{"id":319,"date":"2022-04-10T11:18:59","date_gmt":"2022-04-10T02:18:59","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/weights-for-meta-analysis-in-fixed-and-random-effect-model\/"},"modified":"2024-09-29T23:13:45","modified_gmt":"2024-09-29T14:13:45","slug":"weights-for-meta-analysis-in-fixed-and-random-effect-model","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/weights-for-meta-analysis-in-fixed-and-random-effect-model\/","title":{"rendered":"\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u91cd\u307f\u4ed8\u3051\u306e\u8a71 \u2015 \u56fa\u5b9a\u52b9\u679c\u3068\u5909\u91cf\u52b9\u679c\u306e\u9055\u3044"},"content":{"rendered":"\n

\u8907\u6570\u306e\u7814\u7a76\u3092\u7d71\u5408\u3059\u308b\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3002<\/p>\n\n\n\n

\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u3068\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u304c\u5b58\u5728\u3059\u308b\u3002<\/p>\n\n\n\n

\u7d71\u5408\u3059\u308b\u969b\u306e\u91cd\u307f\u304c\u7570\u306a\u308b\u306e\u304c\u4e00\u756a\u306e\u9055\u3044\u3002<\/p>\n\n\n\n

\u3069\u3093\u306a\u91cd\u307f\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u306e\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3068\u306f\uff1f<\/h2>\n\n\n\n

\u30b7\u30b9\u30c6\u30de\u30c6\u30a3\u30c3\u30af\u30ec\u30d3\u30e5\u30fc\u3092\u884c\u3063\u305f\u8907\u6570\u306e\u7814\u7a76\u306e\u52b9\u679c\u91cf\u3092\u7d71\u5408\u3059\u308b\u89e3\u6790\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u904e\u53bb\u8a18\u4e8b\u306f\u3053\u3061\u3089\u304b\u3089\u3069\u3046\u305e\u3002<\/p>\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9 \u30ab\u30c6\u30b4\u30ea\u30fc\u306e\u904e\u53bb\u8a18\u4e8b<\/a><\/p>\n\n\n\n\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306f\u3069\u3093\u306a\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u306e\u304b\uff1f<\/h2>\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306f\u7d71\u5408\u3057\u305f\u70b9\u63a8\u5b9a\u5024\u3068\u533a\u9593\u63a8\u5b9a\u3092\u884c\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u305d\u306e\u969b\u306b\u3001\u500b\u3005\u306e\u7814\u7a76\u306b\u9069\u5207\u306a\u91cd\u307f\u3092\u4ed8\u3051\u305f\u91cd\u307f\u4ed8\u3051\u5e73\u5747\u3092\u8a08\u7b97\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u7d71\u5408\u65b9\u6cd5\u306b\u306f\u3001\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u3068\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u304c\u3042\u3063\u3066\u3001\u305d\u308c\u305e\u308c\u91cd\u307f\u304c\u7570\u306a\u308b\u3002<\/p>\n\n\n\n

\u4f8b\u3048\u3070\u3001EZR\u516c\u5f0f\u30de\u30cb\u30e5\u30a2\u30eb\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u3092\u7528\u3044\u305f\u30d5\u30a9\u30ec\u30b9\u30c8\u30d7\u30ed\u30c3\u30c8\u3092\u898b\u308b\u3068\u3001\u53f3\u7aef\u306eWeight(common), Weight(random)\u3067\u5024\u304c\u7570\u306a\u3063\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n

Weight(common)\u304c\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u3067\u3001Weight(random)\u304c\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\"\"
\u30d5\u30a9\u30ec\u30b9\u30c8\u30d7\u30ed\u30c3\u30c8\u306e\u4f8b<\/figcaption><\/figure>\n\n\n\n

\u5b9f\u969b\u3069\u3093\u306a\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u304b\u6539\u3081\u3066\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n

