{"id":542,"date":"2018-07-14T20:06:20","date_gmt":"2018-07-14T11:06:20","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-detect-publication-bias-by-rank-cor-and-regression-tests\/"},"modified":"2024-10-14T08:37:32","modified_gmt":"2024-10-13T23:37:32","slug":"how-to-detect-publication-bias-by-rank-cor-and-regression-tests","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-detect-publication-bias-by-rank-cor-and-regression-tests\/","title":{"rendered":"R \u3067\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u306e\u691c\u5b9a\u3092\u884c\u3046\u65b9\u6cd5"},"content":{"rendered":"\n<p>Begg\u691c\u5b9a\u3001Egger\u691c\u5b9a\u3001Macaskill\u691c\u5b9a\u3068\u3044\u3046\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u306e\u691c\u5b9a\u65b9\u6cd5\u306e\u89e3\u8aac\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u691c\u5b9a\u306e\u305f\u3081\u306e\u500b\u3005\u306e\u7814\u7a76\u30c7\u30fc\u30bf\">\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u691c\u5b9a\u306e\u305f\u3081\u306e\u500b\u3005\u306e\u7814\u7a76\u30c7\u30fc\u30bf<\/h2>\n\n\n\n<p>\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u691c\u5b9a\u3059\u308b\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">3<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">7<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">5<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">102<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">28<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">4<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">98<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">60<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">25<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">138<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">64<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">45<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">9<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">57<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">25<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">65<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">17<\/span><span class=\"synSpecial\">)<\/span>\nn1 <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">38<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">114<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">69<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">1533<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">355<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">59<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">945<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">632<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">278<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">1916<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">873<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">263<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">291<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">858<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">154<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">1195<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">298<\/span><span class=\"synSpecial\">)<\/span>\nc <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">3<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">14<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">11<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">127<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">27<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">6<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">152<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">48<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">37<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">188<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">52<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">47<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">16<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">45<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">31<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">62<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">34<\/span><span class=\"synSpecial\">)<\/span>\nn0 <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">39<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">116<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">93<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">1520<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">365<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">52<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">939<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">471<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">282<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">1921<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">583<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">266<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">293<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">883<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">147<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">1200<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">309<\/span><span class=\"synSpecial\">)<\/span>\ndat <span class=\"synStatement\">&lt;-<\/span> <span class=\"synType\">data.frame<\/span><span class=\"synSpecial\">(<\/span>a<span class=\"synSpecial\">,<\/span>n1<span class=\"synSpecial\">,<\/span>c<span class=\"synSpecial\">,<\/span>n0<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>R\u306emetafor\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n<p>metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u521d\u56de\u3060\u3051\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u304c\u5fc5\u8981\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">install.packages<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">\"metafor\"<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306eescalc()\u3067\u3001\u500b\u3005\u306e\u7814\u7a76\u306e\u63a8\u5b9a\u5024\u3068\u5206\u6563\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30c7\u30fc\u30bf\u3067\u306f\u63a8\u5b9a\u5024\u306f\u30aa\u30c3\u30ba\u6bd4\u3002<\/p>\n\n\n\n<p>measure=\u3067\u6307\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u63a8\u5b9a\u5024yi\u3068\u5206\u6563vi\u304c\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306895%\u4fe1\u983c\u533a\u9593\u306f\u3001\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\uff08REML\uff09\u3067\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synPreProc\">library<\/span><span