Tools for Those Who Summarize the Evidence Base
Resources and networking for those who conduct or interpret meta-analyses related to any phenomenon that is gauged in multiple studies.
Since about 2001, my team members and I have done almost all of our meta-analyses using Dave Wilson's macros for SAS, SPSS, or Stata. These save a great deal of work relative to conventional statistical packages because they are designed for meta-analysis and correct biases associated with the standard errors underlying predictors in meta-analysis regression (viz. "meta-regression"--isn't this term an odd one? Following the Greek, it would literally mean "regression of regressions," which is almost never the case in use!).
Other discussions in this group have highlighted Wolfgang Viechtbauer's metafor package for R as a significant upgrade from the macros, adding sophistication and with direct graphing capacities, for example. The main disadvantage to this strategy is that it requires at least a rudimentary grasp of the R platform itself, which for most people is a non-trivial roadblock.
As an alternative to the Wilson macros, Stata has long had a version of metareg that users could install for direct use in meta-analysis, and the latest iteration, available since 2008, and written by Roger Harbord (now a Research Associate in Medical Statistics at the University of Bristol), is quite capable indeed. One big advantage to this version of metareg over the Wilson version is that it can save estimates for use in graphing and for advanced analyses (e.g., a Bayesian function can easily be called following instantiation of a REML-based meta-regression!). Harbord co-wrote with Julian Higgins an extensive chapter describing these functions that has been published in The Stata Journal (click here). My only quibble is that there appears to be no option to get standardized regression weights (betas) in the output.
If you are a committed Stata user (version 8 and higher), then it would seem there are large advantages to going to this macro for use in meta-regression. Now, it still leaves the Wilson meanes and metaf macros as the leaders in their categories... anyone have alternatives for these?
Comments, anyone??
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In regard to my statement about the Wilson macros being the "leader" for producing estimates of weighted mean effect sizes, in fact the Harbord macro under Stata will also produce a mean effect size. It's simple, just launch the metareg command omitting moderators. The result is a meta-regression model without a constant, which is an REML model of the weighted mean effect size. Here's an example:As you can see, it has generated a mean ("Coef.") and tested it against zero (t, P, CI). The macro also calculates I2 (which is rather large for this particular set of effect sizes!) and gives you an estimate of the between-studies variance (tau squared).
Now, if you want to force it into a fixed-effects model (which is not advised for this particular case), then you are stuck.
One more update: In making updated figures for The Moving Constant paper (described elsewhere on this website), we discovered that when you graph results using the Harbord metareg macro, it sizes the bubbles for individual studies according to their fixed effects weight, not the random-effects weights (which the metareg procedure itself actually uses). In some specifiable instances, this practice could change the appearance of the bubbles and thus misrepresent graphically what is happening in the statistical model, especially in cases for which the random-effects variance component is rather large. The Appendix to that paper explains how to make an adjustment so that the bubbles reflect both sources of variance.
And yet another update: If you are still using Wilson's metareg macro and want to create confidence bands for estimates in your model, the document attached, which I co-authored with Tania Huedo-Medina, shows you how to do itstep-by-step, in Stata. It also includes some of my favorite Stata graph formatting commands (like italics in axis headings, and consistent number formats in axis labels).
Doing so using Wilson's metareg macro in SPSS or SAS is an exercise I'll leave to you!
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