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How can I conduct an Egger's test using SPSS17? For each study included in the meta-analysis I know effect size and sample size of patients and controls groups.

Staty Despair
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2 Answers2

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In order to conduct Egger's regression test you will also need the standard errors ($SE_i$) of your effect sizes ($ES_i$). Then generate the so called standard normal deviate (SND) which is defined as effect size divided by its standard error ($ES_i / SE_i$). Next, generate the precision which is $\frac{1}{SE_i}$. The regression model is: $SND = a + b \cdot precision$ (I know the error term is missing but let's keep it simple). Finally, estimate this regression model (unweighted) in SPSS/PASW (see Egger et al 1997: "Methods: Measures of funnel plot asymmetry").

The logic of Egger's regression test in explained in another CrossValidated thread: "Egger’s linear regression method intercept in meta analysis".

Community
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Bernd Weiss
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  • @Andrej @Bernd Thank you for your time. I see that Cochrane handbook, Egger's paper(PMID9310563) and MIX2.0 software use different funnelplots, but they all agree that effect size on the horizontal axon and a meassure of sample size on the vertical axon. I don't have means and standard deviations of the groups (patients, controls) of each study. I have only the effect size, and the sample size n1,n2 of patients and controls. So I cannot calculate SE of the effect sizes to use them in the linear regression. Could I use only a funnel plot with samplesize on vertical and effectsize on horizontal? – Staty Despair Feb 20 '11 at 23:14
  • @Staty Despair: Please be more specific about what type of effect size you have (odds ratio, risk ratio...). Do you know the [Practical Meta-Analysis Effect Size Calculator](http://www.campbellcollaboration.org/resources/effect_size_input.php)? This tool might help you to get the standard errors. – Bernd Weiss Feb 20 '11 at 23:31
  • @Bernd @Andrej Thanks again. I don't know what type is the effect size (SMD, OR, RR etc). I only know that can take values from -1 to +1, to show the size and the direction of the difference. The variable compared between patient and control groups is a typical scale variable, but no means and standard deviations available from the included studies. The effect size is called SDM value (www.sdmproject.com). I know (automatically calculated) the effect size from each included study, but not the formula used for the calculation. I also now sample sizes n1, n2 of patients,controls in each study. – Staty Despair Feb 21 '11 at 00:07
  • @Bernd this website includes probably the most complete and well organized collection of online calculators, ...but still not helpful in my case :( – Staty Despair Feb 21 '11 at 00:18
  • @Staty Despair: I am sorry but I do not have any experience with this type of analysis. You might want to check this paper: [Voxel-wise meta-analysis of grey matter changes in obsessive–compulsive disorder](http://bjp.rcpsych.org/cgi/reprint/195/5/393). – Bernd Weiss Feb 21 '11 at 00:24
  • @Bernd Yes, this is one of the 5 papers using this method of meta-analysis. The other 4 are (Pubmed, PMIDs): 19699306, 20603451, 21078227, 21300524. Despite the analytical description in methods section of the papers, it is still difficult to decide the category of the effect size used (SMD, RR, OR, CC), to understand how it is calculated, and calculate the Standard Errors needed to perform Egger test and synthesise a funnel plot! Thank you for your time... – Staty Despair Feb 21 '11 at 01:20
  • @Staty Despair Consider to use R with meta or rmeta packages. It's much easier than do it from scratch. – Andrej Feb 21 '11 at 07:41
  • @Andrej No experiance with R, unfortunatelly. But I believe that this analysis cannot be done by using the standerd R rmeta pachages, because the dimention of spatial distribution has to be taken into account. Nevertheless, I already have the pooled effect size, my question is how to calculate the standard errors of the sdm values (=effect size) to use them to explore for publication bias, by doing the funnel plot and the Egger test. – Staty Despair Feb 21 '11 at 13:28
  • @Staty Despair: I think we reached a point where you need to contact the authors. This looks promising: "For this analysis, we extracted SDMvalues [...] for each study and calculate the standard error of SDM values based on sample size of patient and controls groups" [(Bora et al 2011)](http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TC2-5243NDH-1&_user=2875156&_coverDate=02%2F06%2F2011&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000056617&_version=1&_urlVersion=0&_userid=2875156&md5=5023f799be7dee0cb0e0a7f1d651f930&searchtype=a). – Bernd Weiss Feb 21 '11 at 14:14
  • @Bernd Unbelievable, but I've already conducted the authors asking for definition on exactly the same line you suggest, from Bora et. al paper... – Staty Despair Feb 21 '11 at 14:45
  • @Bernd I don't close the question until receiving author's answer. As I am waiting, I am thinking constructing an alternative funnel plot, as I cannot calculate standard error, and I start a new discussion on this. – Staty Despair Feb 22 '11 at 00:35
  • @Berndt @Andrej Thank you both for the contribution. The answer is that SDM value could be treated as a SMD. Accordingly, SE could be calculated from the (also suggested by Cochrane) formula SE(SMD)=sqr[N/(n1*n2)+(SMD^2)/(2*(N-3.94))], where SDM=SDMvalue and N=n1+n2. Then, of course, precision can be calculated as precision=1/SE. Nevertheless, I am still not convinced that SDM value could be treated as SMD. Why is a SMD? – Staty Despair Feb 23 '11 at 01:14
  • @Staty Despair: As far as I can see the SDM papers have been published in good journals. So, *I* would trust the authors; of course, you should not trust me because I have absolutely no idea about this SDM stuff. Do you understand how the SDM is actually computed? – Bernd Weiss Feb 23 '11 at 14:08
  • @Bernd No, I ve never seen the SDM value formula. Actually SDM software is something like a black box for me. I enter the data, I take the results and trying to do the interpretation according to the tutorials, manual and published papers. But no much info available about the actual calculations taking place... – Staty Despair Feb 23 '11 at 15:26
  • @Staty Despair So, you have no idea about "voxel-based neuroimaging studies"? I mean I have no idea about "voxel" or "neuroimages". But since you are working with this kind of data, I assume that you have at least a basic understanding. Are you preparing a publication/thesis/whatever? – Bernd Weiss Feb 23 '11 at 15:51
  • @Bernd it is the first time I am involved in the organization of a neuroimaging study. I dont feel familiar with these theories yet. – Staty Despair Feb 23 '11 at 23:12
  • @ Staty Despair I see! Good luck with your further analyzes! – Bernd Weiss Feb 23 '11 at 23:50
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I don't use PASW anymore, but implementation of the Egger's test for asymmetry is quite simple. First please look at the Egger's paper where he propose "theory" behind the test.

Basically you have two variables: (i) normalized effect estimate (your estimate divided by its standard error), and (ii) precision (reciprocal of the standard error of the estimate). Then you should conduct simple linear regression and test for intercept $\beta_0 = 0$.

Andrej
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  • I see... Egger's test of the null hypothesis that intercept b=0 (or tests the null hypothesis that there is no funnel plot asymmetry). In this case the regression line will run through the origin. If the intercept b deviates from zero, the intercept b provides a meassure of asymmetry. The larger the interceptor's deviation from zero point, the larger the asymmetry. The two-sided p-value should be reported. (Synopsis from the book Publication bias in meta-analysis: prevention, assessment and adjustments. Po avtorjih A. J. Sutton). Thanks. – Staty Despair Feb 23 '11 at 02:34