class=\"synSpecial\">(<\/span>metafor<span class=\"synSpecial\">)<\/span>\ndat.escalc <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">escalc<\/span><span class=\"synSpecial\">(<\/span>measure<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"OR\"<\/span><span class=\"synSpecial\">,<\/span> ai<span class=\"synStatement\">=<\/span>a<span class=\"synSpecial\">,<\/span> n1i<span class=\"synStatement\">=<\/span>n1<span class=\"synSpecial\">,<\/span> ci<span class=\"synStatement\">=<\/span>c<span class=\"synSpecial\">,<\/span> n2i<span class=\"synStatement\">=<\/span>n0<span class=\"synSpecial\">,<\/span> data<span class=\"synStatement\">=<\/span>dat<span class=\"synSpecial\">)<\/span>\nres.reml <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">rma.uni<\/span><span class=\"synSpecial\">(<\/span>yi<span class=\"synSpecial\">,<\/span> vi<span class=\"synSpecial\">,<\/span> method<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"REML\"<\/span><span class=\"synSpecial\">,<\/span> data<span class=\"synStatement\">=<\/span>dat.escalc<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u3092\u66f8\u304f\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u3060\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">funnel<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"672\" height=\"672\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203607.png\" alt=\"\" class=\"wp-image-2981\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203607.png 672w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203607-300x300.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203607-150x150.png 150w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3082\u53c2\u7167\u3002<\/p>\n\n\n<div class=\"swell-block-postLink\">\t\t\t<div class=\"p-blogCard -internal\" data-type=\"type1\" data-onclick=\"clickLink\">\n\t\t\t\t<div class=\"p-blogCard__inner\">\n\t\t\t\t\t<span class=\"p-blogCard__caption\">\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t<div class=\"p-blogCard__thumb c-postThumb\"><figure class=\"c-postThumb__figure\"><img decoding=\"async\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20221113094713-300x300.png\" alt=\"\" class=\"c-postThumb__img u-obf-cover\" width=\"320\" height=\"180\"><\/figure><\/div>\t\t\t\t\t<div class=\"p-blogCard__body\">\n\t\t\t\t\t\t<a class=\"p-blogCard__title\" href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-draw-funnel-plot-for-checking-publication-bias\/\">R \u3067\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u3092\u66f8\u304f\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t<span class=\"p-blogCard__excerpt\">\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u3068\u306f\u4f55\u304b\uff1f \u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3068\u306f\u4f55\u304b\uff1f \u30d5\u30a9\u30ec\u30b9\u30c8\u30d7\u30ed\u30c3\u30c8\u3068\u306e\u9055\u3044\u306f\u4f55\u304b\uff1f \u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u306e\u524d\u306b\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3068\u306f\uff1f \u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3068\u306f\u3001\u516c\u8868\u3055\u308c&#8230;<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n<p>yi\u3068vi\u304c\u8a08\u7b97\u3055\u308c\u308c\u3070\u3001\u30aa\u30c3\u30ba\u6bd4\u4ee5\u5916\u306e\u63a8\u5b9a\u5024\u306e\u7d71\u5408\u3082\u53ef\u80fd\u3060\u3002<\/p>\n\n\n\n<p>\u5e73\u5747\u5024\u306e\u5dee\u3082\u7d71\u5408\u53ef\u80fd\u3002<\/p>\n\n\n\n<p>\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306f\u3053\u3061\u3089\u3092\u53c2\u7167\u3002<\/p>\n\n\n<div class=\"swell-block-postLink\">\t\t\t<div class=\"p-blogCard -internal\" data-type=\"type1\" data-onclick=\"clickLink\">\n\t\t\t\t<div class=\"p-blogCard__inner\">\n\t\t\t\t\t<span class=\"p-blogCard__caption\">\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t<div class=\"p-blogCard__thumb c-postThumb\"><figure class=\"c-postThumb__figure\"><img decoding=\"async\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2019\/01\/20190102185519-300x300.png\" alt=\"\" class=\"c-postThumb__img u-obf-cover\" width=\"320\" height=\"180\"><\/figure><\/div>\t\t\t\t\t<div class=\"p-blogCard__body\">\n\t\t\t\t\t\t<a class=\"p-blogCard__title\" href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/meta-analysis-of-mean-differences-in-r\/\">R \u3067\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u89e3\u6790\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t<span class=\"p-blogCard__excerpt\">\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u3092\u89e3\u8aac\u3002 \u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u89e3\u8aac\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf \u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u3092\u89e3\u8aac\u3059\u308b\u305f\u3081\u306e\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002 m\u304c\u5e73\u5747\u3001s\u304c\u6a19\u6e96\u504f\u5dee\u3001n&#8230;<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"Begg\u691c\u5b9a\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u9806\u4f4d\u76f8\u95a2\u3067\u691c\u51fa\u3059\u308b\u65b9\u6cd5\">Begg\u691c\u5b9a\u3000\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u9806\u4f4d\u76f8\u95a2\u3067\u691c\u51fa\u3059\u308b\u65b9\u6cd5<\/h2>\n\n\n\n<p>\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u306e\u691c\u5b9a\u3068\u3057\u3066\u4e00\u3064\u76ee\u306f\u3001Begg\u306e\u9806\u4f4d\u76f8\u95a2\u3068\u3044\u3046\u65b9\u6cd5\u3092\u5b9f\u65bd\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<p>\u5206\u6563\uff08$ s_i^2$ \u30b9\u30af\u30ea\u30d7\u30c8\u3067\u306f si2 \u3068\u3059\u308b\uff09\u306e\u9006\u6570\u3092\u91cd\u307f\u306b\u3057\u305f\u63a8\u5b9a\u5024\u306e\u91cd\u307f\u3065\u3051\u5e73\u5747\uff08$ \\hat{\\theta}$ \u30b9\u30af\u30ea\u30d7\u30c8\u4e2d\u3067\u306f theta \u3068\u3059\u308b\uff09\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<p>R\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>thetai <span class=\"synStatement\">&lt;-<\/span> dat.escalc<span class=\"synSpecial\">$<\/span>yi\nsi2 <span class=\"synStatement\">&lt;-<\/span> dat.escalc<span class=\"synSpecial\">$<\/span>vi\ntheta <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sum<\/span><span class=\"synSpecial\">(<\/span>thetai<span class=\"synStatement\">\/<\/span>si2<span class=\"synSpecial\">)<\/span><span class=\"synStatement\">\/<\/span><span class=\"synIdentifier\">sum<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">1<\/span><span class=\"synStatement\">\/<\/span>si2<span class=\"synSpecial\">)<\/span>\nsi2star <span class=\"synStatement\">&lt;-<\/span> si2 <span class=\"synStatement\">-<\/span> <span class=\"synConstant\">1<\/span><span class=\"synStatement\">\/<\/span><span class=\"synIdentifier\">sum<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">1<\/span><span class=\"synStatement\">\/<\/span>si2<span class=\"synSpecial\">)<\/span>\nsi.star <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sqrt<\/span><span class=\"synSpecial\">(<\/span>si2star<span class=\"synSpecial\">)<\/span>\nti <span class=\"synStatement\">&lt;-<\/span> <span class=\"synSpecial\">(<\/span>thetai<span class=\"synStatement\">-<\/span>theta<span class=\"synSpecial\">)<\/span><span class=\"synStatement\">\/<\/span>si.star\n<\/code><\/pre>\n\n\n\n<p>\u5404\u8a66\u9a13\u306e\u63a8\u5b9a\u5024\u306e\u6a19\u6e96\u504f\u5dee\uff08\u3064\u307e\u308a\u6a19\u6e96\u8aa4\u5dee\uff09\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u5206\u6563\uff08$ s_i^2$\uff09\u304b\u3089\u91cd\u307f\u306e\u5408\u8a08\u306e\u9006\u6570\u3092\u5f15\u3044\u305f\u3082\u306e\u306e\u5e73\u65b9\u6839\u304c\u5404\u8a66\u9a13\u306e\u6a19\u6e96\u8aa4\u5dee $ s_i^*$ \u3060\u3002<\/p>\n\n\n\n<p>$ \\hat{\\theta} $ \u3068 $ s_i^* $ \u3067\u3001\u5404\u8a66\u9a13\u306e\u63a8\u5b9a\u5024 $ \\hat{\\theta}_i $ \u3092\u6a19\u6e96\u5316\u3057\u305f\u3082\u306e\u304c\u3001$ t_i $ \u30b9\u30af\u30ea\u30d7\u30c8\u4e2d\u3067\u306f ti\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>$ t_i $ \u3068 $ s_i^2 $ \u9593\u306eKendall\u306e\u9806\u4f4d\u76f8\u95a2\u304c0\u304b\u3069\u3046\u304b\u3092\u691c\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001\u6a19\u6e96\u5316\u3057\u305f\u5404\u8a66\u9a13\u306e\u63a8\u5b9a\u5024\u3068\u3001\u5404\u8a66\u9a13\u306e\u5206\u6563\u304c\u76f8\u95a2\u3057\u3066\u3044\u308b\u306e\u304b\u3069\u3046\u304b\u3092\u691c\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u5e30\u7121\u4eee\u8aac\u304c\u68c4\u5374\u3067\u304d\u305a\u3001Kendall\u306e\u9806\u4f4d\u76f8\u95a2\u304c0\u3067\u3042\u308b\u3053\u3068\u3092\u5426\u5b9a\u3067\u304d\u306a\u3051\u308c\u3070\u3001\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u306f\u306a\u3044\u3068\u5224\u65ad\u3057\u3066\u3088\u3044\u3002<\/p>\n\n\n\n<p>Kendall\u306e\u9806\u4f4d\u76f8\u95a2\u306f\u3053\u3061\u3089\u3082\u53c2\u7167\u3002<\/p>\n\n\n<div class=\"swell-block-postLink\">\t\t\t<div class=\"p-blogCard -internal\" data-type=\"type1\" data-onclick=\"clickLink\">\n\t\t\t\t<div class=\"p-blogCard__inner\">\n\t\t\t\t\t<span class=\"p-blogCard__caption\">\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t<div class=\"p-blogCard__thumb c-postThumb\"><figure class=\"c-postThumb__figure\"><img decoding=\"async\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/09\/20230204224029-300x300.png\" alt=\"\" class=\"c-postThumb__img u-obf-cover\" width=\"320\" height=\"180\"><\/figure><\/div>\t\t\t\t\t<div class=\"p-blogCard__body\">\n\t\t\t\t\t\t<a class=\"p-blogCard__title\" href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/kendall-rank-correlation-coefficient\/\">R \u3067\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t<span class=\"p-blogCard__excerpt\">\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308b\u304b\u7d39\u4ecb\u3059\u308b \u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 \u30b1\u30f3\u30c9\u30fc\u30eb\uff08Kendall\uff09\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 $ \\tau $ \u306f\u3001\u9806\u4f4d\u3092\u4f7f\u308f\u306a\u3044\u76f8\u95a2\u4fc2\u6570\u3067\u3042\u308b&#8230;<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n<p>\u7d71\u8a08\u5b66\u7684\u6709\u610f\u304b\u3069\u3046\u304b\u306f\u6709\u610f\u6c34\u6e9610%\u3092\u7528\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u5bfe\u8c61\u3068\u306a\u308b\u7814\u7a76\u6570\u304c\u5c11\u306a\u3044\u305f\u3081\u3001\u691c\u51fa\u529b\u304c\u4f4e\u3044\u304b\u3089\u3060\u3002<\/p>\n\n\n\n<p>\u6709\u610f\u6c34\u6e9610%\u306f\u4ed6\u306e2\u3064\u306e\u65b9\u6cd5\u3082\u540c\u69d8\u3060\u3002<\/p>\n\n\n\n<p>$ t_i $ \u3068$ s_i^2 $ \u306e\u6563\u5e03\u56f3\u3092\u63cf\u3044\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">plot<\/span><span class=\"synSpecial\">(<\/span>ti<span class=\"synSpecial\">,<\/span> si2<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"587\" height=\"586\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203741.png\" alt=\"\" class=\"wp-image-2982\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203741.png 587w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203741-300x300.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920203741-150x150.png 150w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>Kendall\u306e\u9806\u4f4d\u76f8\u95a2\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">cor.test<\/span><span class=\"synSpecial\">(<\/span>ti<span class=\"synSpecial\">,<\/span> si2<span class=\"synSpecial\">,<\/span> method<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"kendall\"<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u76f8\u95a2\u4fc2\u6570\u306f-0.059\u3067p\u5024\u306f0.777\u3067\u3001\u76f8\u95a2\u4fc2\u6570\u304c0\u3067\u3042\u308b\u3068\u3044\u3046\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u76f8\u95a2\u4fc2\u6570\u304c\u30bc\u30ed\u3067\u3042\u308b\u3053\u3068\u3092\u5426\u5b9a\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u6a19\u6e96\u5316\u3055\u308c\u305f\u63a8\u5b9a\u5024\u3068\u5404\u7814\u7a76\u306e\u91cd\u307f\u306e\u9006\u6570\uff08\u5206\u6563\uff09\u306e\u9593\u306b\u306f\u76f8\u95a2\u304c\u306a\u304f\u3001\u7814\u7a76\u7d50\u679c\u3084\u7cbe\u5ea6\u306b\u3088\u308b\u30d0\u30a4\u30a2\u30b9\u306f\u691c\u51fa\u3055\u308c\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">cor.test<\/span><span