\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>\r\n

\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f<\/h2>\n\n\n\n

\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u306f\u3001\u6a19\u6e96\u8aa4\u5dee\u306e2\u4e57\u306e\u9006\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u6a19\u6e96\u8aa4\u5dee\u306f\u3001\u70b9\u63a8\u5b9a\u5024\u306e\u63a8\u5b9a\u7cbe\u5ea6\u3092\u8868\u3057\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u3068\u5c0f\u3055\u304f\u306a\u308b\u3002<\/p>\n\n\n\n

\u6a19\u6e96\u8aa4\u5dee\u306e\uff12\u4e57\u306e\u9006\u6570\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5927\u304d\u304f\u5f71\u97ff\u529b\u306e\u5927\u304d\u3044\u7814\u7a76\u306f\u3001\u5c0f\u3055\u3044\u6a19\u6e96\u8aa4\u5dee\u306a\u306e\u3067\u3001\u305d\u306e\uff12\u4e57\u306e\u9006\u6570\u306f\u3001\u5927\u304d\u306a\u91cd\u307f\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\u5358\u7d14\u306a\u5834\u5408\u3092\u8003\u3048\u3066\u3001\u7c97\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u3068\u3059\u308b\u3068\u3001\u307e\u305a\u30aa\u30c3\u30ba\u6bd4\u3068\u6a19\u6e96\u8aa4\u5dee\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

\u3042\u308b\u7814\u7a76\u306e2×2\u5206\u5272\u8868<\/p>\n\n\n\n

<\/th>\u75be\u75c5\u3042\u308a<\/th>\u75be\u75c5\u306a\u3057<\/th><\/tr><\/thead>
\u66dd\u9732\u3042\u308a<\/td>a<\/td>c<\/td><\/tr>
\u66dd\u9732\u306a\u3057<\/td>b<\/td>d<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u30aa\u30c3\u30ba\u6bd4 OR<\/p>\n\n\n\n

$$ OR = \\frac{ad}{bc} $$<\/p>\n\n\n\n\n\n\n\n

\uff08\u306e\u3061\u306e\u8a08\u7b97\u3067\u306f\u5bfe\u6570\u3092\u3068\u3063\u305f $\\log{OR}$ \u3067\u767b\u5834\u3059\u308b\u3002\uff09<\/p>\n\n\n\n

\u6a19\u6e96\u8aa4\u5dee se<\/p>\n\n\n\n

$$ se = \\sqrt{\\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} + \\frac{1}{d}} $$<\/p>\n\n\n\n\n\n\n\n

\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u5404\u7814\u7a76\u306e\u91cd\u307f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u91cd\u307f w<\/p>\n\n\n\n

$$ w = \\frac{1}{se^2} $$<\/p>\n\n\n\n\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f<\/h2>\n\n\n\n

\u91cd\u307f\u306e\u8a08\u7b97\u5f0f\u306b\u305f\u3069\u308a\u7740\u304f\u524d\u306b\u3001\u51fa\u767a\u70b9\u3068\u3057\u3066\u3001\u5747\u8cea\u6027\uff08\u3082\u3057\u304f\u306f\u7570\u8cea\u6027\uff09\u306e\u691c\u5b9a\u7d71\u8a08\u91cfQ1\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

\u5747\u8cea\u6027\u306e\u691c\u5b9a\u7d71\u8a08\u91cfQ1\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\u306f\u3001\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u3067\u306e\u91cd\u307f\u4ed8\u3051\u5e73\u5747\u70b9\u63a8\u5b9a\u5024\u304c\u6c42\u307e\u3063\u3066\u3044\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u3002<\/p>\n\n\n\n

\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u3067\u306e\u7d71\u5408\u70b9\u63a8\u5b9a\u5024 $ \\log{OR_f} $\uff08\u6dfb\u3048\u5b57\u306e f \u306f\u56fa\u5b9aFixed\u3092\u8868\u3057\u3066\u3044\u308b\uff09<\/p>\n\n\n\n

