{"id":4116,"date":"2026-01-03T14:18:49","date_gmt":"2026-01-03T05:18:49","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4116"},"modified":"2026-01-03T14:18:51","modified_gmt":"2026-01-03T05:18:51","slug":"mnar-sensitivity-analysis-in-multiple-imputation-using-mice-insights-into-invisible-missingness","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/mnar-sensitivity-analysis-in-multiple-imputation-using-mice-insights-into-invisible-missingness\/","title":{"rendered":"MICE\u3092\u7528\u3044\u305f\u591a\u91cd\u4ee3\u5165\u306b\u304a\u3051\u308bMNAR\u611f\u5ea6\u5206\u6790\uff1a\u898b\u3048\u306a\u3044\u6b20\u6e2c\u3078\u306e\u6d1e\u5bdf"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u7d71\u8a08\u89e3\u6790\u306b\u304a\u3044\u3066\u3001\u6b20\u6e2c\u30c7\u30fc\u30bf\u306f\u5e38\u306b\u60a9\u307e\u3057\u3044\u554f\u984c\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u6b20\u6e2c\u304c\u30e9\u30f3\u30c0\u30e0\u3067\u306f\u306a\u3044\uff08Missing Not At Random; MNAR\uff09\u5834\u5408\u3001\u591a\u91cd\u4ee3\u5165\uff08Multiple Imputation; MI\uff09\u306e\u3088\u3046\u306a\u6a19\u6e96\u7684\u306a\u5bfe\u51e6\u6cd5\u3092\u7528\u3044\u3066\u3082\u3001\u63a8\u5b9a\u5024\u306b\u30d0\u30a4\u30a2\u30b9\u304c\u751f\u3058\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001mice \u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u591a\u91cd\u4ee3\u5165\u3092\u884c\u3063\u305f\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001<strong>MNAR\u3092\u4eee\u5b9a\u3057\u305f\u611f\u5ea6\u5206\u6790<\/strong>\u3092\u884c\u3046\u65b9\u6cd5\u306b\u3064\u3044\u3066\u89e3\u8aac\u3059\u308b\u3002\u898b\u3048\u306a\u3044\u6b20\u6e2c\u304c\u7d50\u679c\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u8a55\u4fa1\u3057\u3001\u3088\u308a\u30ed\u30d0\u30b9\u30c8\u306a\u7d50\u8ad6\u3092\u5c0e\u304d\u51fa\u3059\u305f\u3081\u306e\u5b9f\u8df5\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u63a2\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">MNAR\u306e\u6982\u8981<\/h2>\n\n\n\n<p><strong>MNAR<\/strong>\uff08Missing Not At Random\uff09\u3068\u306f\u3001\u6b20\u6e2c\u30e1\u30ab\u30cb\u30ba\u30e0\u306e\u4e00\u7a2e\u3067\u3001<strong>\u30c7\u30fc\u30bf\u304c\u6b20\u6e2c\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3001\u3042\u308b\u3044\u306f\u6b20\u6e2c\u5024\u305d\u306e\u3082\u306e\u304c\u3001\u6b20\u6e2c\u3057\u3066\u3044\u308b\u5024\u306b\u4f9d\u5b58\u3057\u3066\u3044\u308b\u72b6\u614b<\/strong>\u3092\u6307\u3059\u3002\u4f8b\u3048\u3070\u3001\u3042\u308b\u8cea\u554f\u3078\u306e\u56de\u7b54\u304c\u300c\u56de\u7b54\u3057\u306b\u304f\u3044\u300d\u3068\u3044\u3046\u7406\u7531\u3067\u6b20\u6e2c\u3057\u3066\u3044\u308b\u5834\u5408\u306a\u3069\u304c\u3053\u308c\u306b\u8a72\u5f53\u3059\u308b\u3002MNAR\u306e\u6b20\u6e2c\u306f\u89b3\u6e2c\u30c7\u30fc\u30bf\u304b\u3089\u305d\u306e\u30e1\u30ab\u6e2c\u30cb\u30ba\u30e0\u3092\u7279\u5b9a\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3042\u308a\u3001\u6a19\u6e96\u7684\u306a\u591a\u91cd\u4ee3\u5165\u6cd5\uff08Missing