{"id":4726,"date":"2026-08-09T20:52:25","date_gmt":"2026-08-09T11:52:25","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4726"},"modified":"2026-08-09T20:52:26","modified_gmt":"2026-08-09T11:52:26","slug":"how-should-you-analyze-multiple-hospitalization-data-from-the-same-patient-extending-the-cox-model-with-the-andersen-gill-approach-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-should-you-analyze-multiple-hospitalization-data-from-the-same-patient-extending-the-cox-model-with-the-andersen-gill-approach-in-r\/","title":{"rendered":"\u540c\u3058\u60a3\u8005\u304c\u4f55\u5ea6\u3082\u518d\u5165\u9662\u3057\u305f\u30c7\u30fc\u30bf\u3092\u3069\u3046\u89e3\u6790\u3059\u3079\u304d\u304b\uff1fCox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u306e\u62e1\u5f35\u3068Andersen-Gill\u30e2\u30c7\u30eb\u306e\u5b9f\u8df5\u624b\u9806"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u300c\u5148\u751f\uff01\u5fc3\u4e0d\u5168\u306e\u60a3\u8005\u3055\u3093\u306e\u518d\u5165\u9662\u30c7\u30fc\u30bf\u3092\u89e3\u6790\u3057\u305f\u304f\u3066\u30012\u56de\u76ee\u30843\u56de\u76ee\u306e\u518d\u5165\u9662\u30c7\u30fc\u30bf\u3082\u305f\u304f\u3055\u3093\u3042\u3063\u305f\u306e\u3067\u3059\u304c\u3001\u89e3\u6790\u65b9\u6cd5\u304c\u3088\u304f\u5206\u304b\u3089\u306a\u304b\u3063\u305f\u306e\u3067\u3001\u3068\u308a\u3042\u3048\u305a\u300e\u521d\u56de\u518d\u5165\u9662\u307e\u3067\u306e\u6642\u9593\uff08Time-to-first event\uff09\u300f\u3060\u3051\u3067Cox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u3092\u5b9f\u884c\u3057\u307e\u3057\u305f\uff01\u7121\u4e8b\u306b\u30cf\u30b6\u30fc\u30c9\u6bd4\u304c\u51fa\u305b\u307e\u3057\u305f\uff01\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2026\u2026\u3061\u3087\u3063\u3068\u5f85\u3063\u3066\u307b\u3057\u3044\u3002\u305d\u308c\u306f\u81e8\u5e8a\u7814\u7a76\u306e\u8ad6\u6587\u67fb\u8aad\uff08Peer Review\uff09\u306b\u304a\u3044\u3066\u3001\u7d71\u8a08\u67fb\u8aad\u8005\u304b\u3089\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u65e5\u4ee5\u964d\u306e\u81a8\u5927\u306a\u81e8\u5e8a\u30c7\u30fc\u30bf\u3092\u5207\u308a\u6368\u3066\u3066\u304a\u308a\u3001\u6cbb\u7642\u306e\u5168\u75be\u75c5\u8ca0\u8377\uff08Cumulative Disease Burden\uff09\u306b\u5bfe\u3059\u308b\u52b9\u679c\u3092\u6b63\u3057\u304f\u8a55\u4fa1\u3067\u304d\u3066\u3044\u306a\u3044\u300d\u3068\u5f37\u304f\u6307\u6458\u3055\u308c\u308b\u5178\u578b\u7684\u306a\u30d1\u30bf\u30fc\u30f3\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<p class=\"wp-block-paragraph\">\u304b\u3068\u3044\u3063\u3066\u3001\u300c1\u4eba\u306e\u60a3\u8005\u304c3\u56de\u518d\u5165\u9662\u3057\u305f\u304b\u3089\u30013\u4eba\u5206\u306e\u30c7\u30fc\u30bf\uff083\u884c\uff09\u3068\u3057\u3066\u901a\u5e38\u306eCox\u30e2\u30c7\u30eb\u306b\u305d\u306e\u307e\u307e\u653e\u308a\u8fbc\u3080\u300d\u3068\u3044\u3046\u89e3\u6790\u3092\u884c\u3063\u3066\u3057\u307e\u3046\u3068\u3001\u751f\u5b58\u6642\u9593\u89e3\u6790\u306e\u6839\u672c\u524d\u63d0\u3067\u3042\u308b\u300c\u89b3\u6e2c\u5024\u306e\u72ec\u7acb\u6027\uff08Independence of observations\uff09\u300d\u304c\u7834\u7834\u7dbb\u3057\u3001\u67fb\u8aad\u3067\u4e00\u767a\u5374\u4e0b\u3055\u308c\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u3001\u306a\u305c\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u306e\u307f\u300d\u3084\u300c\u5168\u30a4\u30d9\u30f3\u30c8\u306e\u5358\u7d14\u6295\u5165\u300d\u304c\u81f4\u547d\u7684\u306a\u5931\u6557\u3092\u62db\u304f\u306e\u304b\u3068\u3044\u3046\u30ed\u30b8\u30c3\u30af\u304b\u3089\u3001\u7e70\u308a\u8fd4\u3057\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u3092\u6b63\u3057\u304f\u89e3\u6790\u3059\u308b\u6a19\u6e96\u624b\u6cd5 <strong>Andersen-Gill\uff08AG\uff09\u30e2\u30c7\u30eb<\/strong> \u3068 <strong><code>cluster(id)<\/code>\uff08\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\uff09<\/strong> \u306e\u6982\u5ff5\u3001Counting Process\u5f62\u5f0f\uff08<code>tstart<\/code>, <code>tstop<\/code>, <code>status<\/code>\uff09\u3078\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3001R\u306b\u3088\u308b\u5b9f\u8df5\u30b3\u30fc\u30c9\u3001\u305d\u3057\u3066\u8ad6\u6587\u3067\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u307e\u3067\u3092\u5fb9\u5e95\u7684\u306b\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1. \u306a\u305c\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u306e\u307f\u300d\u3084\u300c\u5168\u30a4\u30d9\u30f3\u30c8\u306e\u5358\u7d14\u6295\u5165\u300d\u306f\u67fb\u8aad\u3067\u5373\u5374\u4e0b\u3055\u308c\u308b\u306e\u304b\uff1f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f601\uff1a\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\uff08Time-to-first event\uff09\u306b\u3088\u308b\u60c5\u5831\u306e\u5927\u91cf\u5ec3\u68c4<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5fc3\u4e0d\u5168\u306e\u518d\u5165\u9662\u3001\u304c\u3093\u306e\u8907\u6570\u56de\u518d\u767a\u3001\u5598\u606f\u3084COPD\u306e\u5897\u60aa\u306a\u3069\u3001\u81e8\u5e8a\u73fe\u5834\u3067\u306f\u540c\u3058\u60a3\u8005\u306b\u300c\u540c\u3058\u30a4\u30d9\u30f3\u30c8\u304c\u4f55\u5ea6\u3082\u7e70\u308a\u8fd4\u3057\u767a\u751f\u3059\u308b\uff08Recurrent