\uff08\u8a08\u7b97\u306e\u90fd\u5408\u4e0a\u5bfe\u6570\u306e\u307e\u307e\u306b\u3059\u308b\uff09<\/p>\n\n\n\n

$$ \\log{OR_f} = \\frac{\\sum{w \\times \\log{OR}}}{\\sum w} $$<\/p>\n\n\n\n\n\n\n\n

\u5747\u8cea\u6027\u306e\u691c\u5b9a\u7d71\u8a08\u91cfQ1<\/p>\n\n\n\n

$$ Q_1 = \\sum{w \\times (\\log{OR} – \\log{OR_f})^2} $$<\/p>\n\n\n\n\n\n\n\n

\u5747\u8cea\u6027\u306e\u691c\u5b9a\u7d71\u8a08\u91cfQ1\u3068\u5404\u7814\u7a76\u306e\u91cd\u307f w \u3092\u4f7f\u3063\u3066\u3001\u7814\u7a76\u9593\u306e\u3070\u3089\u3064\u304d\u306e\u5927\u304d\u3055 \u03c4\uff08\u30bf\u30a6\uff09\uff12\u4e57\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

$$ \\tau^2 = \\frac{Q_1 – (k – 1)}{\\sum{w} – \\frac{\\sum{w^2}}{\\sum w}} $$<\/p>\n\n\n\n\n\n\n\n

k\u306f\u7d71\u5408\u3059\u308b\u7814\u7a76\u306e\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u30bf\u30a6\uff12\u4e57\u306f\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u3053\u3068\u3082\u3042\u308b\u304c\u3001\u305d\u306e\u5834\u5408\u306f\u30bc\u30ed\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

\u3064\u307e\u308a\u30bc\u30ed\u306e\u6642\u306f\u7814\u7a76\u9593\u306e\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u304f\u306a\u304f\u3001\u30bf\u30a6\uff12\u4e57\u3092\u52a0\u3048\u308b\u5fc5\u8981\u304c\u306a\u3044\u3068\u3044\u3046\u610f\u5473\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u30bf\u30a6\uff12\u4e57\u3092\u8003\u616e\u3057\u305f\u65b9\u6cd5\u304cDerSiminian-Laird (DL) \u306e\u65b9\u6cd5\u3067\u3001\u91cd\u307f\u8a08\u7b97\u306e\u969b\u306b\u5206\u6bcd\u306b\u30bf\u30a6\uff12\u4e57\u3092\u8db3\u3059\u3002<\/p>\n\n\n\n

$$ w_{DL} = \\frac{1}{\\tau^2 + se^2} $$<\/p>\n\n\n\n\n\n\n\n

\u3059\u308b\u3068\u3001\u7814\u7a76\u9593\u306e\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u304f\u30bf\u30a6\uff12\u4e57\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u91cd\u307f\u306f\u5c0f\u3055\u304f\u306a\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u30bf\u30a6\uff12\u4e57\u304c\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u3068\u7570\u306a\u308b\u90e8\u5206\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u6a19\u6e96\u8aa4\u5dee\u304c\u5927\u304d\u3044\uff08\u91cd\u307f\u304c\u5c0f\u3055\u3044\uff09\u7814\u7a76\u306e\u5834\u5408\u3001\u30bf\u30a6\uff12\u4e57\u306f\u305d\u308c\u307b\u3069\u8ca2\u732e\u3057\u306a\u3044\u304c\u3001\u6a19\u6e96\u8aa4\u5dee\u304c\u5c0f\u3055\u3044\uff08\u91cd\u307f\u304c\u5927\u304d\u3044\uff09\u7814\u7a76\u306e\u5834\u5408\u306f\u3001\u30bf\u30a6\uff12\u4e57\u306e\u52b9\u679c\u306f\u76f8\u5bfe\u7684\u306b\u5927\u304d\u304f\u306a\u308b\u3002<\/p>\n\n\n\n