At Random; MAR\u3092\u4eee\u5b9a\uff09\u3067\u306f\u30d0\u30a4\u30a2\u30b9\u3092\u5b8c\u5168\u306b\u9664\u53bb\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">MNAR\u3092\u4eee\u5b9a\u3057\u305f\u3068\u304d\u306e\u611f\u5ea6\u5206\u6790\u306e\u4ee3\u8868\u4f8b<\/h2>\n\n\n\n<p>MNAR\u3092\u4eee\u5b9a\u3057\u305f\u611f\u5ea6\u5206\u6790\u306f\u3001\u4eee\u5b9a\u3059\u308bMNAR\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u5909\u5316\u3055\u305b\u306a\u304c\u3089\u3001\u5206\u6790\u7d50\u679c\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u8a55\u4fa1\u3059\u308b\u624b\u6cd5\u3067\u3042\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001MNAR\u306e\u5b58\u5728\u304c\u7d50\u8ad6\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u306e\u5927\u304d\u3055\u3092\u628a\u63e1\u3067\u304d\u308b\u3002\u4ee3\u8868\u7684\u306a\u611f\u5ea6\u5206\u6790\u306e\u4f8b\u3068\u3057\u3066\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u30e2\u30c7\u30eb (Selection Bias Model):<\/strong> \u6b20\u6e2c\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3001\u305d\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5909\u5316\u3055\u305b\u308b\u3053\u3068\u3067\u611f\u5ea6\u5206\u6790\u3092\u884c\u3046\u3002\u4f8b\u3048\u3070\u3001\u30d7\u30ed\u30d3\u30c3\u30c8\u30e2\u30c7\u30eb\u3084\u30ed\u30b8\u30c3\u30c8\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066\u3001\u6b20\u6e2c\u306e\u78ba\u7387\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30d1\u30bf\u30fc\u30f3\u6df7\u5408\u30e2\u30c7\u30eb (Pattern-Mixture Model):<\/strong> \u6b20\u6e2c\u30d1\u30bf\u30fc\u30f3\u3054\u3068\u306b\u7570\u306a\u308b\u30e2\u30c7\u30eb\u3092\u4eee\u5b9a\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u30e2\u30c7\u30eb\u3067\u4ee3\u5165\u3092\u884c\u3046\u3002<\/li>\n\n\n\n<li><strong>\u30c7\u30eb\u30bf\u8abf\u6574\u6cd5 (Delta Adjustment Method):<\/strong> \u4ee3\u5165\u6642\u306b\u3001\u89b3\u6e2c\u3055\u308c\u3066\u3044\u308b\u5024\u3068\u6b20\u6e2c\u5024\u306e\u9593\u306e\u5dee\uff08\u30c7\u30eb\u30bf\uff09\u3092\u4eee\u5b9a\u3057\u3001\u305d\u306e\u30c7\u30eb\u30bf\u306e\u5024\u3092\u5909\u5316\u3055\u305b\u308b\u3053\u3068\u3067\u611f\u5ea6\u5206\u6790\u3092\u884c\u3046\u3002\u3053\u308c\u306f\u6bd4\u8f03\u7684\u30b7\u30f3\u30d7\u30eb\u3067\u76f4\u611f\u7684\u306a\u65b9\u6cd5\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<div id=\"biost-1121902097\" 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\">\u5177\u4f53\u4f8b<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u30c7\u30eb\u30bf\u8abf\u6574\u6cd5\u3067mice\u3092\u7528\u3044\u305fMNAR\u611f\u5ea6\u5206\u6790\u3092\u5177\u4f53\u7684\u306b\u898b\u3066\u3044\u3053\u3046\u3002<\/p>\n\n\n\n<p><strong>\u30b7\u30ca\u30ea\u30aa:<\/strong> \u3042\u308b\u75be\u60a3\u306e\u6cbb\u7642\u52b9\u679c\u3092\u8a55\u4fa1\u3059\u308b\u81e8\u5e8a\u8a66\u9a13\u306b\u304a\u3044\u3066\u3001\u60a3\u8005\u306eQOL\u30b9\u30b3\u30a2\uff08Quality