Events\uff09\u300d\u30b1\u30fc\u30b9\u304c\u983b\u7e41\u306b\u5b58\u5728\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f93\u6765\u306e\u751f\u5b58\u6642\u9593\u89e3\u6790\uff08Kaplan-Meier\u6cd5\u3084\u6a19\u6e96\u7684\u306aCox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\uff09\u3067\u6700\u3082\u3088\u304f\u7528\u3044\u3089\u308c\u308b\u306e\u304c\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u307e\u3067\u306e\u6642\u9593\uff08Time-to-first event\uff09\u300d\u3092\u8a55\u4fa1\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u306f\u81f4\u547d\u7684\u306a\u81e8\u5e8a\u7684\u5f31\u70b9\u304c\u5b58\u5728\u3059\u308b\u3002<strong>\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3057\u305f\u77ac\u9593\u306b\u305d\u306e\u60a3\u8005\u306e\u8ffd\u8de1\u3092\u6253\u3061\u5207\u308a\uff08Censoring\uff09\u30012\u56de\u76ee\u4ee5\u964d\u306e\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u3092\u3059\u3079\u3066\u30b4\u30df\u7bb1\u306b\u6368\u3066\u3066\u3057\u307e\u3046\u70b9<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6cbb\u7642\u306e\u672c\u5f53\u306e\u75be\u75c5\u6291\u6b62\u52b9\u679c\u304c\u898b\u3048\u306a\u304f\u306a\u308b<\/strong>: \u65b0\u85ac\u306e\u4ecb\u5165\u306b\u3088\u3063\u3066\u300c\u521d\u56de\u518d\u5165\u9662\u300d\u306e\u6642\u671f\u306f\u5909\u308f\u3089\u306a\u304f\u3066\u3082\u3001\u300c2\u56de\u76ee\u30fb3\u56de\u76ee\u306e\u518d\u5165\u9662\u7387\u300d\u304c\u5287\u7684\u306b\u6291\u5236\u3055\u308c\u3066\u3044\u305f\u5834\u5408\u3001\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\u3067\u306f\u305d\u306e\u85ac\u306e\u771f\u306e\u4fa1\u5024\uff08\u5168\u75be\u75c5\u8ca0\u8377\u306e\u8efd\u6e1b\u52b9\u679c\uff09\u3092\u898b\u843d\u3068\u3057\u3066\u3057\u307e\u3046\u3002<\/li>\n\n\n\n<li><strong>\u691c\u51fa\u529b\uff08Statistical Power\uff09\u306e\u8457\u3057\u3044\u4f4e\u4e0b<\/strong>: \u305b\u3063\u304b\u304f\u9577\u671f\u9593\u8ffd\u8de1\u3057\u3066\u96c6\u3081\u305f\u8cb4\u91cd\u306a\u300c2\u56de\u76ee\u4ee5\u964d\u306e\u30a4\u30d9\u30f3\u30c8\u60c5\u5831\u300d\u3092\u4e00\u5207\u6d3b\u7528\u3057\u306a\u3044\u305f\u3081\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u7121\u99c4\u306b\u306a\u308a\u3001\u7d71\u8a08\u7684\u691c\u51fa\u529b\u304c\u5927\u5e45\u306b\u4f4e\u4e0b\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f602\uff1a\u5168\u30a4\u30d9\u30f3\u30c8\u3092\u5358\u4e00Cox\u56de\u5e30\u3078\u7a81\u3063\u8fbc\u3080\u300c\u500b\u4eba\u5185\u76f8\u95a2\uff08Within-subject correlation\uff09\u300d\u306e\u7121\u8996<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u3067\u6368\u3066\u3066\u3057\u307e\u3046\u306e\u304c\u52ff\u4f53\u306a\u3044\u306a\u3089\u30011\u4eba\u306e\u60a3\u8005\u304c3\u56de\u518d\u5165\u9662\u3057\u305f\u30c7\u30fc\u30bf\u30923\u884c\u306e\u7e26\u6301\u3061\u30c7\u30fc\u30bf\u306b\u3057\u3066\u3001\u305d\u306e\u307e\u307eCox\u56de\u5e30\u306b\u5165\u308c\u308c\u3070\u3044\u3044\u306e\u3067\u306f\uff1f\u300d\u3068\u8003\u3048\u305f\u304f\u306a\u308b\u3068\u3053\u308d\u3060\u304c\u3001\u3053\u308c\u306f\u3055\u3089\u306b\u5371\u967a\u306a\u81f4\u547d\u7684\u8aa4\u7528\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6a19\u6e96\u7684\u306aCox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u306f\u3001\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u884c\uff08\u89b3\u6e2c\u5024\uff09\u304c\u4e92\u3044\u306b\u72ec\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\uff08Independence of observations\uff09\u3092\u7d76\u5bfe\u7684\u306a\u524d\u63d0\u6761\u4ef6\u3068\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001<strong>\u300c\u540c\u3058\u60a3\u8005 A \u3055\u3093\u306e1\u56de\u76ee\u306e\u518d\u5165\u9662\u300d\u3068\u300c\u540c\u3058\u60a3\u8005 A \u3055\u3093\u306e2\u56de\u76ee\u306e\u518d\u5165\u9662\u300d\u306f\u72ec\u7acb\u3067\u306f\u306a\u3044\u3002<\/strong> \u305d\u3053\u306b\u306f\u60a3\u8005\u3054\u3068\u306e\u30af\u30bb\uff08\u907a\u4f1d\u7684\u7d20\u56e0\u3001\u751f\u6d3b\u7fd2\u6163\u3001\u57fa\u790e\u75be\u60a3\u306e\u91cd\u75c7\u5ea6\u3001\u30a2\u30c9\u30d2\u30a2\u30e9\u30f3\u30b9\u306a\u3069\uff09\u304c\u5b58\u5728\u3057\u3001\u540c\u4e00\u60a3\u8005\u5185\u306e\u30a4\u30d9\u30f3\u30c8\u540c\u58eb\u306b\u306f\u5f37\u3044 <strong>\u500b\u4eba\u5185\u76f8\u95a2\uff08Within-subject correlation\uff09<\/strong> \u304c\u50cd\u304f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u500b\u4eba\u5185\u76f8\u95a2\u3092\u7121\u8996\u3057\u3066\u6a19\u6e96\u7684\u306aCox\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u30e2\u30c7\u30eb\u306f\u300c\u72ec\u7acb\u3057\u305f\u65b0\u3057\u3044\u60a3\u8005\u304c\u3053\u3093\u306a\u306b\u305f\u304f\u3055\u3093\u30a4\u30d9\u30f3\u30c8\u3092\u8d77\u3053\u3057\u305f\uff01\u300d\u3068\u932f\u899a\u3057\u3066\u3057\u307e\u3046\u3002\u305d\u306e\u7d50\u679c\u3001<strong>\u6a19\u6e96\u8aa4\u5dee\uff08Standard Error: SE\uff09\u304c\u4e0d\u5f53\u306b\u5c0f\u3055\u304f\u898b\u7a4d\u3082\u3089\u308c\u3001<\/strong>$P$<strong> \u5024\u304c\u4eba\u5de5\u7684\u306b\u5c0f\u3055\u304f\u306a\u308a\uff08\u507d\u967d\u6027 \/ \u7b2c\u4e00\u7a2e\u306e\u8aa4\u308a\uff09\u3001\u9593\u9055\u3063\u305f\u6709\u610f\u5dee\u3092\u4f5c\u308a\u51fa\u3057\u3066\u3057\u307e\u3046<\/strong>\u3002\u3053\u308c\u304c\u3001\u67fb\u8aad\u8005\u304b\u3089\u5373\u5ea7\u306b\u5374\u4e0b\u3055\u308c\u308b\u7406\u7531\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u5168\u75be\u75c5\u8ca0\u8377\u3092\u6b63\u3057\u304f\u8a55\u4fa1\u3059\u308b\u300cAndersen-Gill\uff08AG\uff09\u30e2\u30c7\u30eb\u300d\u3068 Robust SE<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Andersen-Gill\uff08AG\uff09\u30e2\u30c7\u30eb\u3068\u306f\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\u306b\u304a\u3044\u3066\u3001\u4e16\u754c\u7684\u306b\u6700\u3082\u6a19\u6e96\u7684\u304b\u3064\u6c4e\u7528\u6027\u306e\u9ad8\u3044\u30a2\u30d7\u30ed\u30fc\u30c1\u304c <strong>Andersen-Gill\uff08AG\uff09\u30e2\u30c7\u30eb<\/strong> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AG\u30e2\u30c7\u30eb\u306f\u3001\u901a\u5e38\u306eCox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u3092\u300cCounting Process\uff08\u8a08\u6570\u904e\u7a0b\uff09\u300d\u306e\u67a0\u7d44\u307f\u3078\u3068\u62e1\u5f35\u3057\u305f\u624b\u6cd5\u3067\u3042\u308b\u3002\u305d\u306e\u57fa\u672c\u30b3\u30f3\u30bb\u30d7\u30c8\u306f\u975e\u5e38\u306b\u660e\u5feb\u3067\u3001<strong>\u300c\u5404\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3057\u305f\u5f8c\u3082\u3001\u60a3\u8005\u306f\u76f4\u3061\u306b\u6b21\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u30ea\u30b9\u30af\u96c6\u5408\uff08At-risk set\uff09\u306b\u623b\u308a\u3001\u5168\u30a4\u30d9\u30f3\u30c8\u3092\u901a\u3057\u3066\u5171\u901a\u306e\u57fa\u5e95\u30cf\u30b6\u30fc\u30c9\uff08Baseline Hazard\uff09\u3092\u6301\u3064\u300d<\/strong> \u3068\u4eee\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u203b\u306a\u304a\u3001\u30a4\u30d9\u30f3\u30c8\u306e\u56de\u6570\uff081\u56de\u76ee\u30fb2\u56de\u76ee\u2026\uff09\u306b\u3088\u3063\u3066\u57fa\u6e96\u30ea\u30b9\u30af\u304c\u5909\u5316\u3059\u308b\u3068\u4eee\u5b9a\u3057\u305f\u3044\u5834\u5408\u306f PWP \u30e2\u30c7\u30eb\u3001\u60a3\u8005\u3054\u3068\u306e\u30e9\u30f3\u30c0\u30e0\u52b9\u679c\u3092\u7d44\u307f\u8fbc\u307f\u305f\u3044\u5834\u5408\u306f Frailty \u30e2\u30c7\u30eb\u306a\u3069\u304c\u7528\u3044\u3089\u308c\u308b\u304c\u3001\u5168\u75be\u75c5\u8ca0\u8377\u306e\u5168\u4f53\u50cf\u3092\u8a55\u4fa1\u3059\u308b\u7b2c\u4e00\u9078\u629e\u3068\u3057\u3066\u56fd\u969b\u7684\u306b\u652f\u6301\u3055\u308c\u3066\u3044\u308b\u306e\u304cAG\u30e2\u30c7\u30eb\u3067\u3042\u308b\u3002\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u500b\u4eba\u5185\u76f8\u95a2\u3092\u6483\u9000\u3059\u308b <code>cluster(id)<\/code>\uff08\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">AG\u30e2\u30c7\u30eb\u3092\u5b9f\u884c\u3059\u308b\u969b\u3001\u524d\u8ff0\u3057\u305f\u300c\u500b\u4eba\u5185\u76f8\u95a2\uff08\u540c\u4e00\u60a3\u8005\u5185\u306e\u76f8\u95a2\uff09\u300d\u3092\u6b63\u3057\u304f\u51e6\u7406\u3059\u308b\u305f\u3081\u306b\u4e0d\u53ef\u6b20\u3068\u306a\u308b\u306e\u304c <strong>\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\uff08Robust Standard Error \/ Sandwich Estimator\uff09<\/strong> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R\u306e <code>coxph<\/code> \u95a2\u6570\u3067\u306f\u3001\u8aac\u660e\u5909\u6570\u5074\u306b <strong><code>cluster(id)<\/code><\/strong> \u3092\u8ffd\u8a18\u3059\u308b\u3060\u3051\u3067\u3053\u306e\u88dc\u6b63\u304c\u5b8c\u4e86\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u70b9\u63a8\u5b9a\u5024\uff08\u30cf\u30b6\u30fc\u30c9\u6bd4\uff1aHR\uff09<\/strong>: \u5168\u8ffd\u8de1\u671f\u9593\u306b\u304a\u3051\u308b\u7dcf\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u7387\u306e\u6bd4\uff08Overall Event Rate Ratio\uff09\u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u6a19\u6e96\u8aa4\u5dee\uff08SE\uff09\u3068 <\/strong>$P$<strong> \u5024<\/strong>: <code>cluster(id)<\/code> \u3092\u6307\u5b9a\u3059\u308b\u3053\u3068\u3067\u3001\u540c\u4e00\u60a3\u8005\uff08ID\uff09\u306e\u30c7\u30fc\u30bf\u3092\u300c1\u3064\u306e\u30af\u30e9\u30b9\u30bf\uff08\u56fa\u307e\u308a\uff09\u300d\u3068\u3057\u3066\u6271\u3044\u3001\u500b\u4eba\u5185\u76f8\u95a2\u306b\u3088\u3063\u3066\u5c0f\u3055\u304f\u306a\u308a\u3059\u304e\u3066\u3044\u305f\u6a19\u6e96\u8aa4\u5dee\u3092\u9069\u5207\u306b\u81a8\u3089\u307e\u305b\u3066\u3001\u6b63\u5f53\u306a $P$ \u5024\u306895%\u4fe1\u983c\u533a\u9593\u3092\u7b97\u51fa\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Andersen-Gill\u30e2\u30c7\u30eb\u306e\u30cf\u30b6\u30fc\u30c9\u5f0f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u88ab\u9a13\u8005 $i$ \u306e\u6642\u523b $t$ \u306b\u304a\u3051\u308b AG \u30e2\u30c7\u30eb\u306e\u30cf\u30b6\u30fc\u30c9\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3002$$\\lambda_i(t) = \\lambda_0(t) \\exp(\\boldsymbol{\\beta}^T \\mathbf{X}_i(t))$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u91cd\u8981\u306a\u306e\u306f\u3001\u57fa\u5e95\u30cf\u30b6\u30fc\u30c9 $\\lambda_0(t)$ \u304c<strong>\u3059\u3079\u3066\u306e\u30a4\u30d9\u30f3\u30c8\u56de\u6570\uff081\u56de\u76ee\u30012\u56de\u76ee\u30013\u56de\u76ee\u2026\uff09\u3092\u901a\u3058\u3066\u5171\u901a<\/strong>\u3067\u3042\u308b\u3068\u3044\u3046\u70b9\u3067\u3042\u308b\u3002\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3057\u3066\u3082\u6642\u9593\u306f\u30ea\u30bb\u30c3\u30c8\u3055\u308c\u305a\u3001\u5171\u901a\u306e\u30bf\u30a4\u30e0\u30e9\u30a4\u30f3 $t$ \u306e\u4e0a\u3067\u30ea\u30b9\u30af\u96c6\u5408\u3078\u3068\u5373\u5ea7\u306b\u5fa9\u5e30\u3057\u3001\u8ffd\u8de1\u304c\u7d99\u7d9a\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<div id=\"biost-2184865444\" 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\">3. Counting Process\u5f62\u5f0f\uff08<code>tstart<\/code>, <code>tstop<\/code>, <code>status<\/code>\uff09\u3078\u306e\u30c7\u30fc\u30bf\u6574\u5f62<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1\u60a3\u80051\u884c\u30c7\u30fc\u30bf\u304b\u3089 Counting Process \u5f62\u5f0f\u3078\u306e\u5909\u63db<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\u3092\u5b9f\u884c\u3059\u308b\u306b\u306f\u3001\u30c7\u30fc\u30bf\u3092\u6a19\u6e96\u7684\u306a\u300c1\u60a3\u80051\u884c\uff08Time-to-first\uff09\u300d\u5f62\u5f0f\u304b\u3089\u3001\u6642\u9593\u3092\u533a\u5207\u3063\u305f <strong>Counting Process \u5f62\u5f0f\uff081\u60a3\u8005\u8907\u6570\u884c\u30c7\u30fc\u30bf\uff09<\/strong> \u3078\u3068\u5909\u63db\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Counting Process \u5f62\u5f0f\u3067\u306f\u3001\u5404\u884c\u306b\u4ee5\u4e0b\u306e3\u3064\u306e\u5fc5\u9808\u30ab\u30e9\u30e0\u3092\u4fdd\u6301\u3055\u305b\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><code>tstart<\/code><\/strong>: \u305d\u306e\u89b3\u5bdf\u533a\u9593\u306e\u958b\u59cb\u6642\u9593<\/li>\n\n\n\n<li><strong><code>tstop<\/code><\/strong>: \u305d\u306e\u89b3\u5bdf\u533a\u9593\u306e\u7d42\u4e86\u6642\u9593<\/li>\n\n\n\n<li><strong><code>status<\/code><\/strong>: \u533a\u9593\u7d42\u4e86\u6642\uff08<code>tstop<\/code>\uff09\u306b\u304a\u3051\u308b\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u306e\u6709\u7121\uff081 = \u30a4\u30d9\u30f3\u30c8\u767a\u751f, 0 = \u6253\u5207\u308a\/\u89b3\u5bdf\u7d99\u7d9a\uff09<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5177\u4f53\u4f8b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u3048\u3070\u3001ID = 1 \u306e\u60a3\u8005\u304c\u300c10\u30f6\u6708\u76ee\u306b1\u56de\u76ee\u306e\u518d\u5165\u9662\u300d\u300c25\u30f6\u6708\u76ee\u306b2\u56de\u76ee\u306e\u518d\u5165\u9662\u300d\u3092\u8d77\u3053\u3057\u3001\u300c60\u30f6\u6708\u76ee\u3067\u8ffd\u8de1\u7d42\u4e86\uff08\u751f\u5b58\u6253\u5207\u308a\uff09\u300d\u3068\u306a\u3063\u305f\u5834\u5408\u3001\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6574\u5f62\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>id<\/strong><\/td><td><strong>tstart<\/strong><\/td><td><strong>tstop<\/strong><\/td><td><strong>status<\/strong><\/td><td><strong>group<\/strong><\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>0<\/td><td>10<\/td><td><strong>1<\/strong><\/td><td>New_Drug<\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>10<\/td><td>25<\/td><td><strong>1<\/strong><\/td><td>New_Drug<\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>25<\/td><td>60<\/td><td><strong>0<\/strong><\/td><td>New_Drug<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1\u884c\u76ee<\/strong>: \u89b3\u5bdf\u958b\u59cb\uff080\u30f6\u6708\uff09\u304b\u308910\u30f6\u6708\u76ee\u307e\u3067\u8ffd\u8de1\u3055\u308c\u30011\u56de\u76ee\u306e\u518d\u5165\u9662\u304c\u767a\u751f\uff08<code>status = 1<\/code>\uff09\u3002<\/li>\n\n\n\n<li><strong>2\u884c\u76ee<\/strong>: 10\u30f6\u6708\u76ee\u304b\u3089\u5373\u5ea7\u306b\u6b21\u306e\u30ea\u30b9\u30af\u96c6\u5408\u306b\u5fa9\u5e30\u3057\u300125\u30f6\u6708\u76ee\u307e\u3067\u8ffd\u8de1\u3055\u308c\u30662\u56de\u76ee\u306e\u518d\u5165\u9662\u304c\u767a\u751f\uff08<code>status = 1<\/code>\uff09\u3002<\/li>\n\n\n\n<li><strong>3\u884c\u76ee<\/strong>: 25\u30f6\u6708\u76ee\u304b\u3089\u30ea\u30b9\u30af\u96c6\u5408\u306b\u5fa9\u5e30\u3057\u300160\u30f6\u6708\u76ee\u307e\u3067\u8ffd\u8de1\u3055\u308c\u3066\u30a4\u30d9\u30f3\u30c8\u306a\u304f\u89b3\u5bdf\u7d42\u4e86\uff08<code>status = 0<\/code>\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u3088\u3046\u306b\u30c7\u30fc\u30bf\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u3067\u3001\u5168\u8ffd\u8de1\u671f\u9593\u306b\u304a\u3051\u308b\u7d2f\u7a4d\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u72b6\u6cc1\u3092\u6b63\u78ba\u306b\u30e2\u30c7\u30eb\u306b\u7d44\u307f\u8fbc\u3080\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u88dc\u8db3\uff08\u95a2\u9023\u8a18\u4e8b\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Counting Process\u5f62\u5f0f\u3078\u306e\u30c7\u30fc\u30bf\u5909\u63db\u624b\u9806\u3084 <code>tmerge<\/code> \u95a2\u6570\u306e\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f <a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/time-dependent-covariates-in-cox-regression-with-r-a-complete-guide-to-handling-repeated-measures-treatment-changes-and-the-tmerge-function\/\">\u6642\u9593\u4f9d\u5b58\u6027\u5171\u5909\u91cf\u3092\u542b\u3080Cox\u56de\u5e30<\/a> \u3092\u53c2\u7167\u3055\u308c\u305f\u3044\u3002<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">4. \u3010\u5b9f\u8df5R\u30b3\u30fc\u30c9\u3011<code>coxph<\/code> \uff0b <code>cluster(id)<\/code> \u306b\u3088\u308b\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\uff08Step by Step\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304b\u3089\u306f\u3001R\u306e <code>survival<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u7528\u3044\u3066\u3001\u7591\u4f3c\u7684\u306a\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3057\u3001\u5f93\u6765\u306e\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\u300d\u3068\u300cAndersen-Gill\u30e2\u30c7\u30eb\u300d\u3092\u6bd4\u8f03\u3057\u306a\u304c\u3089Step by Step\u3067\u5b9f\u884c\u3059\u308b\u624b\u9806\u3092\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: \u7591\u4f3c\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\u3068\u78ba\u8a8d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30c7\u30fc\u30bf\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u624b\u9806\u30924\u3064\u306e\u30b5\u30d6\u30b9\u30c6\u30c3\u30d7\u306b\u5206\u3051\u3066\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1-1: \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u8aad\u307f\u8fbc\u307f\u3068\u57fa\u672c\u60a3\u8005\u30c7\u30fc\u30bf\u306e\u8a2d\u5b9a<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305a\u306f\u5fc5\u8981\u306a\u30d1\u30c3\u30b1\u30fc\u30b8\uff08<code>tidyverse<\/code>, <code>survival<\/code>\uff09\u3092\u8aad\u307f\u8fbc\u307f\u3001\u60a3\u8005\u30ec\u30d9\u30eb\u306e\u80cc\u666f\u60c5\u5831\uff08ID\u3001\u5272\u308a\u4ed8\u3051\u7fa4\u3001\u5e74\u9f62\uff09\u3092\u751f\u6210\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>library(tidyverse)\nlibrary(survival)\n\n# \u4e71\u6570\u30b7\u30fc\u30c9\u306e\u8a2d\u5b9a\nset.seed(123)\nn_patients &lt;- 200\n\n# \u7591\u4f3c\u60a3\u8005\u30c7\u30fc\u30bf\u306e\u751f\u6210\uff08ID, \u30b0\u30eb\u30fc\u30d7, \u5e74\u9f62\uff09\npatients &lt;- tibble(\n  id = 1:n_patients,\n  group = factor(rep(c(\"Control\", \"Treatment\"), each = n_patients \/ 2), levels = c(\"Control\", \"Treatment\")),\n  age = round(rnorm(n_patients, mean = 65, sd = 10))\n)\n<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1-2: \u5404\u60a3\u8005\u306e\u7d2f\u7a4d\u30a4\u30d9\u30f3\u30c8\u6642\u9593\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5404\u60a3\u8005\u306b\u5bfe\u3057\u3066\u3001\u6642\u9593\u306e\u7d4c\u904e\u306b\u4f34\u3044\u7e70\u308a\u8fd4\u3057\u767a\u751f\u3059\u308b\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u306e\u6642\u9593\u9593\u9694\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5404\u60a3\u8005\u306e\u8907\u6570\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u9593\u9694\u3092\u751f\u6210\u3059\u308b\u95a2\u6570\u51e6\u7406\ndf_sim_list &lt;- map(patients$id, function(pid) {\n  p_info &lt;- patients %&gt;% filter(id == pid)\n  \n  # \u30a4\u30d9\u30f3\u30c8\u767a\u751f\u7387\u306e\u8a2d\u5b9a\uff08Treatment\u7fa4\u3067\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u7387\u304c\u4f4e\u3044\uff09\n  rate_param &lt;- if_else(p_info$group == \"Treatment\", 0.03, 0.05)\n  \n  # \u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u9593\u9694\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\uff08\u6700\u592710\u56de\u5206\uff09\n  intervals &lt;- rexp(10, rate = rate_param)\n  cum_times &lt;- cumsum(intervals)\n  \n  # \u6700\u9577\u8ffd\u8de1\u671f\u9593\uff0836\u30f6\u6708\uff1d3\u5e74\uff09\n  max_followup &lt;- 36\n  \n  # \u6700\u9577\u8ffd\u8de1\u671f\u9593\u307e\u3067\u306b\u767a\u751f\u3057\u305f\u30a4\u30d9\u30f3\u30c8\u6642\u523b\u3092\u62bd\u51fa\n  valid_times &lt;- cum_times&#91;cum_times &lt; max_followup]\n  all_times &lt;- c(0, valid_times, max_followup)\n  \n  tibble(\n    id = pid,\n    group = p_info$group,\n    age = p_info$age,\n    times = list(all_times),\n    n_events = length(valid_times)\n  )\n})\n<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1-3: Counting Process\u5f62\u5f0f\uff08<code>tstart<\/code>, <code>tstop<\/code>, <code>status<\/code>\uff09\u3078\u306e\u30c7\u30fc\u30bf\u5909\u63db<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u305f\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u6642\u523b\u3092\u3001AG\u30e2\u30c7\u30eb\u306b\u5fc5\u8981\u306a Counting Process \u5f62\u5f0f\uff081\u60a3\u8005\u8907\u6570\u884c\uff09\u3078\u3068\u6574\u5f62\u3059\u308b\u3002\u8ffd\u8de1\u6642\u9593\u304c0\u306e\u4e0d\u6574\u5408\u884c\u304c\u751f\u3058\u306a\u3044\u3088\u3046\u3001<code>tstart &lt; tstop<\/code> \u306e\u30d0\u30ea\u30c7\u30fc\u30b7\u30e7\u30f3\u51e6\u7406\u3092\u5165\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30bf\u30a4\u30e0\u30e9\u30a4\u30f3\u3092 (tstart, tstop, status) \u5f62\u5f0f\u3078\u5909\u63db\ndf_recurrent &lt;- map_dfr(df_sim_list, function(item) {\n  all_times &lt;- item$times&#91;&#91;1]]\n  n_ev &lt;- item$n_events\n  \n  tibble(\n    id = item$id,\n    group = item$group,\n    age = item$age,\n    tstart = round(all_times&#91;-length(all_times)], 1),\n    tstop = round(all_times&#91;-1], 1),\n    status = c(rep(1, n_ev), 0) # \u6700\u5f8c\u306e\u533a\u9593\u306f\u89b3\u5bdf\u7d42\u4e86\uff08status = 0\uff09\n  )\n}) %>% \n  filter(tstart &lt; tstop) # \u8ffd\u8de1\u6642\u9593\u304c0\u306e\u4e0d\u6574\u5408\u884c\u3092\u9664\u5916\n<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1-4: \u751f\u6210\u3055\u308c\u305f\u7e26\u6301\u3061\u30c7\u30fc\u30bf\u306e\u69cb\u9020\u78ba\u8a8d<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f5c\u6210\u3055\u308c\u305f Counting Process \u5f62\u5f0f\u306e\u30c7\u30fc\u30bf\u306e\u5148\u982d\u884c\u3092\u78ba\u8a8d\u3057\u30011\u4eba\u306e\u60a3\u8005\u304c\u8907\u6570\u306e\u89b3\u5bdf\u533a\u9593\u3092\u6301\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30c7\u30fc\u30bf\u306e\u5148\u982d\uff08ID=1\u306e\u8907\u6570\u533a\u9593\u30c7\u30fc\u30bf\u306a\u3069\uff09\u3092\u78ba\u8a8d\nhead(df_recurrent, 10)\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: \u5f93\u6765\u306e\u300c\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u306e\u307f\u300d\u306eCox\u56de\u5e30\uff08\u6bd4\u8f03\u7528\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u8f03\u306e\u305f\u3081\u306b\u3001\u521d\u56de\u30a4\u30d9\u30f3\u30c8\uff08\u5404\u60a3\u8005\u306e\u6700\u521d\u306e\u533a\u9593 <code>tstart == 0<\/code>\uff09\u306e\u307f\u3092\u5207\u308a\u51fa\u3057\u305f\u5f93\u6765\u901a\u308a\u306eCox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u3092\u5b9f\u884c\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u521d\u56de\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u306e\u307f\u306e\u62bd\u51fa\uff08\u5404\u60a3\u8005\u306e1\u884c\u76ee\u30c7\u30fc\u30bf\uff09\ndf_first_event &lt;- df_recurrent %&gt;%\n  group_by(id) %&gt;%\n  slice(1) %&gt;%\n  ungroup()\n\n# \u521d\u56de\u30a4\u30d9\u30f3\u30c8\u306e\u307f\u306eCox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\nfit_first &lt;- coxph(Surv(tstop, status) ~ group + age, data = df_first_event)\nsummary(fit_first)\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Andersen-Gill\uff08AG\uff09\u30e2\u30c7\u30eb\u306e\u5b9f\u884c\uff08<code>coxph<\/code> \uff0b <code>cluster(id)<\/code>\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5168\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u3092\u7528\u3044\u3001Counting Process\u5f62\u5f0f\u306e <code>Surv(tstart, tstop, status)<\/code> \u3068\u500b\u4eba\u5185\u76f8\u95a2\u3092\u88dc\u6b63\u3059\u308b <code>cluster(id)<\/code> \u3092\u7d44\u307f\u8fbc\u3093\u3067AG\u30e2\u30c7\u30eb\u3092\u5b9f\u884c\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Andersen-Gill \u30e2\u30c7\u30eb\u306e\u5b9f\u884c\uff08Robust SE \u9069\u7528\uff09\nfit_ag &lt;- coxph(\n  Surv(tstart, tstop, status) ~ group + age + cluster(id), \n  data = df_recurrent\n)\n\n# \u30e2\u30c7\u30eb\u7d50\u679c\u306e\u30b5\u30de\u30ea\u30fc\u8868\u793a\nsummary(fit_ag)\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: \u521d\u56de\u30a4\u30d9\u30f3\u30c8\u89e3\u6790 vs AG\u30e2\u30c7\u30eb\u306e\u7d50\u679c\u6bd4\u8f03\u3068\u89e3\u91c8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fa\u529b\u7d50\u679c\u304b\u3089\u3001\u6cbb\u7642\u7fa4\uff08Treatment vs Control\uff09\u306e\u30cf\u30b6\u30fc\u30c9\u6bd4\uff08HR\uff09\u3068 $P$ \u5024\u3092\u6bd4\u8f03\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u30e2\u30c7\u30eb\uff08<code>fit_first<\/code>\uff09<\/strong>: \u521d\u56de\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u307e\u3067\u306e\u9045\u5ef6\u52b9\u679c\u306e\u307f\u3092\u8a55\u4fa1\u3059\u308b\u30022\u56de\u76ee\u4ee5\u964d\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u6368\u3066\u3089\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u4fe1\u983c\u533a\u9593\u304c\u5e83\u304f\uff08SE\u304c\u5927\u304d\u304f\uff09\u306a\u308b\u50be\u5411\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>Andersen-Gill\u30e2\u30c7\u30eb\uff08<code>fit_ag<\/code>\uff09<\/strong>: \u5168\u8ffd\u8de1\u671f\u9593\u4e2d\u306e\u300c\u7dcf\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u7387\uff08Overall Event Rate\uff09\u300d\u3092\u8a55\u4fa1\u3059\u308b\u3002\u3059\u3079\u3066\u306e\u30a4\u30d9\u30f3\u30c8\u60c5\u5831\u3092\u6d3b\u7528\u3059\u308b\u305f\u3081\u3001\u30a4\u30d9\u30f3\u30c8\u6570\u304c\u591a\u304f\u306a\u308a\u691c\u51fa\u529b\u304c\u5411\u4e0a\u3059\u308b\u3068\u540c\u6642\u306b\u3001<code>cluster(id)<\/code> \u306b\u3088\u3063\u3066\u6b63\u78ba\u306a Robust SE \u304c\u7b97\u51fa\u3055\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">5. \u8ad6\u6587\u3067\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\uff08Methods &amp; Results\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ad6\u6587\uff08Methods\u304a\u3088\u3073Results\u30bb\u30af\u30b7\u30e7\u30f3\uff09\u306b\u305d\u306e\u307e\u307e\u8a18\u8ff0\u3067\u304d\u308b\u6a19\u6e96\u7684\u306a\u82f1\u6587\u8868\u73fe\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u3092\u793a\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Methods \u30bb\u30af\u30b7\u30e7\u30f3\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">&#8220;To evaluate the overall disease burden and the effect of intervention on recurrent [events, e.g., heart failure hospitalizations], the Andersen-Gill (AG) extension of the Cox proportional hazards model was performed. Data were formatted into the counting process structure with time-interval variables (<code>tstart<\/code>, <code>tstop<\/code>) and an event indicator (<code>status<\/code>).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To account for within-subject correlation among recurrent events within the same patient, robust standard errors were calculated using a sandwich estimator clustered on patient identity (<code>cluster(id)<\/code>). The treatment effect was presented as an overall event rate ratio (hazard ratio [HR]) with its corresponding 95% confidence interval (CI). For comparison, a conventional time-to-first event Cox regression analysis was also conducted. All analyses were performed using R (version 4.x.x) with the <code>survival<\/code> package.&#8221;<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Results \u30bb\u30af\u30b7\u30e7\u30f3\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">&#8220;Over a median follow-up of [36] months, a total of [245] recurrent [heart failure hospitalizations] occurred among [200] patients ([140] events in the Control group and [105] events in the Treatment group).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the primary Andersen-Gill model evaluating all recurrent events with robust standard errors, [Treatment] was associated with a significant reduction in the overall risk of [hospitalization] (Hazard Ratio [HR], [0.75]; 95% CI, [0.60] to [0.94];$P = 0.013$). In contrast, the conventional time-to-first event analysis demonstrated a HR of [0.78] (95% CI, [0.56] to [1.08];$P = 0.14$), underestimating the cumulative clinical benefit of the treatment by ignoring subsequent recurrent events.&#8221;<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">6. \u307e\u3068\u3081\uff06\u4e00\u62ec\u30b3\u30d4\u30da\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u672c\u8a18\u4e8b\u306e\u30dd\u30a4\u30f3\u30c8\u304a\u3055\u3089\u3044<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u521d\u56de\u30a4\u30d9\u30f3\u30c8\uff08Time-to-first event\uff09\u3060\u3051\u306e\u89e3\u6790\u306f\u52ff\u4f53\u306a\u3044<\/strong>: 2\u56de\u76ee\u4ee5\u964d\u306e\u518d\u767a\u30a4\u30d9\u30f3\u30c8\u3092\u5207\u308a\u6368\u3066\u3066\u3057\u307e\u3046\u305f\u3081\u3001\u75be\u60a3\u306e\u5168\u8ca0\u62c5\uff08Cumulative Disease Burden\uff09\u3092\u898b\u843d\u3068\u3057\u3001\u691c\u51fa\u529b\u3092\u4f4e\u4e0b\u3055\u305b\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5168\u30a4\u30d9\u30f3\u30c8\u306e\u5358\u7d14\u6295\u5165\u306f\u7d76\u5bfeNG<\/strong>: \u500b\u4eba\u5185\u76f8\u95a2\uff08Within-subject correlation\uff09\u3092\u7121\u8996\u3059\u308b\u3068\u6a19\u6e96\u8aa4\u5dee\u304c\u4e0d\u5f53\u306b\u5c0f\u3055\u304f\u306a\u308a\u3001\u507d\u967d\u6027\uff08$P &lt; 0.05$\uff09\u3092\u8d77\u3053\u3057\u3066\u67fb\u8aad\u3067\u5373\u5374\u4e0b\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u89e3\u6c7a\u7b56\u306f Andersen-Gill\uff08AG\uff09\u30e2\u30c7\u30eb \uff0b <code>cluster(id)<\/code><\/strong>: Counting Process\u5f62\u5f0f\uff08<code>tstart<\/code>, <code>tstop<\/code>, <code>status<\/code>\uff09\u306b\u30c7\u30fc\u30bf\u3092\u6574\u5f62\u3057\u3001<code>cluster(id)<\/code> \u3067\u30ed\u30d0\u30b9\u30c8\u6a19\u6e96\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3001\u500b\u4eba\u5185\u76f8\u95a2\u3092\u6b63\u5f53\u306b\u88dc\u6b63\u3057\u305f\u5168\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u7387\u306e\u8a55\u4fa1\u304c\u53ef\u80fd\u3068\u306a\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u62ec\u5b9f\u884c\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\uff06\u30da\u30fc\u30b9\u30c8\u3059\u308b\u3053\u3068\u3067\u3001\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\u3001Counting Process\u5f62\u5f0f\u306e\u78ba\u8a8d\u3001\u521d\u56de\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\u3001AG\u30e2\u30c7\u30eb\u306e\u5b9f\u884c\u3001\u304a\u3088\u3073\u8ad6\u6587\u8868\u793a\u7528\u30c6\u30fc\u30d6\u30eb\uff08<code>gtsummary<\/code>\uff09\u306e\u51fa\u529b\u307e\u3067\u3092\u4e00\u6c17\u901a\u8cab\u3067\u5b9f\u884c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># ==============================================================================\n# \u518d\u767a\u30a4\u30d9\u30f3\u30c8\u751f\u5b58\u6642\u9593\u89e3\u6790\uff08Andersen-Gill Model &amp; Robust