\u3055\u3089\u306b\u3001\u3053\u306e\u30bf\u30a6\uff12\u4e57\u3092\u521d\u671f\u5024\u306b\u3057\u3066\u3001\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\uff08REML estimator) \u3092\u6c42\u3081\u308b\u3068\u3001EZR\u306e\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u7d50\u679c\u306b\u306a\u308b\u3002\uff08\u3082\u3057\u304b\u3059\u308b\u3068\u521d\u671f\u5024\u306f\u9055\u3046\u304b\u3082\u3057\u308c\u306a\u3044\u3002\uff09<\/p>\n\n\n\n

REML\u306f\u3001\u7e70\u308a\u8fd4\u3057\u8a08\u7b97\u3092\u8981\u3059\u308b\u3002<\/p>\n\n\n\n

\u305d\u3057\u3066\u7e70\u308a\u8fd4\u3057\u8a08\u7b97\u3059\u308b\u5f0f\u81ea\u4f53\u306f\u5358\u7d14\u306b\u306f\u66f8\u304d\u8868\u305b\u306a\u3044\u3002<\/p>\n\n\n\n

DL\u306e\u30bf\u30a6\uff12\u4e57\u3092\u3088\u308a\u9069\u5207\u306b\u78e8\u304d\u4e0a\u3052\u305f\u3001\u3088\u308a\u3088\u3044\u5024\u3068\u601d\u3046\u7a0b\u5ea6\u3067\u3088\u3044\u3060\u308d\u3046\u3002<\/p>\n\n\n\n

REML\u6cd5\u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\u3002\uff08\u521d\u671f\u5024\u306fDL\u306e\u30bf\u30a6\uff12\u4e57\u3068\u306f\u7570\u306a\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3068\u601d\u3046\u306e\u306f\u3001\u4ee5\u4e0b\u306e\u30d6\u30ed\u30b0\u8a18\u4e8b\u306e\u6700\u5f8c\u3067\u3001\u8a08\u7b97\u304c\u5408\u308f\u306a\u304b\u3063\u305f\u3053\u3068\u306b\u8d77\u56e0\u3059\u308b\u3002\uff09<\/p>\n\n\n

\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \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\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…<\/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

\u307e\u3068\u3081<\/h2>\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306b\u304a\u3051\u308b\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u3068\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u306e\u9055\u3044\u3092\u6539\u3081\u3066\u78ba\u8a8d\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n

\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u306f\u3001\u7814\u7a76\u5185\u306e\u3070\u3089\u3064\u304d\u306e\u6307\u6a19\uff08\u63a8\u5b9a\u7cbe\u5ea6\u306e\u6307\u6a19\uff09\u3068\u3057\u3066\u6a19\u6e96\u8aa4\u5dee\u3092\u7528\u3044\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u91cd\u307f\u306f\u3001\u6a19\u6e96\u8aa4\u5dee\u306b\u52a0\u3048\u3066\u3001\u30bf\u30a6\uff12\u4e57\u3068\u3044\u3046\u7814\u7a76\u9593\u306e\u3070\u3089\u3064\u304d\u3092\u8868\u3059\u6307\u6a19\u3092\u8003\u616e\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u30bf\u30a6\uff12\u4e57\u304c\u5927\u304d\u304f\u7814\u7a76\u9593\u306e\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u56fa\u5b9a\u52b9\u679c\u3067\u5927\u304d\u306a\u91cd\u307f\u304c\u3042\u3063\u305f\u7814\u7a76\u304c\u76f8\u5bfe\u7684\u306b\u8efd\u304f\u306a\u308b\u7406\u5c48\u306b\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u53c2\u8003\u306b\u306a\u308c\u3070\u3002<\/p>\n\n\n\n

\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n
\"\u65b0\u7248<\/a><\/figure>\n\n\n\n
<\/div>\n\n\n\n
\n

\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