of Life score\uff09\u3092\u6e2c\u5b9a\u3057\u305f\u3002\u3057\u304b\u3057\u3001QOL\u30b9\u30b3\u30a2\u304c\u9ad8\u3044\uff08\u6539\u5584\u3057\u305f\uff09\u60a3\u8005\u307b\u3069\u3001\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u8abf\u67fb\u3078\u306e\u56de\u7b54\u7387\u304c\u4f4e\u3044\u3001\u3068\u3044\u3046MNAR\u306e\u53ef\u80fd\u6027\u304c\u7591\u308f\u308c\u3066\u3044\u308b\u3002\u3064\u307e\u308a\u3001QOL\u30b9\u30b3\u30a2\u306e\u6b20\u6e2c\u306f\u3001\u305d\u306eQOL\u30b9\u30b3\u30a2\u81ea\u4f53\u306b\u4f9d\u5b58\u3057\u3066\u3044\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n<p><strong>\u76ee\u7684:<\/strong> \u3053\u306eMNAR\u306e\u53ef\u80fd\u6027\u3092\u8003\u616e\u3057\u3001\u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a\u5024\u304c\u3069\u306e\u7a0b\u5ea6\u30ed\u30d0\u30b9\u30c8\u3067\u3042\u308b\u304b\u3092\u8a55\u4fa1\u3059\u308b\u3002<\/p>\n\n\n\n<p><strong>\u30c7\u30fc\u30bf:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>treatment<\/code>: \u6cbb\u7642\u7fa4\uff080: \u5bfe\u7167\u7fa4, 1: \u4ecb\u5165\u7fa4\uff09<\/li>\n\n\n\n<li><code>qol_baseline<\/code>: \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3QOL\u30b9\u30b3\u30a2<\/li>\n\n\n\n<li><code>qol_followup<\/code>: \u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7QOL\u30b9\u30b3\u30a2\uff08\u6b20\u6e2c\u3042\u308a\uff09<\/li>\n\n\n\n<li><code>age<\/code>: \u5e74\u9f62<\/li>\n\n\n\n<li><code>sex<\/code>: \u6027\u5225<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001<code>qol_followup<\/code> \u306bMNAR\u3092\u4eee\u5b9a\u3059\u308b\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u300c<code>qol_followup<\/code> \u306e\u771f\u306e\u5024\u304c\u9ad8\u3044\u307b\u3069\u3001\u6b20\u6e2c\u3057\u3084\u3059\u3044\u300d\u3068\u3044\u3046\u30b7\u30ca\u30ea\u30aa\u3092\u8003\u3048\u308b\u3002mice\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u611f\u5ea6\u5206\u6790\u3067\u306f\u3001\u4ee3\u5165\u3055\u308c\u308b\u5024\u306b\u30aa\u30d5\u30bb\u30c3\u30c8\uff08\u30c7\u30eb\u30bf\uff09\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\u3001\u3053\u306e\u4eee\u5b9a\u3092\u8868\u73fe\u3059\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b\u306eR\u3067\u306e\u89e3\u6790<\/h2>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u3067\u306f\u30ab\u30b9\u30bf\u30e0\u4ee3\u5165\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u3066\u3001\u30c7\u30eb\u30bf\u8abf\u6574\u3092\u884c\u3063\u3066\u3044\u308b\u3002\u6a19\u6e96\u306e <code>mice.impute.norm<\/code> \u3092\u30d9\u30fc\u30b9\u306b\u3001\u6b20\u6e2c\u5024\uff08\u306e\u307f\uff09\u306b <code>delta <\/code>\u3092\u52a0\u7b97\u3059\u308b\u95a2\u6570 <code>mice.impute.my.delta<\/code>\u3092\u4f5c\u6210\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p><strong>R \u8a08\u7b97\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>if(!require(mice)) install.packages(\"mice\")\nif(!require(dplyr)) install.packages(\"dplyr\")\nlibrary(mice)\nlibrary(dplyr)\n\n# \u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\uff08MNAR\u3092\u6a21\u64ec\uff09\nset.seed(123)\nn &lt;- 200\ndata &lt;- data.frame(\n  treatment = sample(0:1, n, replace = TRUE),\n  qol_baseline = round(rnorm(n, 70, 10)),\n  age = round(rnorm(n, 50, 10)),\n  sex = sample(c(\"Male\", \"Female\"), n, replace = TRUE, prob = c(0.4, 0.6))\n)\n\n# qol_followup \u3092\u4f5c\u6210\u3057\u3001\u610f\u56f3\u7684\u306bMNAR\u3092\u767a\u751f\u3055\u305b\u308b\ndata$qol_followup &lt;- data$qol_baseline + round(rnorm(n, 5, 5))\n# QOL\u304c\u9ad8\u3044\u307b\u3069\u6b20\u6e2c\u3057\u3084\u3059\u3044\u3088\u3046\u306b\u8abf\u6574\ndata$missing_prob &lt;- plogis((data$qol_followup - 75) \/ 10) # QOL\u304c\u9ad8\u3044\u307b\u3069\u6b20\u6e2c\u78ba\u7387\u3092\u4e0a\u3052\u308b\ndata$qol_followup&#91;runif(n) &lt; data$missing_prob] &lt;- NA\n\n# \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306e\u78ba\u8a8d\nsummary(data)\nstr(data)\ndata$missing_prob &lt;- NULL # \u6b20\u6e2c\u3092\u4f5c\u6210\u3057\u305f\u78ba\u7387\u5024\u306f\u524a\u9664\u3057\u3066\u304a\u304f\n\n# 1. MAR\u3092\u4eee\u5b9a\u3057\u305f\u591a\u91cd\u4ee3\u5165 (\u6a19\u6e96\u7684\u306a MICE)\nini &lt;- mice(data, maxit = 0) # \u521d\u671f\u8a2d\u5b9a\nmeth_ini &lt;- ini$method\nmeth_ini&#91;\"qol_followup\"] &lt;- \"norm\"\n# \u591a\u91cd\u4ee3\u5165\u306e\u5b9f\u884c (m=5)\nimputed_data_mar &lt;- mice(data, m = 5, method = meth_ini, seed = 123)\n\n\n# 2. MNAR\u3092\u4eee\u5b9a\u3057\u305f\u611f\u5ea6\u5206\u6790 (\u30c7\u30eb\u30bf\u8abf\u6574) \nini_mnar &lt;- mice(data, maxit = 0)\n# 1. \u30ab\u30b9\u30bf\u30e0\u4ee3\u5165\u95a2\u6570\u306e\u5b9a\u7fa9\n# \u6a19\u6e96\u306e mice.impute.norm \u3092\u30d9\u30fc\u30b9\u306b\u3001\u6b20\u6e2c\u5024\uff08\u306e\u307f\uff09\u306b delta \u3092\u52a0\u7b97\u3059\u308b\u95a2\u6570\nmice.impute.my.delta &lt;- function(y, ry, x, wy = NULL, ...) {\n  # \u901a\u5e38\u306e\u6b63\u898f\u5206\u5e03\u30e2\u30c7\u30eb\uff08MAR\u4eee\u5b9a\uff09\u3067\u66ab\u5b9a\u7684\u306a\u4ee3\u5165\u5024\u3092\u751f\u6210\n  imp &lt;- mice.impute.norm(y, ry, x, wy = wy, ...)\n  \n  # \u751f\u6210\u3055\u308c\u305f\u4ee3\u5165\u5024\u306b delta (\u30aa\u30d5\u30bb\u30c3\u30c8) \u3092\u52a0\u3048\u308b\n  # \u3053\u308c\u306b\u3088\u308a MNAR (\u975e\u30e9\u30f3\u30c0\u30e0\u306a\u6b20\u6e2c) \u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3059\u308b\n  return(imp + delta_val)\n}\n\n# 2. \u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u5b9f\u884c (\u3054\u63d0\u793a\u306e\u30eb\u30fc\u30d7\u90e8\u5206\u306e\u4fee\u6b63\u7248)\nresults_mnar &lt;- list()\ndeltas &lt;- c(0, 2, 5, 8)\n\nfor (d in deltas) {\n  delta_val &lt;&lt;- d\n  # \u30e1\u30bd\u30c3\u30c9\u306e\u6307\u5b9a\n  meth_mnar &lt;- ini_mnar$method\n  meth_mnar&#91;\"qol_followup\"] &lt;- \"my.delta\" # \u81ea\u4f5c\u95a2\u6570\u3092\u6307\u5b9a\n  \n  # \u591a\u91cd\u4ee3\u5165\u306e\u5b9f\u884c\n  imputed_data_mnar &lt;- mice(\n    data, \n    m = 5, \n    method = meth_mnar, \n    printFlag = FALSE, \n    seed = 123\n  )\n  \n  # \u89e3\u6790\u3068\u30d7\u30fc\u30ea\u30f3\u30b0\n  fit_mnar &lt;- with(imputed_data_mnar, lm(qol_followup ~ treatment + qol_baseline + age + sex))\n  results_mnar&#91;&#91;as.character(d)]] &lt;- pool(fit_mnar)\n}\n\n# \u7d50\u679c\u306e\u8868\u793a\nfor (d in names(results_mnar)) {\n  cat(\"\\n--- Delta =\", d, \" (MNAR Adjustment) ---\\n\")\n  print(summary(results_mnar&#91;&#91;d]]))\n}\n\n\n# MAR\u306e\u7d50\u679c\u3068\u6bd4\u8f03\ncat(\"\\n--- MAR Result (Delta = 0) ---\\n\")\nfit_mar &lt;- with(imputed_data_mar, lm(qol_followup ~ treatment + qol_baseline + age + sex))\npooled_fit_mar &lt;- pool(fit_mar)\nprint(summary(pooled_fit_mar))<\/code><\/pre>\n\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\">\u7d50\u679c\u89e3\u91c8<\/h2>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u7570\u306a\u308b <code>delta<\/code> \u5024\uff080, 2, 5, 8\uff09\u3067\u5206\u6790\u3092\u884c\u3063\u305f\u7d50\u679c\u304c\u51fa\u529b\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> # \u7d50\u679c\u306e\u8868\u793a\n> for (d in names(results_mnar)) {\n+   cat(\"\\n--- Delta =\", d, \" (MNAR Adjustment) ---\\n\")\n+   print(summary(results_mnar&#91;&#91;d]]))\n+ }\n\n--- Delta = 0  (MNAR Adjustment) ---\n          term    estimate  std.error  statistic        df      p.value\n1  (Intercept)  2.63392725 5.44319238  0.4838938  8.168233 6.411680e-01\n2    treatment  0.53426485 0.89486417  0.5970346 24.176959 5.560348e-01\n3 qol_baseline  1.05741561 0.06524959 16.2057058  7.574072 3.750016e-07\n4          age -0.04870436 0.04653048 -1.0467195 17.981612 3.090959e-01\n5      sexMale -0.31366516 0.88395565 -0.3548426 35.046615 7.248340e-01\n\n--- Delta = 2  (MNAR Adjustment) ---\n          term    estimate  std.error  statistic        df      p.value\n1  (Intercept)  0.96596817 5.46990274  0.1765970  8.328498 8.640441e-01\n2    treatment  0.56534053 0.90294630  0.6261065 24.933889 5.369352e-01\n3 qol_baseline  1.09345289 0.06554641 16.6821173  7.713705 2.495390e-07\n4          age -0.04867688 0.04690672 -1.0377378 18.508527 3.127604e-01\n5      sexMale -0.29134230 0.89285311 -0.3263049 36.178271 7.460739e-01\n\n--- Delta = 5  (MNAR Adjustment) ---\n          term    estimate  std.error  statistic        df      p.value\n1  (Intercept) -1.53597045 5.63211769 -0.2727163  9.341514 7.910043e-01\n2    treatment  0.61195405 0.95135836  0.6432424 29.723701 5.249987e-01\n3 qol_baseline  1.14750882 0.06735125 17.0376759  8.594078 6.373378e-08\n4          age -0.04863566 0.04916743 -0.9891844 21.861665 3.333956e-01\n5      sexMale -0.25785802 0.94596994 -0.2725859 43.234480 7.864693e-01\n\n--- Delta = 8  (MNAR Adjustment) ---\n          term    estimate  std.error  statistic       df      p.value\n1  (Intercept) -4.03790908 5.92942436 -0.6809951 11.38449 5.094891e-01\n2    treatment  0.65856757 1.03750858  0.6347587 39.23541 