephen.sharp@@lshtm.ac.uk
Jonathan Sterne United Medical and Dental Schools, UK email: j.sterne@@umds.ac.uk
Also see --------
STB: STB-43 sbe16.2, STB-42 sbe16.1, STB-38 sbe16 On-line: help for @byvar@, @collapse@, @for@, @metareg@ (if installed), @metabias@ (if installed), @metacum@ (if installed)