class=\"synSpecial\">(<\/span>ti<span class=\"synSpecial\">,<\/span> si2<span class=\"synSpecial\">,<\/span> method<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"kendall\"<\/span><span class=\"synSpecial\">)<\/span>\nKendall<span class=\"synConstant\">'s rank correlation tau<\/span>\n<span class=\"synConstant\">data:  ti and si2<\/span>\n<span class=\"synConstant\">T = 64, p-value = 0.7765<\/span>\n<span class=\"synConstant\">alternative hypothesis: true tau is not equal to 0<\/span>\n<span class=\"synConstant\">sample estimates:<\/span>\n<span class=\"synConstant\">        tau <\/span>\n<span class=\"synConstant\">-0.05882353 <\/span>\n<\/code><\/pre>\n\n\n\n<p>metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306eranktest()\u3092\u4f7f\u3046\u3068\u305a\u3063\u3068\u7c21\u5358\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">ranktest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u8a08\u7b97\u7d50\u679c\u304c\u683c\u7d0d\u3055\u308c\u3066\u3044\u308b\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff08\u3053\u3053\u3067\u306fres.reml\uff09\u304c\u3042\u308c\u3070\u3001\u63a8\u5b9a\u5024\u306e\u91cd\u307f\u3065\u3051\u5e73\u5747\u3084\u3001\u5404\u7814\u7a76\u306e\u6a19\u6e96\u504f\u5dee\u3001\u63a8\u5b9a\u5024\u306e\u6a19\u6e96\u5316\u306e\u8a08\u7b97\u306f\u5168\u304f\u4e0d\u8981\u3067\u3001\u4e00\u77ac\u3067\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">ranktest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">)<\/span>\nRank Correlation Test <span class=\"synStatement\">for<\/span> Funnel Plot Asymmetry\nKendall<span class=\"synConstant\">'s tau = -0.0588, p = 0.7765<\/span>\n<\/code><\/pre>\n\n\n\n<div id=\"biost-4167920354\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\" id=\"Egger\u691c\u5b9a\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u56de\u5e30\u5206\u6790\u3067\u691c\u51fa\u3059\u308b\u65b9\u6cd5\">Egger\u691c\u5b9a\u3000\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u56de\u5e30\u5206\u6790\u3067\u691c\u51fa\u3059\u308b\u65b9\u6cd5<\/h2>\n\n\n\n<p>Egger\u306e\u65b9\u6cd5\u306f\u3001\u4ee5\u4e0b\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u7528\u3044\u308b\u3002<\/p>\n\n\n\n<p>$$ \\left( \\frac{\\hat{\\theta}_i}{s_i} \\right) = \\alpha + \\beta \\left( \\frac{1}{s_i} \\right) + \u8aa4\u5dee $$<\/p>\n\n\n\n\n\n\n\n<p>\u5e30\u7121\u4eee\u8aac\u306e\u5143\u3067\u306f\u3001\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u304c\u5de6\u53f3\u5bfe\u79f0\u5f62\u306a\u3089\u3070\u3001\u3053\u306e\u56de\u5e30\u5f0f\u306f\u539f\u70b9\u3092\u901a\u308a\uff08\u03b1= 0\uff09\u3001\u50be\u304d\u306f\u7d71\u5408\u63a8\u5b9a\u5024\u306b\u7b49\u3057\u304f\uff08$ \\hat{\\beta} = \\hat{\\theta} $\uff09\u306a\u308b\u306e\u3067\u3001\u03b1 = 0 \u3092\u691c\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u524d\u7bc0\u3067\u4f7f\u3063\u305f\u5909\u6570\u3092\u5f15\u304d\u7d9a\u304d\u4f7f\u3046\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>si <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sqrt<\/span><span class=\"synSpecial\">(<\/span>si2<span class=\"synSpecial\">)<\/span>\ntheta.si <span class=\"synStatement\">&lt;-<\/span> thetai<span class=\"synStatement\">\/<\/span>si\ninv.si <span class=\"synStatement\">&lt;-<\/span> <span class=\"synConstant\">1<\/span><span class=\"synStatement\">\/<\/span>si\n<\/code><\/pre>\n\n\n\n<p>\u7dda\u5f62\u30e2\u30c7\u30eblm()\u3067\u3001\u4e0a\u8a18\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u63a8\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>res.theta.si <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">lm<\/span><span class=\"synSpecial\">(<\/span>theta.si <span class=\"synStatement\">~<\/span> inv.si<span class=\"synSpecial\">)<\/span>\n<span class=\"synIdentifier\">summary<\/span><span class=\"synSpecial\">(<\/span>res.theta.si<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n<p>(Intercept)\u306e\u884c\u304c \u03b1 = 0 \u306e\u691c\u5b9a\u7d50\u679c\u3002<\/p>\n\n\n\n<p>p\u5024\u304c0.817\u3067\u3001\u30bc\u30ed\u3092\u5426\u5b9a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u3086\u3048\u306b\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u306f\u5de6\u53f3\u5bfe\u79f0\u5f62\u3067\u3042\u308b\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u305a\u3001\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u53ef\u80fd\u6027\u306f\u4f4e\u3044\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">summary<\/span><span class=\"synSpecial\">(<\/span>res.theta.si<span class=\"synSpecial\">)<\/span>\nCall<span class=\"synSpecial\">:<\/span>\n<span class=\"synIdentifier\">lm<\/span><span class=\"synSpecial\">(<\/span>formula <span class=\"synStatement\">=<\/span> theta.si <span class=\"synStatement\">~<\/span> inv.si<span class=\"synSpecial\">)<\/span>\nResiduals<span class=\"synSpecial\">:<\/span>\nMin      1Q  Median      3Q     Max\n<span class=\"synStatement\">-<\/span><span class=\"synConstant\">1.9909<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.7373<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.2046<\/span>  <span class=\"synConstant\">0.8214<\/span>  <span class=\"synConstant\">2.5698<\/span>\nCoefficients<span class=\"synSpecial\">:<\/span>\nEstimate Std. Error t value <span class=\"synIdentifier\">Pr<\/span><span class=\"synSpecial\">(<\/span><span class=\"synStatement\">&gt;|<\/span>t<span class=\"synStatement\">|<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synSpecial\">(<\/span>Intercept<span class=\"synSpecial\">)<\/span>  <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.1518<\/span>     <span class=\"synConstant\">0.6463<\/span>  <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.235<\/span>    <span class=\"synConstant\">0.817<\/span>\ninv.si       <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.2152<\/span>     <span class=\"synConstant\">0.1395<\/span>  <span class=\"synStatement\">-<\/span><span class=\"synConstant\">1.543<\/span>    <span class=\"synConstant\">0.144<\/span>\nResidual standard error<span class=\"synSpecial\">:<\/span> <span class=\"synConstant\">1.194<\/span> on <span class=\"synConstant\">15<\/span> degrees of freedom\nMultiple R<span class=\"synStatement\">-<\/span>squared<span