{"id":4015,"date":"2025-06-17T08:04:21","date_gmt":"2025-06-16T23:04:21","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4015"},"modified":"2025-06-27T15:14:56","modified_gmt":"2025-06-27T06:14:56","slug":"generalized-estimating-equations-gee-fundamentals-and-clinical-research-applications","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/generalized-estimating-equations-gee-fundamentals-and-clinical-research-applications\/","title":{"rendered":"\u4e00\u822c\u5316\u63a8\u5b9a\u65b9\u7a0b\u5f0f(GEE)\u306e\u57fa\u790e\u3068\u81e8\u5e8a\u7814\u7a76\u3067\u306e\u5fdc\u7528"},"content":{"rendered":"\n<p>\u81e8\u5e8a\u7814\u7a76\u3084\u75ab\u5b66\u7814\u7a76\u306b\u304a\u3044\u3066\u3001\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\u3055\u308c\u308b\u30c7\u30fc\u30bf\u3084\u30af\u30e9\u30b9\u30bf\u30fc\u5316\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306f\u983b\u7e41\u306b\u767b\u5834\u3059\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf\u3067\u306f\u3001\u540c\u3058\u88ab\u9a13\u8005\u304b\u3089\u306e\u6e2c\u5b9a\u5024\u3084\u540c\u3058\u30af\u30e9\u30b9\u30bf\u30fc\u5185\u306e\u89b3\u6e2c\u5024\u306b\u306f\u76f8\u95a2\u304c\u3042\u308b\u305f\u3081\u3001\u5f93\u6765\u306e\u72ec\u7acb\u6027\u3092\u4eee\u5b9a\u3059\u308b\u7d71\u8a08\u624b\u6cd5\u3067\u306f\u9069\u5207\u306a\u89e3\u6790\u304c\u3067\u304d\u306a\u3044\u3002\u4e00\u822c\u5316\u63a8\u5b9a\u65b9\u7a0b\u5f0f\uff08Generalized Estimating Equations: GEE\uff09\u306f\u3001\u3053\u306e\u3088\u3046\u306a\u76f8\u95a2\u306e\u3042\u308b\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001\u30ed\u30d0\u30b9\u30c8\u306a\u63a8\u5b9a\u3092\u53ef\u80fd\u306b\u3059\u308b\u5f37\u529b\u306a\u7d71\u8a08\u7684\u624b\u6cd5\u3067\u3042\u308b\u3002\u672c\u7a3f\u3067\u306f\u3001GEE\u306e\u6982\u8981\u304b\u3089\u3001\u985e\u4f3c\u3059\u308b\u624b\u6cd5\u3067\u3042\u308b\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb\uff08GLMM\uff09\u3068\u306e\u9055\u3044\u3001\u5177\u4f53\u7684\u306a\u9069\u7528\u5834\u9762\u3001<strong>4\u3064\u306e\u7570\u306a\u308b\u30c7\u30fc\u30bf\u30bf\u30a4\u30d7\u306b\u5fdc\u3058\u305f\u81e8\u5e8a\u7814\u7a76\u3067\u306e\u5fdc\u7528\u4f8b\u3001\u305d\u3057\u3066\u305d\u308c\u305e\u308c\u306eR\u3092\u7528\u3044\u305f\u8a08\u7b97\u4f8b<\/strong>\u307e\u3067\u3092\u7db2\u7f85\u7684\u306b\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u822c\u5316\u63a8\u5b9a\u65b9\u7a0b\u5f0f\u306e\u6982\u8981<\/h2>\n\n\n\n<p>\u4e00\u822c\u5316\u63a8\u5b9a\u65b9\u7a0b\u5f0f\uff08GEE\uff09\u306f\u3001\u5bfe\u8c61\u5185\u3067\u76f8\u95a2\u306e\u3042\u308b\u30c7\u30fc\u30bf\uff08\u4f8b\u3048\u3070\u3001\u540c\u3058\u60a3\u8005\u304b\u3089\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3084\u3001\u5bb6\u65cf\u5185\u3067\u8907\u6570\u306e\u30e1\u30f3\u30d0\u30fc\u304b\u3089\u5f97\u3089\u308c\u305f\u30c7\u30fc\u30bf\u306a\u3069\uff09\u306e\u89e3\u6790\u306b\u7528\u3044\u3089\u308c\u308b\u7d71\u8a08\u7684\u624b\u6cd5\u3067\u3042\u308b\u3002GEE\u306f\u3001<strong>\u5e73\u5747\u69cb\u9020<\/strong>\uff08\u76ee\u7684\u5909\u6570\u306e\u5e73\u5747\u304c\u4e88\u6e2c\u5909\u6570\u306b\u3088\u3063\u3066\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\uff09\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3053\u3068\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001<strong>\u76f8\u95a2\u69cb\u9020\u3092\u300c\u30cb\u30e5\u30fc\u30b5\u30f3\u30b9\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\u300d\uff08\u5f8c\u8ff0\uff09\u3068\u3057\u3066\u6271\u3046<\/strong>\u3053\u3068\u3067\u3001\u76f8\u95a2\u69cb\u9020\u304c\u8aa4\u3063\u3066\u6307\u5b9a\u3055\u308c\u305f\u5834\u5408\u3067\u3082\u56de\u5e30\u4fc2\u6570\u306e\u63a8\u5b9a\u5024\u304c\u30ed\u30d0\u30b9\u30c8\uff08\u9811\u5065\uff09\u3067\u3042\u308b\u3053\u3068\u304c\u7279\u5fb4\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>GEE\u306f\u3001\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb\uff08GLM\uff09\u306e\u67a0\u7d44\u307f\u3092\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3042\u308a\u3001\u5fdc\u7b54\u5909\u6570\u306e\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u306b\u9650\u3089\u305a\u3001\u4e8c\u9805\u5206\u5e03\u3001\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3001\u9806\u5e8f\u30ed\u30b8\u30c3\u30c8\u306a\u3069\u3001<strong>\u6307\u6570\u578b\u5206\u5e03\u65cf\u306b\u5c5e\u3059\u308b\u69d8\u3005\u306a\u5206\u5e03\u306b\u5bfe\u5fdc<\/strong>\u3067\u304d\u308b\u3002\u63a8\u5b9a\u306f\u3001\u5404\u5bfe\u8c61\u5185\u3067\uff08\u672c\u5f53\u306f\u72ec\u7acb\u3067\u306f\u306a\u3044\u304c\u3001\u3042\u3048\u3066\uff09\u72ec\u7acb\u306a\u89b3\u6e2c\u5024\u304c\u5b58\u5728\u3059\u308b\u3068\u3044\u3046\u4eee\u5b9a\u306e\u4e0b\u3067\u5f97\u3089\u308c\u308b\u6a19\u6e96\u8aa4\u5dee\u3092\u3001\u30b5\u30f3\u30c9\u30a4\u30c3\u30c1\u63a8\u5b9a\uff08\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\uff09\u306b\u3088\u3063\u3066\u8abf\u6574\u3059\u308b\u3053\u3068\u3067\u884c\u308f\u308c\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u76f8\u95a2\u306e\u5177\u4f53\u7684\u306a\u69cb\u9020\u3092\u6b63\u78ba\u306b\u7279\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u306a\u304f\u3001\u89e3\u6790\u306e\u67d4\u8edf\u6027\u304c\u9ad8\u307e\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30cb\u30e5\u30fc\u30b5\u30f3\u30b9\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u306e\u76f8\u95a2\u69cb\u9020<\/h3>\n\n\n\n<p>GEE\u306b\u304a\u3051\u308b\u300c\u30cb\u30e5\u30fc\u30b5\u30f3\u30b9\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\uff08Nuisance Parameter\uff09\u300d\uff08\u5c40\u5916\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3082\u8a00\u308f\u308c\u308b\uff09\u3068\u3057\u3066\u306e\u76f8\u95a2\u69cb\u9020\u306e\u6271\u3044\u306f\u3001\u3053\u306e\u624b\u6cd5\u306e\u91cd\u8981\u306a\u7279\u5fb4\u3067\u3042\u308a\u3001\u5f37\u307f\u306e\u4e00\u3064\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u306b\u304a\u3044\u3066\u3001\u95a2\u5fc3\u306e\u3042\u308b\u4e3b\u8981\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u4f8b\u3048\u3070\u3001\u6cbb\u7642\u52b9\u679c\u3092\u793a\u3059\u56de\u5e30\u4fc2\u6570\uff09\u3068\u306f\u5225\u306b\u3001\u30e2\u30c7\u30eb\u306e\u9069\u5408\u306b\u5fc5\u8981\u3067\u306f\u3042\u308b\u3082\u306e\u306e\u3001\u76f4\u63a5\u7684\u306a\u7814\u7a76\u76ee\u7684\u306e\u5bfe\u8c61\u3067\u306f\u306a\u3044\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u300c\u30cb\u30e5\u30fc\u30b5\u30f3\u30b9\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\u300d\u3068\u547c\u3076\u3002GEE\u3067\u306f\u3001\u30c7\u30fc\u30bf\u5185\u306e\u76f8\u95a2\u69cb\u9020\uff08\u4f8b\uff1a\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\u9593\u306e\u76f8\u95a2\u306e\u30d1\u30bf\u30fc\u30f3\uff09\u304c\u3053\u308c\u306b\u8a72\u5f53\u3059\u308b\u3002<\/p>\n\n\n\n<p>GEE\u306e\u8a2d\u8a08\u601d\u60f3\u306f\u3001\u300c<strong>\u5e73\u5747\u69cb\u9020\u3092\u6b63\u3057\u304f\u6307\u5b9a\u3059\u308c\u3070\u3001\u76f8\u95a2\u69cb\u9020\u304c\u5b8c\u74a7\u306b\u6307\u5b9a\u3055\u308c\u3066\u3044\u306a\u304f\u3066\u3082\u3001\u56de\u5e30\u4fc2\u6570\u306e\u63a8\u5b9a\u5024\u306f\u4e00\u81f4\u6027\u3092\u4fdd\u3064\uff08\u6b63\u3057\u3044\u5024\u306b\