{"id":1074,"date":"2015-04-07T21:54:44","date_gmt":"2015-04-07T20:54:44","guid":{"rendered":"https:\/\/blogs.bmj.com\/adc\/?p=1074"},"modified":"2015-04-07T21:54:44","modified_gmt":"2015-04-07T20:54:44","slug":"statsminiblog-i-squared","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/adc\/2015\/04\/07\/statsminiblog-i-squared\/","title":{"rendered":"StatsMiniBlog: I-squared"},"content":{"rendered":"<p><a href=\"https:\/\/blogs.bmj.com\/adc\/files\/2014\/02\/20140205-091454.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-859\" src=\"https:\/\/blogs.bmj.com\/adc\/files\/2014\/02\/20140205-091454.jpg\" alt=\"20140205-091454.jpg\" width=\"180\" height=\"76\" \/><\/a>No, not -1, the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Imaginary_number\">self-multiplication of that fancy imaginary number<\/a> that helps aircraft designers make wings work properly, but a (semi) quantitative assessment of how much heterogeneity there is in a meta-analysis: I\u00b2<\/p>\n<p>You&#8217;ll recall that the<a title=\"What about mixedupness?\" href=\"https:\/\/blogs.bmj.com\/adc\/2015\/03\/27\/what-about-mixedupness\/\"> idea of heterogeneity (mixed-up-ness) comes in both statistical and clinical flavours<\/a>. This measure &#8211;\u00a0I\u00b2 &#8211; assesses the statistical aspect. It&#8217;s often to be found at the bottom of a forest plot, near some other numbers (Tau\u00b2 and Chi\u00b2).<\/p>\n<p>The principle of\u00a0I\u00b2 is straightforward &#8211; it gives you an idea of the &#8216;percentage of variation which is beyond that you&#8217;d expect by chance alone&#8217;. It can be interpreted, approximately*, like this:<!--more--><\/p>\n<p>0-25% &#8211; just chance, really<\/p>\n<p>25-50% &#8211; bit more than just chance, but unless clinically odd, probably OKish. With a grain of salt.<\/p>\n<p>51%+ &#8211; Woah! Really quite different. Should you be doing a summary estimate here at all?<\/p>\n<p>(Flashback again &#8211; the underlying assumption of <a title=\"It\u2019s how mixed up? Meta analysis models step one.\" href=\"https:\/\/blogs.bmj.com\/adc\/2011\/03\/27\/its-how-mixed-up-meta-analysis-models-step-one\/\">fixed effect meta-analysis <\/a>is that the only variation between the studies is chance. <a title=\"Confident in predicting? Meta analysis models step two.\" href=\"https:\/\/blogs.bmj.com\/adc\/2011\/03\/27\/confident-in-predicting-meta-analysis-models-step-two\/\">Random effects <\/a>gives you an average effect over an average population in an average trial .. etc etc ..)<\/p>\n<p>There are problems with\u00a0I\u00b2; if there are very few studies (&lt;5) it probably underestimates heterogeneity, and if there are lots of studies (&gt;40 or so) then it certainly overestimates it. And it&#8217;s actually a point estimate in itself (and should be given with its own confidence interval &#8230; but that&#8217;s just too complicated to try ..). And it&#8217;s not really giving you a value you can assess the absolute amount of &#8216;extra&#8217; to try to assess how clinically meaningful that &#8216;beyond chance&#8217;ness would be. But frankly, if those sorts of things really bother you, then you&#8217;ll probably be able to interpret\u00a0Tau\u00b2 directly and calculate your own <a title=\"Confident in predicting? Meta analysis models step two.\" href=\"https:\/\/blogs.bmj.com\/adc\/2011\/03\/27\/confident-in-predicting-meta-analysis-models-step-two\/\">prediction intervals<\/a>.<\/p>\n<p>&#8211; Archi<\/p>\n<p>* There are other versions. <a href=\"http:\/\/handbook.cochrane.org\/chapter_9\/9_5_2_identifying_and_measuring_heterogeneity.htm\">For example<\/a><!--TrendMD v2.4.8--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>No, not -1, the self-multiplication of that fancy imaginary number that helps aircraft designers make wings work properly, but a (semi) quantitative assessment of how much heterogeneity there is in a meta-analysis: I\u00b2 You&#8217;ll recall that the idea of heterogeneity (mixed-up-ness) comes in both statistical and clinical flavours. This measure &#8211;\u00a0I\u00b2 &#8211; assesses the statistical [&#8230;]<\/p>\n<p><a class=\"btn btn-secondary understrap-read-more-link\" href=\"https:\/\/blogs.bmj.com\/adc\/2015\/04\/07\/statsminiblog-i-squared\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2676],"tags":[],"class_list":["post-1074","post","type-post","status-publish","format-standard","hentry","category-stats"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>StatsMiniBlog: I-squared - ADC Online Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.bmj.com\/adc\/2015\/04\/07\/statsminiblog-i-squared\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"StatsMiniBlog: I-squared - ADC Online Blog\" \/>\n<meta property=\"og:description\" content=\"No, not -1, the self-multiplication of that fancy imaginary number that helps aircraft designers make wings work properly, but a (semi) quantitative assessment of how much heterogeneity there is in a meta-analysis: I\u00b2 You&#8217;ll recall that the idea of heterogeneity (mixed-up-ness) comes in both statistical and clinical flavours. 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