class=\"synSpecial\">:<\/span>  <span class=\"synConstant\">0.1369<\/span><span class=\"synSpecial\">,<\/span>    Adjusted R<span class=\"synStatement\">-<\/span>squared<span class=\"synSpecial\">:<\/span>  <span class=\"synConstant\">0.07937<\/span>\n<span class=\"synConstant\">F<\/span><span class=\"synStatement\">-<\/span>statistic<span class=\"synSpecial\">:<\/span> <span class=\"synConstant\">2.379<\/span> on <span class=\"synConstant\">1<\/span> and <span class=\"synConstant\">15<\/span> DF<span class=\"synSpecial\">,<\/span>  p<span class=\"synStatement\">-<\/span>value<span class=\"synSpecial\">:<\/span> <span class=\"synConstant\">0.1438<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u5404\u7814\u7a76\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u3001\u56de\u5e30\u76f4\u7dda\u3092\u5f15\u3044\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<p>\u56de\u5e30\u76f4\u7dda\uff08\u7834\u7dda\uff09\u306f\u307b\u307c\u539f\u70b9\u3092\u901a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">plot<\/span><span class=\"synSpecial\">(<\/span>theta.si <span class=\"synStatement\">~<\/span> inv.si<span class=\"synSpecial\">,<\/span> xlab<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"1\/SE\"<\/span><span class=\"synSpecial\">,<\/span> ylab<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"log(OR)\/SE\"<\/span><span class=\"synSpecial\">,<\/span> xlim<span class=\"synStatement\">=<\/span><span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">0<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">10<\/span><span class=\"synSpecial\">))<\/span>\n<span class=\"synIdentifier\">abline<\/span><span class=\"synSpecial\">(<\/span>h<span class=\"synStatement\">=<\/span><span class=\"synConstant\">0<\/span><span class=\"synSpecial\">,<\/span> v<span class=\"synStatement\">=<\/span><span class=\"synConstant\">0<\/span><span class=\"synSpecial\">,<\/span> lty<span class=\"synStatement\">=<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synIdentifier\">abline<\/span><span class=\"synSpecial\">(<\/span>res.theta.si<span class=\"synSpecial\">,<\/span> lty<span class=\"synStatement\">=<\/span><span class=\"synConstant\">2<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"587\" height=\"586\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204155.png\" alt=\"\" class=\"wp-image-2985\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204155.png 587w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204155-300x300.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204155-150x150.png 150w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306eregtest()\u3092\u4f7f\u3046\u3068\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">regtest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">,<\/span> model<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"lm\"<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n<p>t\u5024\u3068p\u5024\u304c\u3001regtest()\u3092\u4f7f\u308f\u306a\u3044\u7d50\u679c\u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">regtest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">,<\/span> model<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"lm\"<\/span><span class=\"synSpecial\">)<\/span>\nRegression Test <span class=\"synStatement\">for<\/span> Funnel Plot Asymmetry\nModel<span class=\"synSpecial\">:<\/span>     weighted regression with multiplicative dispersion\nPredictor<span class=\"synSpecial\">:<\/span> standard error\nTest <span class=\"synStatement\">for<\/span> Funnel Plot Asymmetry<span class=\"synSpecial\">:<\/span> t <span class=\"synStatement\">=<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.2349<\/span><span class=\"synSpecial\">,<\/span> df <span class=\"synStatement\">=<\/span> <span class=\"synConstant\">15<\/span><span class=\"synSpecial\">,<\/span> p <span class=\"synStatement\">=<\/span> <span class=\"synConstant\">0.8175<\/span>\nLimit <span class=\"synIdentifier\">Estimate <\/span><span class=\"synSpecial\">(<\/span>as sei <span class=\"synStatement\">-&gt;<\/span> <span class=\"synConstant\">0<\/span><span class=\"synSpecial\">):<\/span>   b <span class=\"synStatement\">=<\/span> <span class=\"synStatement\">-<\/span><span class=\"synIdentifier\">0.2152 <\/span><span class=\"synSpecial\">(<\/span>CI<span class=\"synSpecial\">:<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.5126<\/span><span class=\"synSpecial\">,<\/span> <span class=\"synConstant\">0.0822<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u3061\u306a\u307f\u306b\u3001\u7814\u7a76\u9593\u306b\u7121\u8996\u3067\u304d\u306a\u3044\u7570\u8cea\u6027\u304c\u691c\u51fa\u3055\u308c\u305f\u5834\u5408\u3001\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u3067\u7d71\u5408\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u304c\u3001\u305d\u306e\u3068\u304d\u306fEgger\u306e\u65b9\u6cd5\u3082\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u3067\u5b9f\u65bd\u3059\u308b\u3068\u3088\u3044\u3002<\/p>\n\n\n\n<p>\u4eca\u56de\u306e\u4f8b\u984c\u306f\u3059\u3067\u306bREML\u3092\u7528\u3044\u3066\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u3067\u7d71\u5408\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u89e3\u6790\u7d50\u679c\u306e\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306f\u305d\u306e\u307e\u307e\u3067OK\u3002<\/p>\n\n\n<div class=\"swell-block-postLink\">\t\t\t<div class=\"p-blogCard -internal\" data-type=\"type1\" data-onclick=\"clickLink\">\n\t\t\t\t<div class=\"p-blogCard__inner\">\n\t\t\t\t\t<span class=\"p-blogCard__caption\">\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t<div class=\"p-blogCard__thumb c-postThumb\"><figure class=\"c-postThumb__figure\"><img decoding=\"async\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920205407-300x300.png\" alt=\"\" class=\"c-postThumb__img u-obf-cover\" width=\"320\" height=\"180\"><\/figure><\/div>\t\t\t\t\t<div class=\"p-blogCard__body\">\n\t\t\t\t\t\t<a class=\"p-blogCard__title\" href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-integrate-odds-ratios-by-reml\/\">R \u3067\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf REML \u3067\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9<\/a>\n\t\t\t\t\t\t<span class=\"p-blogCard__excerpt\">\u30aa\u30c3\u30ba\u6bd4\u3092\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf REML \u3067\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u306e\u89e3\u8aac\u3002 R \u3067\u5b9f\u884c\u3059\u308b\u3002 \u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\u3067\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u610f\u5473 \u30aa\u30c3\u30ba\u6bd4\u306e\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3092\u3059\u308b\u3068\u304d\u306b\u3001\u5bfe\u6570&#8230;<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n<p>\u5148\u307b\u3069 model = &#8220;lm&#8221; \u3068\u3044\u3046\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u5165\u308c\u305f\u304c\u3001\u305d\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u5165\u308c\u306a\u3044\u3068\u3001\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u7d50\u679c\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">regtest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">)<\/span>\nRegression Test <span class=\"synStatement\">for<\/span> Funnel Plot Asymmetry\nModel<span class=\"synSpecial\">:<\/span>     mixed<span class=\"synStatement\">-<\/span>effects meta<span class=\"synStatement\">-<\/span>regression model\nPredictor<span class=\"synSpecial\">:<\/span> standard error\nTest <span class=\"synStatement\">for<\/span> Funnel Plot Asymmetry<span class=\"synSpecial\">:<\/span> z <span class=\"synStatement\">=<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.7411<\/span><span class=\"synSpecial\">,<\/span> p <span class=\"synStatement\">=<\/span> <span class=\"synConstant\">0.4586<\/span>\nLimit <span class=\"synIdentifier\">Estimate <\/span><span class=\"synSpecial\">(<\/span>as sei <span class=\"synStatement\">-&gt;<\/span> <span class=\"synConstant\">0<\/span><span class=\"synSpecial\">):<\/span>   b <span class=\"synStatement\">=<\/span> <span class=\"synStatement\">-<\/span><span class=\"synIdentifier\">0.1311 <\/span><span class=\"synSpecial\">(<\/span>CI<span class=\"synSpecial\">:<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.4408<\/span><span class=\"synSpecial\">,<\/span> <span class=\"synConstant\">0.1787<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u6709\u610f\u78ba\u7387\u306f p=0.4586 \u3068\u3084\u3084\u4f4e\u4e0b\u3057\u305f\u304c\u3001\u6709\u610f\u6c34\u6e9610\uff05\u3068\u3057\u3066\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u306f\u306a\u304f\u3001\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u3068\u306f\u8a00\u3048\u306a\u3044\u3068\u3044\u3046\u7d50\u679c\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"Macaskill\u691c\u5b9a\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u56de\u5e30\u5206\u6790\u3067\u691c\u51fa\u3059\u308b\u65b9\u6cd5\">Macaskill\u691c\u5b9a\u3000\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u3092\u56de\u5e30\u5206\u6790\u3067\u691c\u51fa\u3059\u308b\u65b9\u6cd5<\/h2>\n\n\n\n<p>Macaskill\u306e\u65b9\u6cd5\u306f\u3001\u4ee5\u4e0b\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u7528\u3044\u305f\u91cd\u307f\u3065\u3051\u56de\u5e30\u5206\u6790\u3060\u3002<\/p>\n\n\n\n<p>$$ \\hat{\\theta}_i = \\alpha + \\beta n_i + \u8aa4\u5dee $$<\/p>\n\n\n\n\n\n\n\n<p>\u63a8\u5b9a\u5024 $ \\hat{\\theta}_i $ \u3092\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba $ n_i $ \u3067\u4e88\u6e2c\u3059\u308b\u56de\u5e30\u5f0f\u3060\u3002<\/p>\n\n\n\n<p>\u91cd\u307f\u306f\u5206\u6563\u306e\u9006\u6570\u3092\u7528\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u56de\u5e30\u6cd5\u3068\u3082\u547c\u3070\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u3082\u3057\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u306a\u3089\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u7814\u7a76\u307b\u3069\u3001\u7814\u7a76\u7d50\u679c\u306e\u63a8\u5b9a\u5024\u304c\u5927\u304d\u3044\u307b\u3046\u306b\u504f\u308b\u306f\u305a\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u306f\u3001\u771f\u306e\u63a8\u5b9a\u5024\u304c\u6b63\u306e\u5834\u5408\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u8ca0\u306e\u5834\u5408\u306f\u3001\u5c0f\u3055\u3044\u307b\u3046\u306b\u504f\u308b\u3002<\/p>\n\n\n\n<p>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u3068\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u306a\u308a\u306b\u304f\u304f\u3001\u63a8\u5b9a\u5024\u304c\u5927\u304d\u3044\u304c\u305f\u3081\u306b\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u306a\u3063\u305f\u3068\u3044\u3046\u504f\u3063\u305f\u7814\u7a76\u306e\u307f\u304c\u63a1\u629e\u3055\u308c\u3066\u3044\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u504f\u308a\u3092\u691c\u51fa\u3059\u308b\u308f\u3051\u3060\u3002<\/p>\n\n\n\n<p>\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u304c\u5de6\u53f3\u5bfe\u79f0\u5f62\u306a\u3089\u3001\u56de\u5e30\u5f0f\u306e\u50be\u304d\u304c\u30bc\u30ed\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u3059\u306a\u308f\u3061\u5e30\u7121\u4eee\u8aac\u306f \u03b2 = 0 \u3060\u3002<\/p>\n\n\n\n<p>\u5404\u7814\u7a76\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba $ n_i $ \u3092\u8a08\u7b97\u3057\u3066\u3001\u5148\u307b\u3069\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3067 \u03b2 \u3092\u63a8\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ni\u3000<span class=\"synStatement\">&lt;-<\/span> dat<span class=\"synSpecial\">$<\/span>n1<span class=\"synStatement\">+<\/span>dat<span class=\"synSpecial\">$<\/span>n0\nres.theta.n <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">lm<\/span><span class=\"synSpecial\">(<\/span>thetai <span class=\"synStatement\">~<\/span> ni<span class=\"synSpecial\">,<\/span> weights<span class=\"synStatement\">=<\/span><span class=\"synConstant\">1<\/span><span class=\"synStatement\">\/<\/span>dat.escalc<span class=\"synSpecial\">$<\/span>vi<span class=\"synSpecial\">)<\/span>\n<span class=\"synIdentifier\">summary<\/span><span class=\"synSpecial\">(<\/span>res.theta.n<span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">summary<\/span><span class=\"synSpecial\">(<\/span>res.theta.n<span class=\"synSpecial\">)<\/span>\nCall<span class=\"synSpecial\">:<\/span>\n<span class=\"synIdentifier\">lm<\/span><span class=\"synSpecial\">(<\/span>formula <span class=\"synStatement\">=<\/span> thetai <span class=\"synStatement\">~<\/span> ni<span class=\"synSpecial\">,<\/span> weights <span