u8fd1\u3065\u304f\uff09<\/strong>\u300d\u3068\u3044\u3046\u70b9\u306b\u3042\u308b\u3002\u3053\u308c\u306f\u3001GEE\u304c\u3001\u5404\u89b3\u6e2c\u5358\u4f4d\uff08\u4f8b\uff1a\u60a3\u8005\uff09\u5185\u306e\u76f8\u95a2\u3092\u660e\u793a\u7684\u306b\u30e2\u30c7\u30eb\u5316\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u305d\u306e\u5b58\u5728\u3092\u300c\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\u300d\u3068\u3044\u3046\u5f62\u3067\u88dc\u6b63\u3059\u308b\u3053\u3068\u3067\u8003\u616e\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001GEE\u306f\u4ee5\u4e0b\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u63a8\u5b9a\u3092\u884c\u3046\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u307e\u305a\u3001\u5404\u89b3\u6e2c\u5358\u4f4d\u5185\u306e\u30c7\u30fc\u30bf\u304c\u72ec\u7acb\u3067\u3042\u308b\u3068\u3044\u3046\u300c\u4f5c\u696d\u72ec\u7acb\u6027\u300d\u3092\u4eee\u5b9a\u3057\u3066\u3001\u5e73\u5747\u69cb\u9020\u306e\u56de\u5e30\u4fc2\u6570\u3092\u66ab\u5b9a\u7684\u306b\u63a8\u5b9a\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u3053\u306e\u66ab\u5b9a\u7684\u306a\u56de\u5e30\u4fc2\u6570\u3092\u7528\u3044\u3066\u3001\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf\u9593\u306e\u76f8\u95a2\u3092\u63a8\u5b9a\u3059\u308b\uff08\u4f8b\u3048\u3070\u3001\u300c\u4ea4\u63db\u53ef\u80fd\u300d\u3084\u300cAR(1)\u300d\u3068\u3044\u3063\u305f\u4eee\u5b9a\u306b\u57fa\u3065\u304d\u3001\u30af\u30e9\u30b9\u30bf\u30fc\u5185\u306e\u76f8\u95a2\u3092\u8a08\u7b97\u3059\u308b\uff09\u3002<\/li>\n\n\n\n<li>\u3053\u306e\u63a8\u5b9a\u3055\u308c\u305f\u76f8\u95a2\u69cb\u9020\u3092\u7528\u3044\u3066\u3001\u56de\u5e30\u4fc2\u6570\u3092\u518d\u63a8\u5b9a\u3059\u308b\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u53ce\u675f\u3059\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3059\u3002<\/li>\n\n\n\n<li>\u6700\u7d42\u7684\u306a\u56de\u5e30\u4fc2\u6570\u306e\u63a8\u5b9a\u5024\u304c\u5f97\u3089\u308c\u305f\u3089\u3001\u305d\u306e\u6a19\u6e96\u8aa4\u5dee\u3092\u300c<strong>\u30b5\u30f3\u30c9\u30a4\u30c3\u30c1\u63a8\u5b9a\u91cf\uff08\u307e\u305f\u306f\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\uff09<\/strong>\u300d\u3068\u3044\u3046\u7279\u6b8a\u306a\u65b9\u6cd5\u3067\u7b97\u51fa\u3059\u308b\u3002\u3053\u306e\u30b5\u30f3\u30c9\u30a4\u30c3\u30c1\u63a8\u5b9a\u91cf\u306b\u3088\u3063\u3066\u3001\u76f8\u95a2\u69cb\u9020\u306e\u4eee\u5b9a\u304c\u591a\u5c11\u9593\u9055\u3063\u3066\u3044\u3066\u3082\u3001\u6a19\u6e96\u8aa4\u5dee\u306e\u63a8\u5b9a\u3092\u9811\u5065\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u3088\u308a\u3001\u5206\u6790\u8005\u306f\u76f8\u95a2\u69cb\u9020\u306e\u8907\u96d1\u306a\u8a73\u7d30\u306b\u904e\u5ea6\u306b\u3053\u3060\u308f\u308b\u5fc5\u8981\u304c\u306a\u304f\u306a\u308b\u3002\u4f8b\u3048\u3070\u3001\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\u30c7\u30fc\u30bf\u306b\u304a\u3044\u3066\u3001\u6e2c\u5b9a\u6642\u70b9\u304c\u4e0d\u898f\u5247\u3067\u3042\u3063\u305f\u308a\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u304c\u591a\u304b\u3063\u305f\u308a\u3059\u308b\u5834\u5408\u3067\u3082\u3001GEE\u306f\u6bd4\u8f03\u7684\u5bb9\u6613\u306b\u9069\u7528\u3067\u304d\u308b\u3002\u3053\u306e\u67d4\u8edf\u6027\u3068\u30ed\u30d0\u30b9\u30c8\u6027\u304c\u3001GEE\u304c\u81e8\u5e8a\u7814\u7a76\u3067\u7528\u3044\u3089\u308c\u308b\u7406\u7531\u3068\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb (GLMM) \u3068\u306e\u9055\u3044<\/h2>\n\n\n\n<p>GEE\u3068\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb\uff08GLMM\uff09\u306f\u3001\u3044\u305a\u308c\u3082\u76f8\u95a2\u306e\u3042\u308b\u30c7\u30fc\u30bf\u306b\u5bfe\u5fdc\u3067\u304d\u308b\u5f37\u529b\u306a\u624b\u6cd5\u3067\u3042\u308b\u304c\u3001\u305d\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3068\u76ee\u7684\u306b\u306f\u91cd\u8981\u306a\u9055\u3044\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\u7279\u5fb4<\/td><td>\u4e00\u822c\u5316\u63a8\u5b9a\u65b9\u7a0b\u5f0f (GEE)<\/td><td>\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb (GLMM)<\/td><\/tr><tr><td>\u30a2\u30d7\u30ed\u30fc\u30c1<\/td><td>\u6bcd\u96c6\u56e3\u5e73\u5747\u306b\u5bfe\u3059\u308b\u56de\u5e30\u4fc2\u6570\u306e\u63a8\u5b9a\uff08\u96c6\u56e3\u5e73\u5747\u52b9\u679c\uff09<\/td><td>\u500b\u4f53\u5dee\u3092\u8003\u616e\u3057\u305f\u56de\u5e30\u4fc2\u6570\u306e\u63a8\u5b9a\uff08\u500b\u4f53\u30ec\u30d9\u30eb\u3067\u306e\u52b9\u679c\uff09<\/td><\/tr><tr><td>\u63a8\u5b9a\u306e\u7126\u70b9<\/td><td>\u5e73\u5747\u69cb\u9020\u306e\u63a8\u5b9a\u306b\u4e3b\u773c\u3002\u76f8\u95a2\u69cb\u9020\u306f\u30cb\u30e5\u30fc\u30b5\u30f3\u30b9\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u6271\u3046\u3002<\/td><td>\u5e73\u5747\u69cb\u9020\u3068\u5206\u6563\u5171\u5206\u6563\u69cb\u9020\u306e\u4e21\u65b9\u3092\u660e\u793a\u7684\u306b\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3002<\/td><\/tr><tr><td>\u76f8\u95a2\u69cb\u9020<\/td><td>\u8aa4\u3063\u3066\u6307\u5b9a\u3057\u3066\u3082\u63a8\u5b9a\u5024\u306f\u30ed\u30d0\u30b9\u30c8\u3002<\/td><td>\u660e\u793a\u7684\u306b\u6307\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u8aa4\u308b\u3068\u63a8\u5b9a\u306b\u504f\u308a\u304c\u751f\u3058\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/td><\/tr><tr><td>\u6b20\u640d\u30c7\u30fc\u30bf<\/td><td>\u6b20\u640d\u30e1\u30ab\u30cb\u30ba\u30e0\u304cMCAR (Missing Completely at Random) \u307e\u305f\u306f MAR (Missing at Random) \u306e\u5834\u5408\u306b\u5bfe\u5fdc\u53ef\u80fd\u3002MCAR\u304c\u7406\u60f3\u7684\u3002<\/td><td>MAR (Missing at Random) \u306e\u6b20\u640d\u30c7\u30fc\u30bf\u306b\u5bfe\u5fdc\u3057\u3084\u3059\u3044\u3002<\/td><\/tr><tr><td>\u4eee\u5b9a<\/td><td>\u89b3\u6e2c\u5024\u306e\u72ec\u7acb\u6027\u306b\u5bfe\u3059\u308b\u4eee\u5b9a\u306f\u4e0d\u8981\u3002\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\u3092\u7528\u3044\u308b\u3002<\/td><td>\u30e9\u30f3\u30c0\u30e0\u52b9\u679c\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3068\u3044\u3046\u4eee\u5b9a\u306a\u3069\u304c\u5fc5\u8981\u3002<\/td><\/tr><tr><td>\u4e3b\u306a\u7528\u9014<\/td><td>\u96c6\u56e3\u30ec\u30d9\u30eb\u306e\u52b9\u679c\u3092\u63a8\u5b9a\u3057\u305f\u3044\u5834\u5408\u3002<\/td><td>\u500b\u4f53\u30ec\u30d9\u30eb\u306e\u5909\u52d5\u3084\u500b\u4f53\u9593\u306e\u7570\u8cea\u6027\u3092\u8003\u616e\u3057\u305f\u3044\u5834\u5408\u3002<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u7c21\u5358\u306b\u8a00\u3048\u3070\u3001GEE\u306f\u300c\u96c6\u56e3\u5168\u4f53\u3068\u3057\u3066\u3069\u3046\u304b\u300d\u3068\u3044\u3046\u554f\u3044\u306b\u7b54\u3048\u308b\u306e\u306b\u9069\u3057\u3066\u304a\u308a\u3001GLMM\u306f\u300c\u500b\u3005\u306e\u500b\u4f53\u304c\u3069\u306e\u3088\u3046\u306b\u7570\u306a\u308b\u304b\u300d\u3068\u3044\u3046\u554f\u3044\u306b\u7b54\u3048\u308b\u306e\u306b\u9069\u3057\u3066\u3044\u308b\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u822c\u5316\u63a8\u5b9a\u65b9\u7a0b\u5f0f\u306e\u4f7f\u3044\u6240<\/h3>\n\n\n\n<p>GEE\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u72b6\u6cc1\u3067\u7279\u306b\u6709\u7528\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\u30c7\u30fc\u30bf<\/strong>: \u540c\u3058\u88ab\u9a13\u8005\u304b\u3089\u8907\u6570\u56de\u306b\u308f\u305f\u3063\u3066\u6e2c\u5b9a\u3055\u308c\u305f\u30c7\u30fc\u30bf\uff08\u4f8b\uff1a\u85ac\u7269\u6295\u4e0e\u5f8c\u306e\u8840\u5727\u306e\u7d4c\u6642\u5909\u5316\u3001\u6cbb\u7642\u52b9\u679c\u306e\u8ffd\u8de1\uff09\u3002<\/li>\n\n\n\n<li><strong>\u30af\u30e9\u30b9\u30bf\u30fc\u5316\u30c7\u30fc\u30bf<\/strong>: \u5bb6\u65cf\u3001\u5b66\u6821\u3001\u75c5\u9662\u306a\u3069\u3001\u7279\u5b9a\u306e\u30b0\u30eb\u30fc\u30d7\u5185\u306b\u5c5e\u3059\u308b\u500b\u4eba\u304b\u3089\u306e\u30c7\u30fc\u30bf\uff08\u4f8b\uff1a\u540c\u3058\u5bb6\u65cf\u5185\u306e\u30e1\u30f3\u30d0\u30fc\u306e\u5065\u5eb7\u72b6\u614b\u3001\u540c\u3058\u5b66\u6821\u306e\u751f\u5f92\u306e\u5b66\u7fd2\u6210\u7e3e\uff09\u3002<\/li>\n\n\n\n<li><strong>\u7e26\u65ad\u7814\u7a76<\/strong>: \u9577\u671f\u9593\u306b\u308f\u305f\u3063\u3066\u8ffd\u8de1\u8abf\u67fb\u3055\u308c\u308b\u7814\u7a76\u3067\u3001\u88ab\u9a13\u8005\u5185\u306e\u76f8\u95a2\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5834\u5408\u3002<\/li>\n\n\n\n<li><strong>\u96c6\u56e3\u30ec\u30d9\u30eb\u306e\u52b9\u679c\u63a8\u5b9a<\/strong>: \u500b\u3005\u306e\u5909\u52d5\u3088\u308a\u3082\u3001\u4ecb\u5165\u3084\u56e0\u5b50\u306e\u96c6\u56e3\u5168\u4f53\u3078\u306e\u5e73\u5747\u7684\u306a\u52b9\u679c\u306b\u95a2\u5fc3\u304c\u3042\u308b\u5834\u5408\u3002<\/li>\n\n\n\n<li><strong>\u975e\u6b63\u898f\u5206\u5e03\u306e\u5fdc\u7b54\u5909\u6570<\/strong>: \u4e8c\u9805\u30c7\u30fc\u30bf\uff08\u6210\u529f\/\u5931\u6557\uff09\u3001\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\uff08\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u6570\uff09\u3001\u9806\u5e8f\u5c3a\u5ea6\u30c7\u30fc\u30bf\u306a\u3069\u3001\u5fdc\u7b54\u5909\u6570\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u308f\u306a\u3044\u5834\u5408\u3002<\/li>\n<\/ul>\n\n\n\n<div id=\"biost-2119215349\" 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\">\u81e8\u5e8a\u7814\u7a76\u306e\u5177\u4f53\u4f8b\u3068R\u306b\u3088\u308b\u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u30014\u3064\u306e\u7570\u306a\u308b\u30c7\u30fc\u30bf\u30bf\u30a4\u30d7\uff08\u9023\u7d9a\u30c7\u30fc\u30bf\u30012\u9805\u30a2\u30a6\u30c8\u30ab\u30e0\u3001\u9806\u5e8f\u30ab\u30c6\u30b4\u30ea\u3001\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\uff09\u306b\u3064\u3044\u3066\u3001GEE\u306e\u5177\u4f53\u7684\u306a\u9069\u7528\u4f8b\u3068R\u306b\u3088\u308b\u8a08\u7b97\u4f8b\u3092\u793a\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u9023\u7d9a\u30c7\u30fc\u30bf\uff1a\u9ad8\u8840\u5727\u6cbb\u7642\u85ac\u306e\u52b9\u679c\u691c\u8a3c<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u76ee\u7684<\/strong>: \u65b0\u3057\u3044\u964d\u5727\u5264\u306e\u8840\u5727\u964d\u4e0b\u52b9\u679c\u3092\u3001\u5f93\u6765\u85ac\u3068\u6bd4\u8f03\u3057\u3066\u8a55\u4fa1\u3059\u308b\u3002 <\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf<\/strong>: \u8907\u6570\u306e\u60a3\u8005\u3092\u65b0\u85ac\u7fa4\u3068\u5f93\u6765\u85ac\u7fa4\u306b\u5272\u308a\u4ed8\u3051\u3001\u6cbb\u7642\u958b\u59cb\u524d\u30011\u30f6\u6708\u5f8c\u30013\u30f6\u6708\u5f8c\u30016\u30f6\u6708\u6642\u70b9\u3067\u306e\u53ce\u7e2e\u671f\u8840\u5727\u3092\u6e2c\u5b9a\u3002 <\/li>\n\n\n\n<li><strong>GEE\u306e\u9069\u7528<\/strong>: \u60a3\u8005\u5185\u306e\u8840\u5727\u6e2c\u5b9a\u5024\u306e\u76f8\u95a2\uff08\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\uff09\u3092\u8003\u616e\u3057\u3001\u65b0\u85ac\u306e\u5e73\u5747\u7684\u306a\u52b9\u679c\u3092\u5f93\u6765\u85ac\u3068\u6bd4\u8f03\u3057\u3066\u63a8\u5b9a\u3059\u308b\u3002\u5fdc\u7b54\u5909\u6570\u306f\u9023\u7d9a\u5909\u6570\uff08\u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>R \u306b\u3088\u308b\u8a08\u7b97\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3068\u8aad\u307f\u8fbc\u307f\n# install.packages(\"geepack\")\nlibrary(geepack)\n\n# \u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u4f5c\u6210 (\u9023\u7d9a\u30c7\u30fc\u30bf)\nset.seed(123)\nid &lt;- rep(1:100, each = 4) # \u60a3\u8005ID (100\u4eba)\ntime &lt;- rep(c(0, 1, 3, 6), times = 100) # \u6e2c\u5b9a\u6642\u70b9 (0\u30f6\u6708, 1\u30f6\u6708, 3\u30f6\u6708, 6\u30f6\u6708)\n# \u6cbb\u7642\u30b0\u30eb\u30fc\u30d7 (0:\u5f93\u6765\u7fa4, 1:\u65b0\u85ac\u7fa4) - \u30e9\u30f3\u30c0\u30e0\u306b\u5272\u308a\u4ed8\u3051\ntrt &lt;- rep(sample(c(0, 1), 100, replace = TRUE), each = 4)\n\n# \u53ce\u7e2e\u671f\u8840\u5727\u306e\u751f\u6210 (\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u306f\u9ad8\u3081\u3001\u6642\u9593\u7d4c\u904e\u3068\u6cbb\u7642\u52b9\u679c\u3067\u4f4e\u4e0b)\n# \u5f93\u6765\u7fa4: \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3140 mmHg, \u6642\u9593\u7d4c\u904e\u3067\u7de9\u3084\u304b\u306b\u4f4e\u4e0b\n# \u65b0\u85ac\u7fa4: \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3140 mmHg, \u6642\u9593\u7d4c\u904e\u3067\u3088\u308a\u5927\u304d\u304f\u4f4e\u4e0b\nsbp &lt;- numeric(length(id))\nfor (i in 1:length(id)) {\n    base_sbp &lt;- rnorm(1, 140, 5) # \u500b\u4f53\u3054\u3068\u306e\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u306e\u3070\u3089\u3064\u304d\n    if (trt&#91;i] == 0) { # \u5f93\u6765\u7fa4\n        sbp&#91;i] &lt;- base_sbp - 2 * time&#91;i] + rnorm(1, 0, 3)\n    } else { # \u65b0\u85ac\u7fa4\n        sbp&#91;i] &lt;- base_sbp - 5 * time&#91;i] + rnorm(1, 0, 3)\n    }\n}\n# \u8840\u5727\u304c\u6975\u7aef\u306b\u4f4e\u304f\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u8abf\u6574\nsbp&#91;sbp &lt; 100] &lt;- 100 + rnorm(sum(sbp &lt; 100), 0, 2)\n\ndata_sbp &lt;- data.frame(id, time, trt, round(sbp))\nhead(data_sbp)\n\n# GEE\u30e2\u30c7\u30eb\u306e\u5b9f\u884c (\u9023\u7d9a\u30c7\u30fc\u30bf)\n# family = gaussian: \u5fdc\u7b54\u5909\u6570\u304c\u9023\u7d9a\u3067\u3042\u308b\u305f\u3081\n# link = \"identity\": \u6052\u7b49\u30ea\u30f3\u30af\u95a2\u6570\nmodel_sbp_gee &lt;- geeglm(sbp ~ trt + time + trt:time,\n    id = id,\n    data = data_sbp,\n    family = gaussian(link = \"identity\"),\n    corstr = \"exchangeable\"\n) # \u4ea4\u63db\u53ef\u80fd\u306a\u76f8\u95a2\u69cb\u9020\u3092\u4eee\u5b9a\n\n# \u7d50\u679c\u306e\u8868\u793a\nsummary(model_sbp_gee)\n<\/code><\/pre>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt; # \u7d50\u679c\u306e\u8868\u793a\n&gt; summary(model_sbp_gee)\n\nCall:\ngeeglm(formula = sbp ~ trt + time + trt:time, family = gaussian(link = \"identity\"), \n    data = data_sbp, id = id, corstr = \"exchangeable\")\n\n Coefficients:\n            Estimate  Std.err     Wald Pr(&gt;|W|)    \n(Intercept) 140.5775   0.5688 61089.83   &lt;2e-16 ***\ntrt          -0.8562   0.8976     0.91     0.34    \ntime         -2.1036   0.1609   170.90   &lt;2e-16 ***\ntrt:time     -2.7607   0.2770    99.36   &lt;2e-16 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nCorrelation structure = exchangeable \nEstimated Scale Parameters:\n\n            Estimate Std.err\n(Intercept)    30.98   2.114\n  Link = identity \n\nEstimated Correlation Parameters:\n      Estimate Std.err\nalpha -0.02664 0.04149\nNumber of clusters:   100  Maximum cluster size: 4 \n&gt; <\/code><\/pre>\n\n\n\n<p>\u7d50\u679c\u306e\u898b\u65b9\u3068\u3057\u3066\u306f\u3001<code>trt<\/code>\uff08\u6cbb\u7642\u30b0\u30eb\u30fc\u30d7\uff09\u3001<code>time<\/code>\uff08\u6e2c\u5b9a\u6642\u70b9\uff09\u3001<code>trt:time<\/code>\uff08\u6cbb\u7642\u30b0\u30eb\u30fc\u30d7\u3068\u6642\u9593\u306e\u4ea4\u4e92\u4f5c\u7528\uff09\u306e\u4fc2\u6570\u3092\u78ba\u8a8d\u3059\u308b\u3002\u7279\u306b<code>trt:time<\/code>\u306e\u4fc2\u6570\u304c\u7d71\u8a08\u7684\u306b\u6709\u610f\u3067\u3042\u308c\u3070\u3001\u65b0\u85ac\u7fa4\u3068\u5f93\u6765\u7fa4\u3067\u8840\u5727\u306e\u7d4c\u6642\u5909\u5316\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002\u4eca\u56de\u306e\u7d50\u679c\u3067\u306f\u3001\u4ea4\u4e92\u4f5c\u7528\u304c\u6709\u610f\u3067\u3042\u308b\u305f\u3081\u3001\u65b0\u85ac\u7fa4\u3068\u5f93\u6765\u7fa4\u3067\u8840\u5727\u306e\u7d4c\u6642\u5909\u5316\u306b\u5dee\u7570\u304c\u3042\u308b\u3053\u3068\u304c\u793a\u5506\u3055\u308c\u3066\u3044\u308b\u304c\u3001\u4e3b\u52b9\u679c\u81ea\u4f53\u306f\u3001\u6709\u610f\u3067\u306f\u306a\u304f\u3001\u65b0\u85ac\u7fa4\u306e\u52b9\u679c\u304c\u793a\u5506\u3055\u308c\u305f\u308f\u3051\u3067\u306f\u306a\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2\u9805\u30a2\u30a6\u30c8\u30ab\u30e0\uff1a\u65b0\u898f\u6cbb\u7642\u6cd5\u306b\u3088\u308b\u75be\u60a3\u5bdb\u89e3\u7387\u306e\u6bd4\u8f03<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u76ee\u7684<\/strong>: \u65b0\u898f\u6cbb\u7642\u6cd5\u304c\u3001\u3042\u308b\u75be\u60a3\u306e\u5bdb\u89e3\uff08\u75c5\u72b6\u304c\u4e00\u6642\u7684\u307e\u305f\u306f\u6c38\u7d9a\u7684\u306b\u6d88\u5931\u3059\u308b\u3053\u3068\uff09\u9054\u6210\u7387\u3092\u3001\u5f93\u6765\u6cbb\u7642\u6cd5\u3068\u6bd4\u8f03\u3057\u3066\u5411\u4e0a\u3055\u305b\u308b\u304b\u3092\u8a55\u4fa1\u3059\u308b\u3002 <\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf<\/strong>: \u60a3\u8005\u3092\u65b0\u898f\u6cbb\u7642\u7fa4\u3068\u5f93\u6765\u6cbb\u7642\u7fa4\u306b\u5272\u308a\u4ed8\u3051\u3001\u6cbb\u7642\u958b\u59cb\u304b\u30891\u30f6\u6708\u30013\u30f6\u6708\u30016\u30f6\u6708\u5f8c\u306b\u5bdb\u89e3\u306e\u6709\u7121\uff080:\u306a\u3057, 1:\u3042\u308a\uff09\u3092\u8a55\u4fa1\u3002 <\/li>\n\n\n\n<li><strong>GEE\u306e\u9069\u7528<\/strong>: \u5404\u60a3\u8005\u306e\u5bdb\u89e3\u72b6\u6cc1\u306e\u7d4c\u6642\u5909\u5316\u306b\u304a\u3051\u308b\u76f8\u95a2\u3092\u8003\u616e\u3057\u3001\u65b0\u898f\u6cbb\u7642\u6cd5\u3068\u5f93\u6765\u6cbb\u7642\u6cd5\u306e\u5bdb\u89e3\u9054\u6210\u7387\u306e\u7fa4\u9593\u5dee\u3092\u8a55\u4fa1\u3059\u308b\u3002\u5fdc\u7b54\u5909\u6570\u306f\u4e8c\u5024\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>R \u306b\u3088\u308b\u8a08\u7b97\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3068\u8aad\u307f\u8fbc\u307f\n# install.packages(\"geepack\")\nlibrary(geepack)\n\n# \u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u4f5c\u6210 (2\u9805\u30a2\u30a6\u30c8\u30ab\u30e0)\nset.seed(456)\nid_binary &lt;- rep(1:80, each = 3) # \u60a3\u8005ID (80\u4eba)\ntime_binary &lt;- rep(c(1, 3, 6), times = 80) # \u6e2c\u5b9a\u6642\u70b9 (1\u30f6\u6708, 3\u30f6\u6708, 6\u30f6\u6708)\n# \u6cbb\u7642\u30b0\u30eb\u30fc\u30d7 (0:\u5f93\u6765\u7fa4, 1:\u65b0\u898f\u6cbb\u7642\u7fa4)\ntrt_binary &lt;- rep(sample(c(0, 1), 80, replace = TRUE), each = 3)\n\n# \u5bdb\u89e3\u306e\u6709\u7121 (0:\u306a\u3057, 1:\u3042\u308a) \u306e\u751f\u6210\n# \u65b0\u898f\u6cbb\u7642\u7fa4\u306f\u5bdb\u89e3\u7387\u304c\u9ad8\u304f\u3001\u6642\u9593\u7d4c\u904e\u3067\u5bdb\u89e3\u3057\u3084\u3059\u304f\u306a\u308b\nremission &lt;- numeric(length(id_binary))\nfor (i in 1:length(id_binary)) {\n    prob_remission &lt;- 0.2 # \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u306e\u78ba\u7387\n    if (trt_binary&#91;i] == 1) { # \u65b0\u898f\u6cbb\u7642\u7fa4\n        prob_remission &lt;- prob_remission + 0.1 * time_binary&#91;i] + 0.2 # \u6642\u9593\u3068\u6cbb\u7642\u52b9\u679c\n    } else { # \u5f93\u6765\u7fa4\n        prob_remission &lt;- prob_remission + 0.05 * time_binary&#91;i]\n    }\n    remission&#91;i] &lt;- rbinom(1, 1, min(prob_remission, 0.9)) # \u78ba\u7387\u304c1\u3092\u8d85\u3048\u306a\u3044\u3088\u3046\u306b\n}\n\ndata_remission &lt;- data.frame(id = id_binary, time = time_binary, trt = trt_binary, remission)\nhead(data_remission)\n\n# GEE\u30e2\u30c7\u30eb\u306e\u5b9f\u884c (2\u9805\u30a2\u30a6\u30c8\u30ab\u30e0)\n# family = binomial: \u5fdc\u7b54\u5909\u6570\u304c\u4e8c\u5024\u3067\u3042\u308b\u305f\u3081\n# link = \"logit\": \u30ed\u30b8\u30c3\u30c8\u30ea\u30f3\u30af\u95a2\u6570\nmodel_remission_gee &lt;- geeglm(remission ~ trt * as.factor(time),\n    id = id,\n    data = data_remission,\n    family = binomial(link = \"logit\"),\n    corstr = \"exchangeable\"\n)\n\n# \u7d50\u679c\u306e\u8868\u793a\nsummary(model_remission_gee)\n\n\nOR &lt;- exp(coef(model_remission_gee))\nCI_lower &lt;- exp(coef(model_remission_gee) - 1.96 * sqrt(diag(vcov(model_remission_gee)))) # vcov \u30ed\u30d0\u30b9\u30c8\u5206\u6563\u5171\u5206\u6563\u884c\u5217\nCI_upper &lt;- exp(coef(model_remission_gee) + 1.96 * sqrt(diag(vcov(model_remission_gee)))) # vcov \u30ed\u30d0\u30b9\u30c8\u5206\u6563\u5171\u5206\u6563\u884c\u5217\np_value &lt;- ifelse(summary(model_remission_gee)$coefficients&#91;, 4] &lt; 0.001, \"&lt;0.001\", round(summary(model_remission_gee)$coefficients&#91;, 4], 3))\n\nodds_ratios &lt;- data.frame(\n    OR = round(OR, 2),\n    CI_lower = round(CI_lower, 2),\n    CI_upper = round(CI_upper, 2),\n    p_value = p_value\n)\n\nprint(\"\u30aa\u30c3\u30ba\u6bd4\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593:\")\nprint(odds_ratios)\n<\/code><\/pre>\n\n\n\n<p>\u5b9f\u884c\u7d50\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;1] \"\u30aa\u30c3\u30ba\u6bd4\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593:\"\n&gt; print(odds_ratios)\n                       OR CI_lower CI_upper p_value\n(Intercept)          0.33     0.16     0.68   0.003\ntrt                  3.67     1.42     9.47   0.007\nas.factor(time)3     2.00     0.77     5.20   0.155\nas.factor(time)6     3.32     1.34     8.20   0.009\ntrt:as.factor(time)3 1.23     0.34     4.45   0.755\ntrt:as.factor(time)6 2.22     0.43    11.36   0.338<\/code><\/pre>\n\n\n\n<p>\u7d50\u679c\u306e\u89e3\u91c8\u3068\u3057\u3066\u306f\u3001<code>trt<\/code>\u306e\u4fc2\u6570\u304c\u7d71\u8a08\u7684\u306b\u6709\u610f\u3067\u3042\u308c\u3070\u3001\u65b0\u898f\u6cbb\u7642\u7fa4\u3068\u5f93\u6765\u7fa4\u306e\u9593\u3067\u5bdb\u89e3\u7387\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002\u307e\u305f\u3001\u4ea4\u4e92\u4f5c\u7528\u9805 <code>trt:as.factor <\/code>\u304c\u6709\u610f\u3067\u3042\u308c\u3070\u3001\u6642\u9593\u7684\u306a\u5909\u5316\u304c\u7570\u306a\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u4eca\u56de\u306f\u3001\u4ea4\u4e92\u4f5c\u7528\u306f\u6709\u610f\u3067\u306f\u306a\u304f\u3001\u6642\u9593\u306b\u3088\u3063\u3066\u7fa4\u9593\u5dee\u304c\u7570\u306a\u308b\u3068\u306f\u8a00\u3048\u306a\u3044\u3002<code>trt <\/code>\u306f \u30aa\u30c3\u30ba\u6bd4 3.67 \u3068\u8a08\u7b97\u3055\u308c\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u308b\uff08P = 0.007\uff09\u3068\u3044\u3046\u7d50\u679c\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u9806\u5e8f\u30ab\u30c6\u30b4\u30ea\uff1a\u75bc\u75db\u30b9\u30b3\u30a2\u306e\u7d4c\u6642\u7684\u5909\u5316\u306e\u6bd4\u8f03<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u76ee\u7684<\/strong>: \u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u304c\u3001\u547c\u5438\u5668\u75be\u60a3\u60a3\u8005\u306e\u5168\u822c\u7684\u75c7\u72b6\u30ec\u30d9\u30eb\u3092\u3001\u30d7\u30e9\u30bb\u30dc\u3068\u6bd4\u8f03\u3057\u3066\u52b9\u679c\u7684\u306b\u6539\u5584\u3059\u308b\u304b\u3092\u8a55\u4fa1\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf<\/strong>: \u60a3\u8005\u3092\u65b0\u6cbb\u7642\u7fa4\u3068\u30d7\u30e9\u30bb\u30dc\u7fa4\u306b\u5272\u308a\u4ed8\u3051\u3001\u51684\u56de\u306e\u6765\u9662\u6642\uff08y1, y2, y3, y4\uff09\u306b\u5168\u822c\u7684\u75c7\u72b6\u30ec\u30d9\u30eb\u30923\u6bb5\u968e\uff081 = poor\uff08\u60aa\u3044\uff09\u30012 = good\uff08\u826f\u3044\uff09\u30013 = excellent\uff08\u975e\u5e38\u306b\u826f\u3044\uff09\u3067\u8a55\u4fa1\u3002<\/li>\n\n\n\n<li><strong>GEE\u306e\u9069\u7528<\/strong>: \u5404\u60a3\u8005\u306e\u5168\u822c\u6027\u75c7\u72b6\u30ec\u30d9\u30eb\u306e\u7d4c\u6642\u5909\u5316\u306b\u304a\u3051\u308b\u76f8\u95a2\u3092\u8003\u616e\u3057\u3001\u4e21\u7fa4\u9593\u306e\u75c7\u72b6\u6539\u5584\u52b9\u679c\u3092\u6bd4\u8f03\u3059\u308b\u3002\u5fdc\u7b54\u5909\u6570\u306f\u9806\u5e8f\u30ab\u30c6\u30b4\u30ea\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>R\u306b\u3088\u308b\u8a08\u7b97\u4f8b:<\/strong><\/p>\n\n\n\n\n\n\n\n<pre class=\"wp-block-code\"><code>library(geepack)\ndata(respdis)\nhead(respdis)\n\n# \u30c7\u30fc\u30bf\u306e\u6574\u5f62(\u30ef\u30a4\u30c9\u5f62\u5f0f\u304b\u3089\u30ed\u30f3\u30b0\u5f62\u5f0f\u306b\u5909\u63db)\nresp.l &lt;- reshape(respdis,\n    varying = list(c(\"y1\", \"y2\", \"y3\", \"y4\")),\n    v.names = \"resp\", direction = \"long\"\n)\nhead(resp.l)\n\n# \u30c7\u30fc\u30bf\u306e\u4e26\u3079\u66ff\u3048(id\u3068time\u3067\u30bd\u30fc\u30c8)\nresp.l &lt;- resp.l&#91;order(resp.l$id, resp.l$time), ]\nhead(resp.l)\n\n# \u30c7\u30fc\u30bf\u306e\u78ba\u8a8d(time, resp, trt\u306e\u30af\u30ed\u30b9\u8868)\ntable(resp.l$time, resp.l$resp, resp.l$trt)\n\n# \u30e2\u30c7\u30eb\u306e\u63a8\u5b9a(\u6642\u9593\u3068\u51e6\u7f6e\u306e\u4ea4\u4e92\u4f5c\u7528\u3092\u8003\u616e)\nfit &lt;- ordgee(ordered(resp) ~ trt * time, id = id, data = resp.l, corstr = \"exchangeable\")\nsummary(fit)\n\n# \u30aa\u30c3\u30ba\u6bd4\u306e\u8a08\u7b97\nOR &lt;- exp(fit$beta)\nCI_lower &lt;- exp(fit$beta - 1.96 * sqrt(diag(fit$vbeta))) # vbeta \u30ed\u30d0\u30b9\u30c8\u5206\u6563\u5171\u5206\u6563\u884c\u5217\nCI_upper &lt;- exp(fit$beta + 1.96 * sqrt(diag(fit$vbeta))) # vbeta \u30ed\u30d0\u30b9\u30c8\u5206\u6563\u5171\u5206\u6563\u884c\u5217\nP &lt;- 1 - pchisq((fit$beta \/ sqrt(diag(fit$vbeta)))^2, df = 1)\np_value &lt;- ifelse(P &lt; 0.001, \"&lt;0.001\", round(P, 3))\n\nodds_ratios &lt;- data.frame(\n    OR = round(OR, 2),\n    CI_lower = round(CI_lower, 2),\n    CI_upper = round(CI_upper, 2),\n    p_value = p_value\n)\n\nprint(\"\u30aa\u30c3\u30ba\u6bd4\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593:\")\nprint(odds_ratios)\n<\/code><\/pre>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;1] \"\u30aa\u30c3\u30ba\u6bd4\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593:\"\n> print(odds_ratios)\n           OR CI_lower CI_upper p_value\nInter:1  3.61     2.10     6.21  &lt;0.001\nInter:2  0.37     0.21     0.65  &lt;0.001\ntrt      3.59     1.42     9.07   0.007\ntime     0.95     0.81     1.11   0.508\ntrt:time 0.92     0.70     1.21   0.541<\/code><\/pre>\n\n\n\n<p>\u307e\u305a\u6700\u521d\u306b\u76ee\u306b\u5165\u308b Inter:1, Inter:2 \u3067\u3042\u308b\u304c\u3001\u3053\u308c\u306f\u3001\u30a2\u30a6\u30c8\u30ab\u30e0\u306e 3\u3064\u306e\u30ab\u30c6\u30b4\u30ea\u306e1\u756a\u76ee\u306e\u30ab\u30c3\u30c8\u30dd\u30a4\u30f3\u30c8\uff081\u3092\u8d85\u3048\u308b\u3001\u3064\u307e\u308a2\u307e\u305f\u306f3\u306b\u306a\u308b\u30dd\u30a4\u30f3\u30c8\uff09\u30682\u756a\u3081\u306e\u30ab\u30c3\u30c8\u30dd\u30a4\u30f3\u30c8\uff082\u3092\u8d85\u3048\u308b\u3001\u3064\u307e\u308a\u30ab\u30c6\u30b4\u30ea3\u306b\u306a\u308b\u30dd\u30a4\u30f3\u30c8\uff09\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u306f\u8868\u793a\u3055\u308c\u308b\u306e\u3060\u304c\u3001\u3053\u306e\u30ab\u30c3\u30c8\u30dd\u30a4\u30f3\u30c8\u306f\u63d0\u793a\u304c\u5fc5\u8981\u306a\u5024\u3067\u306f\u306a\u304f\u3001\u89e3\u91c8\u3082\u4e0d\u8981\u3067\u3042\u308b\u30021\uff0c2\uff0c3\u306e\u30ab\u30c3\u30c8\u30dd\u30a4\u30f3\u30c8\u306e\u5e45\u306f\u300c1\u300d\u3067\u306f\u306a\u3044\u3053\u3068\u304c\u7279\u5fb4\u3067\u3001\u305d\u306e\u70b9\u304c\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u7684\uff08\u3064\u307e\u308a\u9806\u5e8f\u306b\u904e\u304e\u306a\u3044\uff09\u306a\u3093\u3060\u3068\u7406\u89e3\u3059\u308c\u3070\u826f\u3044\u3002<\/p>\n\n\n\n<p>trt, time, trt:time \u304c\u898b\u308b\u3079\u304d\u884c\u3067\u3042\u308b\u3002trt \u304c1\u3088\u308a\u5927\u304d\u304f\u7d71\u8a08\u5b66\u7684\u306b\u6709\u610f\uff08P &lt; 0.05\uff09\u3067\u3042\u308b\u305f\u3081\u3001\u65b0\u6cbb\u7642\u304c\u30d7\u30e9\u30bb\u30dc\u306b\u6bd4\u3079\u3066\u3001\u75c7\u72b6\u3092\u6539\u5584\u3059\u308b\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002time, trt:time \u306f OR \u304c 1 \u306b\u8fd1\u304f\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u3082\u306a\u3044\u305f\u3081\u3001\u7d4c\u6642\u7684\u306a\u52b9\u679c\u3084\u6cbb\u7642\u6cd5\u3068\u6642\u9593\u306e\u4ea4\u4e92\u4f5c\u7528\u306f\u660e\u3089\u304b\u3067\u306f\u306a\u3044\u3068\u89e3\u91c8\u3067\u304d\u308b\u3002<\/p>\n\n\n\n\n\n\n\n<h3 class=\"wp-block-heading\">\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\uff1a\u611f\u67d3\u75c7\u306e\u767a\u751f\u4ef6\u6570\u6bd4\u8f03<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u76ee\u7684<\/strong>: \u65b0\u3057\u3044\u4e88\u9632\u4ecb\u5165\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u3001\u3042\u308b\u96c6\u56e3\u306b\u304a\u3051\u308b\u611f\u67d3\u75c7\u306e\u5e74\u9593\u767a\u751f\u4ef6\u6570\u3092\u3001\u5f93\u6765\u306e\u4ecb\u5165\u3068\u6bd4\u8f03\u3057\u3066\u524a\u6e1b\u3059\u308b\u304b\u3092\u8a55\u4fa1\u3059\u308b\u3002 <\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf<\/strong>: \u8907\u6570\u306e\u5bfe\u8c61\u96c6\u56e3\uff08\u4f8b\uff1a\u5730\u57df\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u3001\u65bd\u8a2d\u306a\u3069\uff09\u3092\u65b0\u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0\u5c0e\u5165\u7fa4\u3068\u5f93\u6765\u4e88\u9632\u7b56\u5b9f\u65bd\u7fa4\u306b\u5272\u308a\u4ed8\u3051\u3002\u5404\u96c6\u56e3\u306b\u3064\u3044\u3066\u3001<strong>\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\uff08\u4ecb\u5165\u524d1\u5e74\u9593\uff09<\/strong>\u3001<strong>\u8ffd\u8de1\u958b\u59cb1\u5e74\u5f8c<\/strong>\u3001<strong>\u8ffd\u8de1\u958b\u59cb2\u5e74\u5f8c<\/strong>\u306e\u5e74\u9593\u611f\u67d3\u75c7\u767a\u751f\u4ef6\u6570\u3092\u8a18\u9332\u3002 <\/li>\n\n\n\n<li><strong>GEE\u306e\u9069\u7528<\/strong>: \u5404\u96c6\u56e3\u5185\u306e\u7d4c\u6642\u7684\u306a\u611f\u67d3\u75c7\u767a\u751f\u4ef6\u6570\u306e\u76f8\u95a2\u3092\u8003\u616e\u3057\u3001\u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5168\u4f53\u7684\u306a\u52b9\u679c\u3092\u63a8\u5b9a\u3059\u308b\u3002\u5fdc\u7b54\u5909\u6570\u306f\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\u3002\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u5927\u304d\u3055\u3082\u30aa\u30d5\u30bb\u30c3\u30c8\uff08\u5f8c\u8ff0\uff09\u3067\u8003\u616e\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>R \u306b\u3088\u308b\u8a08\u7b97\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u8aad\u307f\u8fbc\u307f\nlibrary(geepack)\n\n# \u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u4f5c\u6210 (\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf) - population \u3092\u8ffd\u52a0\nset.seed(2024)\ncommunity_id &lt;- rep(1:50, each = 3) # \u96c6\u56e3ID (50\u30b3\u30df\u30e5\u30cb\u30c6\u30a3)\n# \u6e2c\u5b9a\u6642\u70b9 (0:\u30d9\u30fc\u30b9\u30e9\u30a4\u30f31\u5e74\u9593, 1:\u8ffd\u8de11\u5e74\u9593, 2:\u8ffd\u8de12\u5e74\u9593)\nmeasurement_period &lt;- rep(c(0, 1, 2), times = 50)\n# \u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0 (0:\u5f93\u6765\u4e88\u9632\u7b56, 1:\u65b0\u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0)\nprogram &lt;- rep(sample(c(0, 1), 50, replace = TRUE), each = 3)\n\n# \u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u4eba\u53e3 (\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u3067\u56fa\u5b9a\u3001\u5404\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u3067\u7570\u306a\u308b)\n# \u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3001\u5404\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u4eba\u53e3\u3092 period \u3054\u3068\u306b\u6301\u3064\u5834\u5408\u3082\u3042\u308a\u307e\u3059\u304c\u3001\n# \u3053\u306e\u4f8b\u3067\u306f\u30b7\u30f3\u30d7\u30eb\u306b\u30b3\u30df\u30e5\u30cb\u30c6\u30a3ID\u3054\u3068\u306b\u56fa\u5b9a\u3068\u3057\u307e\u3059\u3002\npopulation_base &lt;- rep(sample(5000:20000, 50, replace = TRUE), each = 3)\n\n# \u5404\u671f\u9593\u306b\u304a\u3051\u308b\u611f\u67d3\u75c7\u767a\u751f\u4ef6\u6570\u306e\u751f\u6210\n# population \u306e\u5f71\u97ff\u3092\u8003\u616e\u3057\u3001\u611f\u67d3\u7387\u3092\u57fa\u6e96\u306b\u751f\u6210\ninfection_count &lt;- numeric(length(community_id))\nfor (i in 1:length(community_id)) {\n    # \u4eba\u53e3\u3042\u305f\u308a\u306e\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u611f\u67d3\u7387 (\u4f8b: 1000\u4eba\u3042\u305f\u308a15\u4ef6)\n    # rate_per_1000 = 15\n    # base_expected_count = (population_base&#91;i] \/ 1000) * rate_per_1000\n    base_expected_count &lt;- (population_base&#91;i] \/ 1000) * 15 # \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u3067\u4eba\u53e31000\u4eba\u3042\u305f\u308a15\u4ef6\n\n    if (measurement_period&#91;i] == 0) { # \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\n        # \u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u304b\u3089\u751f\u6210\u3001\u671f\u5f85\u5024\u306f\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u306e\u4eba\u53e3\u306b\u5fdc\u3058\u308b\n        infection_count&#91;i] &lt;- rpois(1, base_expected_count)\n    } else if (program&#91;i] == 0) { # \u5f93\u6765\u4e88\u9632\u7b56\u7fa4 (\u8ffd\u8de1\u671f\u9593)\n        # \u7de9\u3084\u304b\u306b\u6e1b\u5c11 (\u4f8b: 1000\u4eba\u3042\u305f\u308a\u5e740.5\u4ef6\u6e1b\u5c11)\n        infection_count&#91;i] &lt;- rpois(1, max(0.1, base_expected_count - (measurement_period&#91;i] * 0.5 * (population_base&#91;i] \/ 1000))))\n    } else { # \u65b0\u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0\u7fa4 (\u8ffd\u8de1\u671f\u9593)\n        # \u3088\u308a\u5927\u304d\u304f\u6e1b\u5c11 (\u4f8b: 1000\u4eba\u3042\u305f\u308a\u5e742\u4ef6\u6e1b\u5c11)\n        infection_count&#91;i] &lt;- rpois(1, max(0.1, base_expected_count - (measurement_period&#91;i] * 2 * (population_base&#91;i] \/ 1000))))\n    }\n    infection_count&#91;i] &lt;- max(0, infection_count&#91;i]) # \u8ca0\u306e\u6570\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306b\n}\n\ndata_infection_count &lt;- data.frame(\n    id = community_id,\n    period = measurement_period,\n    program = program,\n    population = population_base, # \u4eba\u53e3\u3092\u8ffd\u52a0\n    infection_count\n)\nhead(data_infection_count)\n\n# GEE\u30e2\u30c7\u30eb\u306e\u5b9f\u884c (\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf) - \u30aa\u30d5\u30bb\u30c3\u30c8\u3092\u8ffd\u52a0\n# family = poisson: \u5fdc\u7b54\u5909\u6570\u304c\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\u3067\u3042\u308b\u305f\u3081\n# link = \"log\": \u5bfe\u6570\u30ea\u30f3\u30af\u95a2\u6570\n# offset = log(population): \u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u4eba\u53e3\u306e\u5bfe\u6570\u3092\u30aa\u30d5\u30bb\u30c3\u30c8\u3068\u3057\u3066\u6307\u5b9a\nmodel_infection_gee_offset &lt;- geeglm(infection_count ~ program + as.factor(period) + program:as.factor(period),\n    id = id,\n    data = data_infection_count,\n    family = poisson(link = \"log\"),\n    corstr = \"exchangeable\",\n    offset = log(population)\n) # \u30aa\u30d5\u30bb\u30c3\u30c8\u306e\u6307\u5b9a\n\n# \u7d50\u679c\u306e\u8868\u793a\nsummary(model_infection_gee_offset)\n\nRR &lt;- exp(coef(model_infection_gee_offset))\nCI_lower &lt;- exp(coef(model_infection_gee_offset) - 1.96 * sqrt(diag(vcov(model_infection_gee_offset)))) # vcov \u30ed\u30d0\u30b9\u30c8\u5206\u6563\u5171\u5206\u6563\u884c\u5217\nCI_upper &lt;- exp(coef(model_infection_gee_offset) + 1.96 * sqrt(diag(vcov(model_infection_gee_offset)))) # vcov \u30ed\u30d0\u30b9\u30c8\u5206\u6563\u5171\u5206\u6563\u884c\u5217\np_value &lt;- ifelse(summary(model_infection_gee_offset)$coefficients&#91;, 4] &lt; 0.001, \"&lt;0.001\", round(summary(model_infection_gee_offset)$coefficients&#91;, 4], 3))\n\nrate_ratios &lt;- data.frame(\n    RR = round(RR, 2),\n    CI_lower = round(CI_lower, 2),\n    CI_upper = round(CI_upper, 2),\n    p_value = p_value\n)\n\nprint(\"\u30ec\u30fc\u30c8\u6bd4\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593:\")\nprint(rate_ratios)\n<\/code><\/pre>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt; # \u7d50\u679c\u306e\u8868\u793a\n&gt; summary(model_infection_gee_offset)\n\nCall:\ngeeglm(formula = infection_count ~ program + as.factor(period) + \n    program:as.factor(period), family = poisson(link = \"log\"), \n    data = data_infection_count, offset = log(population), id = id, \n    corstr = \"exchangeable\")\n\n Coefficients:\n                           Estimate  Std.err     Wald Pr(&gt;|W|)    \n(Intercept)                -4.18028  0.01472 80688.53  &lt; 2e-16 ***\nprogram                     0.00188  0.01945     0.01  0.92293    \nas.factor(period)1         -0.04594  0.02427     3.58  0.05831 .  \nas.factor(period)2         -0.08454  0.01449    34.05  5.4e-09 ***\nprogram:as.factor(period)1 -0.12009  0.03280    13.41  0.00025 ***\nprogram:as.factor(period)2 -0.28120  0.02262   154.52  &lt; 2e-16 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nCorrelation structure = exchangeable \nEstimated Scale Parameters:\n\n            Estimate Std.err\n(Intercept)     1.04   0.106\n  Link = identity \n\nEstimated Correlation Parameters:\n      Estimate Std.err\nalpha    0.101    0.09\nNumber of clusters:   50  Maximum cluster size: 3 \n&gt; <\/code><\/pre>\n\n\n\n<p><strong>\u7d50\u679c\u306e\u89e3\u91c8:<\/strong><\/p>\n\n\n\n<p> <code>program<\/code>\u306e\u4fc2\u6570\u306f\u3001\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u6642\u70b9\u3067\u306e\u4e21\u7fa4\u9593\u306e\u5e73\u5747\u7684\u306a\u767a\u751f\u4ef6\u6570\u306e\u5dee\uff08\u5bfe\u6570\u30ec\u30fc\u30c8\u6bd4\uff09\u3092\u793a\u3057\u3066\u3044\u308b\u3002<code>as.factor(period)1<\/code>\u3084<code>as.factor(period)2<\/code>\u306e\u4fc2\u6570\u306f\u3001\u5f93\u6765\u7fa4\u306b\u304a\u3051\u308b\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u304b\u3089\u306e\u5404\u671f\u9593\u3078\u306e\u5909\u5316\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u6700\u3082\u91cd\u8981\u306a\u306e\u306f<strong>\u4ea4\u4e92\u4f5c\u7528\u9805 <code>program:as.factor(period)1<\/code> \u3068 <code>program:as.factor(period)2<\/code><\/strong> \u3067\u3042\u308b\u3002\u3053\u308c\u3089\u306e\u4fc2\u6570\u304c\u7d71\u8a08\u7684\u306b\u6709\u610f\u3067\u3042\u308c\u3070\u3001\u65b0\u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u5f93\u6765\u4e88\u9632\u7b56\u3068\u6bd4\u8f03\u3057\u3066\u3001\u5404\u8ffd\u8de1\u671f\u9593\u306b\u304a\u3044\u3066\u611f\u67d3\u75c7\u767a\u751f\u4ef6\u6570\u306e\u5909\u5316\u306b\u6709\u610f\u306a\u5dee\u3092\u3082\u305f\u3089\u3057\u305f\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p><strong><code>population<\/code><\/strong>\u306f\u3001\u5404<code>community_id<\/code>\u306b\u5bfe\u5fdc\u3059\u308b\u67b6\u7a7a\u306e<code>population<\/code>\uff08\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u5927\u304d\u3055\uff09\u3092\u8868\u3057\u3066\u3044\u3066\u3001<code>geeglm<\/code>\u95a2\u6570\u306e\u5f15\u6570\u306b<code>offset = log(population)<\/code>\u3092\u8ffd\u52a0\u3057\u3066\u3001\u30aa\u30d5\u30bb\u30c3\u30c8\u3092\u8a2d\u5b9a\u3059\u308b\u3002\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u3067\u306f\u5bfe\u6570\u30ea\u30f3\u30af\u95a2\u6570\u3092\u4f7f\u3046\u305f\u3081\u3001\u30aa\u30d5\u30bb\u30c3\u30c8\u3082\u5bfe\u6570\u5909\u63db\u3057\u305f\u3082\u306e\u3092\u6307\u5b9a\u3059\u308b\u3002\u30aa\u30d5\u30bb\u30c3\u30c8\u9805\u3068\u3057\u3066<code>log(population)<\/code>\u3092\u542b\u3081\u308b\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u306e\u4fc2\u6570\u306f\u4eba\u53e3\u3042\u305f\u308a\u306e\u611f\u67d3\u75c7\u767a\u751f\u7387\uff08\u30ec\u30fc\u30c8\uff09\u306b\u5bfe\u3059\u308b\u52b9\u679c\u3068\u3057\u3066\u89e3\u91c8\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;1] \"\u30ec\u30fc\u30c8\u6bd4\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593:\"\n&gt; print(rate_ratios)\n                             RR CI_lower CI_upper p_value\n(Intercept)                0.02     0.01     0.02  &lt;0.001\nprogram                    1.00     0.96     1.04   0.923\nas.factor(period)1         0.96     0.91     1.00   0.058\nas.factor(period)2         0.92     0.89     0.95  &lt;0.001\nprogram:as.factor(period)1 0.89     0.83     0.95  &lt;0.001\nprogram:as.factor(period)2 0.75     0.72     0.79  &lt;0.001<\/code><\/pre>\n\n\n\n<p>\u4fc2\u6570\u306f\u5bfe\u6570\u30ec\u30fc\u30c8\u6bd4\u3067\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3001<code>exp()<\/code>\u95a2\u6570\u3067\u30ec\u30fc\u30c8\u6bd4\u306b\u5909\u63db\u3059\u308b\u3068\u76f4\u611f\u7684\u306a\u89e3\u91c8\u304c\u53ef\u80fd\u306b\u306a\u308b\u3002\u30ec\u30fc\u30c8\u6bd4\u3068\u306a\u308b\u3068\u3001\u65b0\u4e88\u9632\u30d7\u30ed\u30b0\u30e9\u30e0\u7fa4\u306e\u767a\u751f\u7387\u304c\u5f93\u6765\u7fa4\u306e\u767a\u751f\u7387\u306e\u4f55\u500d\u306b\u306a\u308b\u304b\u3068\u3044\u3046\u89e3\u91c8\u304c\u53ef\u80fd\u3067\u3042\u308b\u3002\u4eca\u56de\u306f\u3001program \u306e\u30ec\u30fc\u30c8\u6bd4\u3092\u898b\u308b\u3068 1 \u3067\u3042\u308b\u304c\u3001\u4ea4\u4e92\u4f5c\u7528\u306e\u4fc2\u6570\u306f1\u3088\u308a\u4e0b\u56de\u3063\u3066\u304a\u308a\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306a\u306e\u3067\u3001\u5f93\u6765\u7fa4\u3068\u6bd4\u8f03\u3057\u3066\u65b0\u4e88\u9632\u7fa4\u3067\u306f\u3001\u4ea4\u4e92\u4f5c\u7528\u3042\u308a\u3067\u6e1b\u5c11\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u4f3a\u3048\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u30aa\u30d5\u30bb\u30c3\u30c8\u3068\u306f\uff1f<\/h4>\n\n\n\n<p>\u30aa\u30d5\u30bb\u30c3\u30c8\uff08offset\uff09\u306f\u3001GLMM\u306e\u3088\u3046\u306a\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb\u3084 GEE \u306b\u304a\u3044\u3066\u3001\u30e2\u30c7\u30eb\u306e\u7dda\u5f62\u4e88\u6e2c\u5b50\u306b<strong>\u65e2\u77e5\u306e\u56fa\u5b9a\u3055\u308c\u305f\u5024<\/strong>\u3092\u8ffd\u52a0\u3059\u308b\u9805\u306e\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u5024\u306f\u3001\u901a\u5e38\u3001\u76ee\u7684\u5909\u6570\u306e\u671f\u5f85\u5024\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u30a8\u30af\u30b9\u30dd\u30fc\u30b8\u30e3\u30fc\uff08\u9732\u51fa\uff09\u3084\u80cc\u666f\u306e\u5927\u304d\u3055\u3092\u8868\u3059\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u4e0a\u8a18\u306e\u4f8b\u3067\u300c\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u5927\u304d\u3055\uff08\u4f8b\uff1a\u5404\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u4eba\u53e3\uff09\u300d\u304c\u7570\u306a\u308b\u5834\u5408\u3001\u611f\u67d3\u75c7\u767a\u751f\u4ef6\u6570\u306f\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u898f\u6a21\u306b\u4f9d\u5b58\u3059\u308b\u3068\u8003\u3048\u3089\u308c\u308b\u3002\u3053\u306e\u5834\u5408\u3001\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u5927\u304d\u3055\u3092\u30aa\u30d5\u30bb\u30c3\u30c8\u3068\u3057\u3066\u52a0\u3048\u308b\u3053\u3068\u3067\u3001<strong>\u4eba\u53e31000\u4eba\u3042\u305f\u308a\u306e\u611f\u67d3\u75c7\u767a\u751f\u7387<\/strong>\u306a\u3069\u306e\u30ec\u30fc\u30c8\u3092\u6bd4\u8f03\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u4e0a\u8a18\u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u306b\u306f\u3001<code>population<\/code>\u3068\u3044\u3046\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u898f\u6a21\u3092\u793a\u3059\u5909\u6570\u304c\u3042\u308a\u3001\u30aa\u30d5\u30bb\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\u3057\u305f\u4f8b\u3092\u793a\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u81e8\u5e8a\u7814\u7a76\u306b\u304a\u3051\u308bGLMM\u512a\u5148\u306e\u7406\u7531\uff08\u63a8\u6e2c\uff09<\/h2>\n\n\n\n<p>GEE\u304c\u975e\u5e38\u306b\u6709\u7528\u3067\u3042\u308b\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u81e8\u5e8a\u7814\u7a76\u3067GLMM\uff08\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb\uff09\u306e\u65b9\u304c\u591a\u304f\u898b\u3089\u308c\u308b\u3002\u3044\u304f\u3064\u304b\u7406\u7531\u304c\u8003\u3048\u3089\u308c\u308b\u304c\u3001\u4e3b\u306b\u4ee5\u4e0b\u306e\u70b9\u304c\u80cc\u666f\u306b\u3042\u308b\u3068\u63a8\u6e2c\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u500b\u4f53\u30ec\u30d9\u30eb\u306e\u7570\u8cea\u6027\uff08Subject-Specific