5.292701e-01\n3 qol_baseline  1.20156476 0.07066824 17.0028957 10.36146 6.630430e-09\n4          age -0.04859443 0.05321642 -0.9131473 28.64594 3.687870e-01\n5      sexMale -0.22437374 1.03984718 -0.2157757 56.67338 8.299373e-01\n> # MAR\u306e\u7d50\u679c\u3068\u6bd4\u8f03\n> cat(\"\\n--- MAR Result (Delta = 0) ---\\n\")\n\n--- MAR Result (Delta = 0) ---\n> fit_mar &lt;- with(imputed_data_mar, lm(qol_followup ~ treatment + qol_baseline + age + sex))\n> pooled_fit_mar &lt;- pool(fit_mar)\n> print(summary(pooled_fit_mar))\n          term    estimate  std.error  statistic        df      p.value\n1  (Intercept)  2.63392725 5.44319238  0.4838938  8.168233 6.411680e-01\n2    treatment  0.53426485 0.89486417  0.5970346 24.176959 5.560348e-01\n3 qol_baseline  1.05741561 0.06524959 16.2057058  7.574072 3.750016e-07\n4          age -0.04870436 0.04653048 -1.0467195 17.981612 3.090959e-01\n5      sexMale -0.31366516 0.88395565 -0.3548426 35.046615 7.248340e-01<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><code>delta = 0<\/code> \u306e\u7d50\u679c<\/strong>: \u3053\u308c\u306fMAR\u3092\u4eee\u5b9a\u3057\u305f\u5834\u5408\u306e\u7d50\u679c\u3068\u540c\u4e00\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001<code>treatment<\/code> \u306e\u4fc2\u6570\uff08\u6cbb\u7642\u52b9\u679c\uff09\u304c\u6709\u610f\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3001\u305d\u306e\u52b9\u679c\u91cf\u306a\u3069\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong><code>delta = 2, 5, 8<\/code> \u306e\u7d50\u679c<\/strong>: <code>delta<\/code> \u306e\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\uff08\u3064\u307e\u308a\u3001\u6b20\u6e2c\u3057\u3066\u3044\u308bQOL\u304c\u3088\u308a\u9ad8\u3044\u3068\u4eee\u5b9a\u3059\u308b\u306b\u3064\u308c\u3066\uff09\u3001<code>treatment<\/code> \u306e\u4fc2\u6570\u3084\u305d\u306e\u6709\u610f\u6027\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u89b3\u5bdf\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u7d50\u679c\u89e3\u91c8\u306e\u30dd\u30a4\u30f3\u30c8:<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u4fc2\u6570\u306e\u5909\u5316:<\/strong> <code>treatment<\/code> \u306e\u4fc2\u6570\u304c <code>delta<\/code> \u306e\u5897\u52a0\u3068\u3068\u3082\u306b\u5897\u52a0\u3057\u3066\u3044\u308b\u304c\u3001\u5927\u304d\u306a\u5dee\u7570\u306f\u306a\u3044\u3002<\/li>\n\n\n\n<li><strong>\u6a19\u6e96\u8aa4\u5dee\u306e\u5909\u5316:<\/strong> \u4fc2\u6570\u3060\u3051\u3067\u306a\u304f\u3001\u6a19\u6e96\u8aa4\u5dee\u3084p\u5024\u306e\u5909\u5316\u3082\u91cd\u8981\u3067\u3042\u308b\u3002\u6a19\u6e96\u8aa4\u5dee\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u4fe1\u983c\u533a\u9593\u304c\u5e83\u304c\u308a\u3001\u7d50\u8ad6\u306e\u4e0d\u78ba\u5b9f\u6027\u304c\u5897\u3059\u3002\u4eca\u56de\u306e\u4f8b\u3067\u306f\u3001\u5927\u304d\u306a\u5dee\u7570\u306f\u306a\u3044\u3002<\/li>\n\n\n\n<li><strong>\u7d50\u8ad6\u306e\u30ed\u30d0\u30b9\u30c8\u6027:<\/strong> <code>delta<\/code> \u306e\u5024\u