class=\"synStatement\">=<\/span> <span class=\"synConstant\">1<\/span><span class=\"synStatement\">\/<\/span>dat.escalc<span class=\"synSpecial\">$<\/span>vi<span class=\"synSpecial\">)<\/span>\nWeighted Residuals<span class=\"synSpecial\">:<\/span>\nMin      1Q  Median      3Q     Max\n<span class=\"synStatement\">-<\/span><span class=\"synConstant\">1.9432<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.7026<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.3085<\/span>  <span class=\"synConstant\">0.7728<\/span>  <span class=\"synConstant\">2.5467<\/span>\nCoefficients<span class=\"synSpecial\">:<\/span>\nEstimate Std. Error t value <span class=\"synIdentifier\">Pr<\/span><span class=\"synSpecial\">(<\/span><span class=\"synStatement\">&gt;|<\/span>t<span class=\"synStatement\">|<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synSpecial\">(<\/span>Intercept<span class=\"synSpecial\">)<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">2.269e-01<\/span>  <span class=\"synConstant\">1.250e-01<\/span>  <span class=\"synStatement\">-<\/span><span class=\"synConstant\">1.816<\/span>   <span class=\"synConstant\">0.0895<\/span> .\nni          <span class=\"synStatement\">-<\/span><span class=\"synConstant\">8.469e-06<\/span>  <span class=\"synConstant\">5.209e-05<\/span>  <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.163<\/span>   <span class=\"synConstant\">0.8730<\/span>\n<span class=\"synStatement\">---<\/span>\nSignif. codes<span class=\"synSpecial\">:<\/span>  <span class=\"synConstant\">0<\/span> \u2018<span class=\"synError\">***<\/span>\u2019 <span class=\"synConstant\">0.001<\/span> \u2018<span class=\"synStatement\">**<\/span>\u2019 <span class=\"synConstant\">0.01<\/span> \u2018<span class=\"synStatement\">*<\/span>\u2019 <span class=\"synConstant\">0.05<\/span> \u2018.\u2019 <span class=\"synConstant\">0.1<\/span> \u2018 \u2019 <span class=\"synConstant\">1<\/span>\nResidual standard error<span class=\"synSpecial\">:<\/span> <span class=\"synConstant\">1.196<\/span> on <span class=\"synConstant\">15<\/span> degrees of freedom\nMultiple R<span class=\"synStatement\">-<\/span>squared<span class=\"synSpecial\">:<\/span>  <span class=\"synConstant\">0.001759<\/span><span class=\"synSpecial\">,<\/span>  Adjusted R<span class=\"synStatement\">-<\/span>squared<span class=\"synSpecial\">:<\/span>  <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.06479<\/span>\n<span class=\"synConstant\">F<\/span><span class=\"synStatement\">-<\/span>statistic<span class=\"synSpecial\">:<\/span> <span class=\"synConstant\">0.02643<\/span> on <span class=\"synConstant\">1<\/span> and <span class=\"synConstant\">15<\/span> DF<span class=\"synSpecial\">,<\/span>  p<span class=\"synStatement\">-<\/span>value<span class=\"synSpecial\">:<\/span> <span class=\"synConstant\">0.873<\/span>\n<\/code><\/pre>\n\n\n\n<p>ni\u306eCoefficient\u306eEstimate\u3092\u898b\u308b\u3068\u307b\u307c\u30bc\u30ed\u3002<\/p>\n\n\n\n<p>p\u5024\uff08Pr(>|t|)\uff09\u3092\u898b\u308b\u30680.873\u3067\u3001\u03b2 = 0 \u306e\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001\u03b2 = 0 \u304c\u5426\u5b9a\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u3059\u306a\u308f\u3061\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u53ef\u80fd\u6027\u306f\u4f4e\u3044\u3068\u8003\u3048\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u5404\u7814\u7a76\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u3001\u56de\u5e30\u76f4\u7dda\u3092\u5f15\u3044\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<p>\u50be\u304d\u304c\u307b\u307c\u30bc\u30ed\u3067\u3042\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u3068\u306f\u65ad\u5b9a\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">plot<\/span><span class=\"synSpecial\">(<\/span>thetai <span class=\"synStatement\">~<\/span> ni<span class=\"synSpecial\">,<\/span> xlab<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"Sample Size\"<\/span><span class=\"synSpecial\">,<\/span> ylab<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"log(OR)\"<\/span><span class=\"synSpecial\">,<\/span> xlim<span class=\"synStatement\">=<\/span><span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">0<\/span><span class=\"synSpecial\">,<\/span><span class=\"synConstant\">4000<\/span><span class=\"synSpecial\">))<\/span>\n<span class=\"synIdentifier\">abline<\/span><span class=\"synSpecial\">(<\/span>h<span class=\"synStatement\">=<\/span><span class=\"synConstant\">0<\/span><span class=\"synSpecial\">,<\/span> v<span class=\"synStatement\">=<\/span><span class=\"synConstant\">0<\/span><span class=\"synSpecial\">,<\/span> lty<span class=\"synStatement\">=<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synIdentifier\">abline<\/span><span class=\"synSpecial\">(<\/span>res.theta.n<span class=\"synSpecial\">,<\/span> lty<span class=\"synStatement\">=<\/span><span class=\"synConstant\">2<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"587\" height=\"586\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204301.png\" alt=\"\" class=\"wp-image-2986\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204301.png 587w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204301-300x300.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204301-150x150.png 150w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306eregtest()\u3092\u4f7f\u3046\u3068\u3053\u3061\u3089\u3082\u7c21\u5358\u3060\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synIdentifier\">regtest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">,<\/span> model<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"lm\"<\/span><span class=\"synSpecial\">,<\/span> predictor<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"ni\"<\/span><span class=\"synSpecial\">)<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3001<\/p>\n\n\n\n<p>t\u5024\u3068p\u5024\u304c\u3001regtest()\u3092\u4f7f\u308f\u306a\u3044\u65b9\u6cd5\u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">regtest<\/span><span class=\"synSpecial\">(<\/span>res.reml<span class=\"synSpecial\">,<\/span> model<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"lm\"<\/span><span class=\"synSpecial\">,<\/span> predictor<span class=\"synStatement\">=<\/span><span class=\"synConstant\">\"ni\"<\/span><span