Effects\uff09\u3078\u306e\u95a2\u5fc3<\/h3>\n\n\n\n<p>\u81e8\u5e8a\u7814\u7a76\u3001\u7279\u306b\u85ac\u5264\u958b\u767a\u3084\u500b\u5225\u5316\u533b\u7642\u306e\u6587\u8108\u3067\u306f\u3001<strong>\u500b\u3005\u306e\u60a3\u8005\u306e\u53cd\u5fdc\u306e\u3070\u3089\u3064\u304d\u3084\u3001\u6cbb\u7642\u52b9\u679c\u304c\u60a3\u8005\u306b\u3088\u3063\u3066\u3069\u306e\u3088\u3046\u306b\u7570\u306a\u308b\u304b<\/strong>\u306b\u95a2\u5fc3\u304c\u9ad8\u3044\u3053\u3068\u304c\u591a\u3044\u3002GLMM\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u52b9\u679c\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u3001\u3053\u306e\u3088\u3046\u306a\u500b\u4f53\u9593\u306e\u7570\u8cea\u6027\u3092\u76f4\u63a5\u30e2\u30c7\u30eb\u5316\u3057\u3001\u60a3\u8005\u3054\u3068\u306e\u4e88\u6e2c\u3084\u52b9\u679c\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u4e00\u65b9\u3001GEE\u306f\u96c6\u56e3\u5e73\u5747\u52b9\u679c\uff08Population-Average Effects\uff09\u306e\u63a8\u5b9a\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u3044\u308b\u3002\u3053\u308c\u306f\u3001\u3042\u308b\u6cbb\u7642\u304c\u300c\u5e73\u5747\u7684\u306b\u300d\u3069\u306e\u7a0b\u5ea6\u52b9\u679c\u304c\u3042\u308b\u304b\u3092\u77e5\u308b\u306b\u306f\u9069\u3057\u3066\u3044\u308b\u304c\u3001\u500b\u3005\u306e\u60a3\u8005\u306e\u6cbb\u7642\u8a08\u753b\u3092\u7acb\u3066\u308b\u4e0a\u3067\u306f\u3001\u500b\u5225\u306e\u53cd\u5fdc\u3092\u8003\u616e\u3067\u304d\u308bGLMM\u306e\u65b9\u304c\u3088\u308a\u60c5\u5831\u91cf\u304c\u591a\u3044\u3068\u611f\u3058\u3089\u308c\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n<p><strong>\u306a\u305cGEE\u3088\u308aGLMM\u304b:<\/strong> \u591a\u304f\u306e\u81e8\u5e8a\u8a66\u9a13\u306f\u3001\u6cbb\u7642\u304c\u300c\u8ab0\u306b\u300d\u3069\u306e\u7a0b\u5ea6\u52b9\u304f\u304b\u3068\u3044\u3046\u554f\u3044\u306b\u95a2\u5fc3\u304c\u3042\u308b\u3002GLMM\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u52b9\u679c\u3092\u901a\u3058\u3066\u3001\u3053\u306e\u300c\u8ab0\u306b\u300d\u3068\u3044\u3046\u8981\u7d20\u3092\u8aac\u660e\u3067\u304d\u308b\u3002\u4f8b\u3048\u3070\u3001\u3042\u308b\u60a3\u8005\u306f\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u306e\u7279\u6027\u304c\u4f3c\u3066\u3044\u3066\u3082\u3001\u5225\u306e\u60a3\u8005\u3088\u308a\u85ac\u304c\u52b9\u304d\u306b\u304f\u3044\u3001\u3042\u308b\u3044\u306f\u52b9\u304d\u3084\u3059\u3044\u3068\u3044\u3063\u305f\u500b\u4f53\u5dee\u3092\u30e2\u30c7\u30eb\u306b\u7d44\u307f\u8fbc\u3081\u308b\u306e\u306fGLMM\u306e\u5f37\u307f\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6b20\u640d\u30c7\u30fc\u30bf\u3078\u306e\u5bfe\u5fdc\u80fd\u529b<\/h3>\n\n\n\n<p>\u81e8\u5e8a\u7814\u7a76\u3067\u306f\u3001\u60a3\u8005\u306e\u30c9\u30ed\u30c3\u30d7\u30a2\u30a6\u30c8\u3084\u6e2c\u5b9a\u5fd8\u308c\u306a\u3069\u306b\u3088\u308a\u3001<strong>\u6b20\u640d\u30c7\u30fc\u30bf<\/strong>\u304c\u983b\u7e41\u306b\u767a\u751f\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>GLMM<\/strong>: <strong>MAR (Missing At Random)<\/strong> \u306e\u6b20\u640d\u30e1\u30ab\u30cb\u30ba\u30e0\u306b\u5bfe\u5fdc\u3059\u308b\u80fd\u529b\u304c\u9ad8\u3044\u3068\u3055\u308c\u3066\u3044\u308b\u3002\u3053\u308c\u306f\u3001\u6b20\u640d\u304c\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf\uff08\u4f8b\uff1a\u3053\u308c\u307e\u3067\u306e\u6e2c\u5b9a\u5024\u3084\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u306e\u7279\u6027\uff09\u306b\u4f9d\u5b58\u3059\u308b\u304c\u3001\u6b20\u640d\u3057\u305f\u5024\u305d\u306e\u3082\u306e\u306b\u306f\u4f9d\u5b58\u3057\u306a\u3044\u5834\u5408\u3092\u6307\u3059\u3002GLMM\u306f\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u3092\u5c24\u5ea6\u30d9\u30fc\u30b9\u3067\u81ea\u7136\u306b\u6271\u3048\u308b\u305f\u3081\u3001\u8ffd\u52a0\u306e\u8abf\u6574\u306a\u3057\u306bMAR\u306e\u6b20\u640d\u306b\u5bfe\u5fdc\u3057\u3084\u3059\u3044\u3002<\/li>\n\n\n\n<li><strong>GEE<\/strong>: GEE\u306f\u3001\u57fa\u672c\u7684\u306b\u306f\u6b20\u640d\u304c<strong>MCAR (Missing Completely At Random)<\/strong> \u3067\u3042\u308b\u5834\u5408\u306b\u6700\u9069\u306b\u6a5f\u80fd\u3059\u308b\u3002MCAR\u306f\u3001\u6b20\u640d\u304c\u5b8c\u5168\u306b\u30e9\u30f3\u30c0\u30e0\u3067\u3001\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3082\u6b20\u640d\u3057\u305f\u30c7\u30fc\u30bf\u3082\u3001\u3044\u305a\u308c\u306b\u3082\u4f9d\u5b58\u3057\u306a\u3044\u72b6\u6cc1\u3092\u6307\u3059\u3002\u3082\u3057\u6b20\u640d\u304cMAR\u306e\u5834\u5408\u3001GEE\u306f\u5358\u7d14\u306b\u6b20\u640d\u3057\u305f\u89b3\u6e2c\u3092\u524a\u9664\uff08\u5b8c\u5168\u30b1\u30fc\u30b9\u89e3\u6790\uff09\u3059\u308b\u3068\u30d0\u30a4\u30a2\u30b9\u304c\u751f\u3058\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002GEE\u3067MAR\u306e\u6b20\u640d\u306b\u5bfe\u5fdc\u3059\u308b\u306b\u306f\u3001\u9006\u78ba\u7387\u91cd\u307f\u4ed8\u3051\uff08Inverse Probability Weighting: IPW\uff09\u306a\u3069\u306e\u3088\u308a\u8907\u96d1\u306a\u624b\u6cd5\u3068\u7d44\u307f\u5408\u308f\u305b\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u89e3\u6790\u306e\u30cf\u30fc\u30c9\u30eb\u304c\u4e0a\u304c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u306a\u305cGEE\u3088\u308aGLMM\u304b<\/strong>: \u81e8\u5e8a\u7814\u7a76\u306b\u304a\u3051\u308b\u6b20\u640d\u30c7\u30fc\u30bf\u306fMAR\u3067\u3042\u308b\u3053\u3068\u304c\u591a\u304f\u3001GLMM\u306e\u65b9\u304c\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u3088\u308a\u30ed\u30d0\u30b9\u30c8\u306b\u5bfe\u5fdc\u3067\u304d\u308b\u305f\u3081\u3001\u89e3\u6790\u306e\u624b\u9593\u3084\u30d0\u30a4\u30a2\u30b9\u306e\u61f8\u5ff5\u304c\u5c11\u306a\u3044\u3068\u8a8d\u8b58\u3055\u308c\u3066\u3044\u308b\u304b\u3089\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30e2\u30c7\u30eb\u306e\u89e3\u91c8\u3068\u76f4\u611f\u7684\u306a\u7406\u89e3<\/h3>\n\n\n\n<p>GLMM\u306f\u3001\u56fa\u5b9a\u52b9\u679c\u3068\u5909\u91cf\u52b9\u679c\u3068\u3044\u3046\u660e\u78ba\u306a\u67a0\u7d44\u307f\u3067\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u3001\u7d71\u8a08\u5c02\u9580\u5bb6\u3067\u306a\u304f\u3068\u3082\u3001\u305d\u306e\u6982\u5ff5\u304c\u6bd4\u8f03\u7684\u7406\u89e3\u3057\u3084\u3059\u3044\u3068\u611f\u3058\u3089\u308c\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u5909\u91cf\u52b9\u679c\u306f\u3001\u300c\u500b\u4f53\u5dee\u304c\u3069\u308c\u304f\u3089\u3044\u3042\u308b\u304b\u300d\u3092\u5206\u6563\u6210\u5206\u3068\u3057\u3066\u76f4\u63a5\u7684\u306b\u63a8\u5b9a\u3059\u308b\u305f\u3081\u3001\u30c7\u30fc\u30bf\u306e\u80cc\u5f8c\u306b\u3042\u308b\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u3088\u308a\u8a73\u7d30\u306b\u8a18\u8ff0\u3057\u3066\u3044\u308b\u3068\u7406\u89e3\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>GEE\u306e\u300c\u30cb\u30e5\u30fc\u30b5\u30f3\u30b9\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u306e\u76f8\u95a2\u69cb\u9020\u300d\u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u3001\u6570\u7406\u7d71\u8a08\u5b66\u7684\u306a\u80cc\u666f\u304c\u306a\u3044\u3068\u76f4\u611f\u7684\u306b\u7406\u89e3\u3057\u306b\u304f\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u76f8\u95a2\u69cb\u9020\u3092\u9593\u9055\u3048\u3066\u3082\u4fc2\u6570\u304c\u30ed\u30d0\u30b9\u30c8\u3067\u3042\u308b\u3001\u3068\u3044\u3046\u5229\u70b9\u306f\u5f37\u529b\u3067\u3042\u308b\u304c\u3001\u305d\u306e\u300c\u4ed5\u7d44\u307f\u300d\u304c\u5206\u304b\u308a\u306b\u304f\u3044\u3068\u611f\u3058\u3089\u308c\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n<p><strong>\u306a\u305cGEE\u3088\u308aGLMM\u304b<\/strong>: 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