SE\uff09\u4e00\u62ec\u5b9f\u884c\u30b9\u30af\u30ea\u30d7\u30c8\n# \u30d1\u30c3\u30b1\u30fc\u30b8: survival, tidyverse, gtsummary\n# ==============================================================================\n\nif (!requireNamespace(\"survival\", quietly = TRUE)) install.packages(\"survival\")\nif (!requireNamespace(\"tidyverse\", quietly = TRUE)) install.packages(\"tidyverse\")\nif (!requireNamespace(\"gtsummary\", quietly = TRUE)) install.packages(\"gtsummary\")\n\nlibrary(survival)\nlibrary(tidyverse)\nlibrary(gtsummary)\n\n# 1. \u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\uff08Counting Process\u5f62\u5f0f\uff09\nset.seed(123)\nn_patients &lt;- 200\n\npatients &lt;- tibble(\n  id = 1:n_patients,\n  group = factor(rep(c(\"Control\", \"Treatment\"), each = n_patients \/ 2), levels = c(\"Control\", \"Treatment\")),\n  age = round(rnorm(n_patients, mean = 65, sd = 10))\n)\n\ndf_recurrent &lt;- map_dframe(patients$id, function(pid) {\n  p_info &lt;- patients %&gt;% filter(id == pid)\n  rate_param &lt;- if_else(p_info$group == \"Treatment\", 0.03, 0.05)\n  \n  intervals &lt;- rexp(10, rate = rate_param)\n  cum_times &lt;- cumsum(intervals)\n  max_followup &lt;- 36\n  \n  valid_times &lt;- cum_times&#91;cum_times &lt; max_followup]\n  all_times &lt;- c(0, valid_times, max_followup)\n  \n  tibble(\n    id = pid,\n    group = p_info$group,\n    age = p_info$age,\n    tstart = round(all_times&#91;-length(all_times)], 1),\n    tstop = round(all_times&#91;-1], 1),\n    status = c(rep(1, length(valid_times)), 0)\n  )\n}) %&gt;% filter(tstart &lt; tstop)\n\n# 2. \u521d\u56de\u30a4\u30d9\u30f3\u30c8\u89e3\u6790\uff08Time-to-first event\uff09\ndf_first &lt;- df_recurrent %&gt;% group_by(id) %&gt;% slice(1) %&gt;% ungroup()\nfit_first &lt;- coxph(Surv(tstop, status) ~ group + age, data = df_first)\n\n# 3. Andersen-Gill \u30e2\u30c7\u30eb\u89e3\u6790\uff08Recurrent Events + Robust SE\uff09\nfit_ag &lt;- coxph(Surv(tstart, tstop, status) ~ group + age + cluster(id), data = df_recurrent)\n\n# 4. \u7d50\u679c\u306e\u51fa\u529b\ncat(\"\\n==============================================================================\\n\")\ncat(\"                  1. \u521d\u56de\u30a4\u30d9\u30f3\u30c8\u306e\u307f\u306e\u89e3\u6790 (Time-to-First)                   \\n\")\ncat(\"==============================================================================\\n\")\nprint(summary(fit_first))\n\ncat(\"\\n==============================================================================\\n\")\ncat(\"            2. Andersen-Gill \u30e2\u30c7\u30eb\u89e3\u6790 (Recurrent Events + Robust SE)        \\n\")\ncat(\"==============================================================================\\n\")\nprint(summary(fit_ag))\n\n# 5. gtsummary \u306b\u3088\u308b\u8ad6\u6587\u7528\u30c6\u30fc\u30d6\u30eb\u306e\u4f5c\u6210\ntbl_ag &lt;- fit_ag %&gt;%\n  tbl_regression(exponentiate = TRUE) %&gt;%\n  bold_p() %&gt;%\n  modify_caption(\"**Table. Multivariable Andersen-Gill Model for Recurrent Events**\")\n\nprint(tbl_ag)\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"578\" height=\"301\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/recurrent_event_AG_result.png\" alt=\"\" class=\"wp-image-4727\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/recurrent_event_AG_result.png 578w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/recurrent_event_AG_result-300x156.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/amzn.to\/4hohe8C\">\u8ab0\u3082\u6559\u3048\u3066\u304f\u308c\u306a\u304b\u3063\u305f\u3000\u533b\u7642\u7d71\u8a08\u306e\u4f7f\u3044\u5206\u3051\u301c\u8ff7\u3044\u3084\u3059\u3044\u89e3\u6790\u624b\u6cd5\u306e\u9078\u3073\u65b9\u304c\uff0cR\u3067\u5b9f\u611f\u3057\u306a\u304c\u3089\u308f\u304b\u308b\uff01<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u300c\u5148\u751f\uff01\u5fc3\u4e0d\u5168\u306e\u60a3\u8005\u3055\u3093\u306e\u518d\u5165\u9662\u30c7\u30fc\u30bf\u3092\u89e3\u6790\u3057\u305f\u304f\u3066\u30012\u56de\u76ee\u30843\u56de\u76ee\u306e\u518d\u5165\u9662\u30c7\u30fc\u30bf\u3082\u305f\u304f\u3055\u3093\u3042\u3063\u305f\u306e\u3067\u3059\u304c\u3001\u89e3\u6790\u65b9\u6cd5\u304c\u3088\u304f\u5206\u304b\u3089\u306a\u304b\u3063\u305f\u306e\u3067\u3001\u3068\u308a\u3042\u3048\u305a\u300e\u521d\u56de\u518d\u5165\u9662\u307e\u3067\u306e\u6642\u9593\uff08Time-to-first event\uff09\u300f\u3060 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4728,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[21],"tags":[],"class_list":["post-4726","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/\u4f55\u5ea6\u3082\u518d\u5165\u9662AG\u30e2\u30c7\u30eb-scaled.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4726","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=4726"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4726\/revisions"}],"predecessor-version":[{"id":4730,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4726\/revisions\/4730"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4728"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}