class=\"synSpecial\">)<\/span>\nRegression Test <span class=\"synStatement\">for<\/span> Funnel Plot Asymmetry\nmodel<span class=\"synSpecial\">:<\/span>     weighted regression with multiplicative dispersion\npredictor<span class=\"synSpecial\">:<\/span> sample size\ntest <span class=\"synStatement\">for<\/span> funnel plot asymmetry<span class=\"synSpecial\">:<\/span> t <span class=\"synStatement\">=<\/span> <span class=\"synStatement\">-<\/span><span class=\"synConstant\">0.1626<\/span><span class=\"synSpecial\">,<\/span> df <span class=\"synStatement\">=<\/span> <span class=\"synConstant\">15<\/span><span class=\"synSpecial\">,<\/span> p <span class=\"synStatement\">=<\/span> <span class=\"synConstant\">0.8730<\/span>\n<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u307e\u3068\u3081\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u306e\u6709\u7121\u3092\u691c\u8a0e\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001Begg\u306e\u65b9\u6cd5\u3001Egger\u306e\u65b9\u6cd5\u3001Macaskill\u306e\u65b9\u6cd5\u3092\u5b9f\u65bd\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n<p>\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u3068\u6bd4\u3079\u3066\u6570\u5024\u3068\u7d71\u8a08\u5b66\u7684\u691c\u5b9a\u3067\u5224\u65ad\u3067\u304d\u308b\u306e\u3067\u3001\u767d\u9ed2\u3064\u3051\u3084\u3059\u304f\u308f\u304b\u308a\u3084\u3059\u3044\u304c\u3001\u30d5\u30a1\u30f3\u30cd\u30eb\u30d7\u30ed\u30c3\u30c8\u3068\u5408\u308f\u305b\u3066\u7dcf\u5408\u7684\u306b\u5224\u65ad\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>R\u306emetafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u95a2\u6570\u3092\u4f7f\u3046\u3068\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u4f55\u3089\u304b\u53c2\u8003\u306b\u306a\u308c\u3070\u5e78\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u53c2\u8003\u66f8\u7c4d\">\u53c2\u8003\u66f8\u7c4d<\/h2>\n\n\n\n<p>\u4e39\u5f8c\u4fca\u90ce\u8457\u3000\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u3000\u671d\u5009\u66f8\u5e97<br>6. Publication bias\u3078\u306e\u6311\u6226<br>6.1 \u516c\u8868\u30d0\u30a4\u30a2\u30b9\u306e\u691c\u51fa<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a class=\"hatena-asin-detail-image-link\" href=\"https:\/\/www.amazon.co.jp\/dp\/4254127545?tag=ttyotani-22&amp;linkCode=ogi&amp;th=1&amp;psc=1\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/m.media-amazon.com\/images\/I\/41PBSEteD0L._SL500_.jpg\" alt=\"\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u2015\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)\" title=\"\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u2015\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)\"\/><\/a><\/figure>\n\n\n\n<div class=\"hatena-asin-detail\"><\/div>\n\n\n\n<div class=\"hatena-asin-detail-info\">\n<p class=\"hatena-asin-detail-title\"><a href=\"https:\/\/www.amazon.co.jp\/dp\/4254127545?tag=ttyotani-22&amp;linkCode=ogi&amp;th=1&amp;psc=1\" target=\"_blank\" rel=\"noopener\">\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u2015\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)<\/a><\/p>\n<ul class=\"hatena-asin-detail-meta\">\n<li><span class=\"hatena-asin-detail-label\">\u4f5c\u8005:<\/span><a href=\"https:\/\/d.hatena.ne.jp\/keyword\/%BD%D3%CF%BA%2C%20%C3%B0%B8%E5\" class=\"keyword\">\u4fca\u90ce, \u4e39\u5f8c<\/a><\/li>\n<li>\u671d\u5009\u66f8\u5e97<\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.amazon.co.jp\/dp\/4254127545?tag=ttyotani-22&amp;linkCode=ogi&amp;th=1&amp;psc=1\" class=\"asin-detail-buy\" target=\"_blank\" rel=\"noopener\">Amazon<\/a><\/p>\n<\/div>\n\n\n\n<p>\u65b0\u7248\u3082\u51fa\u3066\u308b<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a class=\"hatena-asin-detail-image-link\" href=\"https:\/\/www.amazon.co.jp\/dp\/425412760X?tag=ttyotani-22&amp;linkCode=ogi&amp;th=1&amp;psc=1\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/m.media-amazon.com\/images\/I\/41P-7dAdGgL._SL500_.jpg\" alt=\"\u65b0\u7248 \u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580 \u2500\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5\u2500 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)\" title=\"\u65b0\u7248 \u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580 \u2500\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5\u2500 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)\"\/><\/a><\/figure>\n\n\n\n<div class=\"hatena-asin-detail\"><\/div>\n\n\n\n<div class=\"hatena-asin-detail-info\">\n<p class=\"hatena-asin-detail-title\"><a href=\"https:\/\/www.amazon.co.jp\/dp\/425412760X?tag=ttyotani-22&amp;linkCode=ogi&amp;th=1&amp;psc=1\" target=\"_blank\" rel=\"noopener\">\u65b0\u7248 \u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580 \u2500\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5\u2500 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)<\/a><\/p>\n<ul class=\"hatena-asin-detail-meta\">\n<li><span class=\"hatena-asin-detail-label\">\u4f5c\u8005:<\/span><a href=\"https:\/\/d.hatena.ne.jp\/keyword\/%C3%B0%B8%E5%20%BD%D3%CF%BA\" class=\"keyword\">\u4e39\u5f8c \u4fca\u90ce<\/a><\/li>\n<li>\u671d\u5009\u66f8\u5e97<\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.amazon.co.jp\/dp\/425412760X?tag=ttyotani-22&amp;linkCode=ogi&amp;th=1&amp;psc=1\" class=\"asin-detail-buy\" target=\"_blank\" rel=\"noopener\">Amazon<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Begg\u691c\u5b9a\u3001Egger\u691c\u5b9a\u3001Macaskill\u691c\u5b9a\u3068\u3044\u3046\u51fa\u7248\u30d0\u30a4\u30a2\u30b9\u306e\u691c\u5b9a\u65b9\u6cd5\u306e\u89e3\u8aac\u3002<\/p>\n","protected":false},"author":2,"featured_media":2985,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,37,46],"tags":[],"class_list":["post-542","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","category-37","category-46"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200920204155.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/542","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=542"}],"version-history":[{"count":4,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/542\/revisions"}],"predecessor-version":[{"id":2988,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/542\/revisions\/2988"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/2985"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}