304c\u73fe\u5b9f\u7684\u306b\u8003\u3048\u3089\u308c\u308b\u7bc4\u56f2\u3067\u5909\u5316\u3057\u3066\u3082\u3001\u4e3b\u8981\u306a\u7d50\u8ad6\uff08\u4f8b\uff1a\u6cbb\u7642\u52b9\u679c\u306e\u6709\u7121\u3001\u65b9\u5411\u6027\uff09\u304c\u5909\u308f\u3089\u306a\u3044\u5834\u5408\u3001\u305d\u306e\u7d50\u8ad6\u306fMNAR\u306b\u5bfe\u3057\u3066\u6bd4\u8f03\u7684\u30ed\u30d0\u30b9\u30c8\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u3002\u4e0b\u8a18\u306e\u56f3\u3067\u3082\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u611f\u5ea6\u304c\u9ad8\u3044\u5834\u5408:<\/strong> \u7279\u5b9a\u306e <code>delta<\/code> \u306e\u4eee\u5b9a\u3067\u7d50\u679c\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u5834\u5408\u3001MNAR\u306e\u5b58\u5728\u304c\u7d50\u8ad6\u306b\u6df1\u523b\u306a\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u3053\u306e\u5834\u5408\u3001\u7814\u7a76\u8005\u306f\u305d\u306e\u4e0d\u78ba\u5b9f\u6027\u3092\u660e\u78ba\u306b\u793a\u3057\u3001\u7d50\u679c\u306e\u89e3\u91c8\u306b\u614e\u91cd\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u7d50\u679c\u306e\u53ef\u8996\u5316<\/h2>\n\n\n\n<p>\u4e0a\u8a18\u7d50\u679c\u3092 treatment \u306e\u504f\u56de\u5e30\u4fc2\u6570\u304c delta \u306b\u3088\u3063\u3066\u7570\u306a\u308b\u306e\u304b\u3069\u3046\u304b\u3092\u793a\u3059\u56f3\u3092\u4f5c\u6210\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># MAR + MNAR visualization\n# 1. MAR\u306e\u7d50\u679c\u3092\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u5316\nsumm_mar &lt;- summary(pooled_fit_mar, conf.int = TRUE)\ntarget_mar &lt;- summ_mar&#91;summ_mar$term == \"treatment\", ]\n\nmar_plot_data &lt;- data.frame(\n  type = \"MAR (Standard)\",\n  delta = -1, # \u30b0\u30e9\u30d5\u4e0a\u3067\u5de6\u5074\u306b\u914d\u7f6e\u3059\u308b\u305f\u3081\u306e\u30c0\u30df\u30fc\u5024\n  estimate = target_mar$estimate,\n  std.error = target_mar$std.error,\n  conf.low = target_mar$`2.5 %`,\n  conf.high = target_mar$`97.5 %`\n)\n\n# 2. MNAR\u306e\u7d50\u679c\u3092\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u5316\nmnar_plot_data &lt;- data.frame()\nfor (d in names(results_mnar)) {\n  summ &lt;- summary(results_mnar&#91;&#91;d]], conf.int = TRUE)\n  target &lt;- summ&#91;summ$term == \"treatment\", ]\n  \n  mnar_plot_data &lt;- rbind(mnar_plot_data, data.frame(\n    type = \"MNAR (Delta-adjusted)\",\n    delta = as.numeric(d),\n    estimate = target$estimate,\n    std.error = target$std.error,\n    conf.low = target$`2.5 %`,\n    conf.high = target$`97.5 %`\n  ))\n}\n\n# 3. \u30c7\u30fc\u30bf\u306e\u7d50\u5408\nfinal_plot_data &lt;- rbind(mar_plot_data, mnar_plot_data)\n\n# 4. \u53ef\u8996\u5316\nggplot(final_plot_data, aes(x = delta, y = estimate, color = type)) +\n  geom_point(size = 3) +\n  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), width = 0.3) +\n  # MNAR\u306e\u70b9\u3060\u3051\u3092\u7dda\u3067\u7d50\u3076\n  geom_line(data = subset(final_plot_data, type == \"MNAR (Delta-adjusted)\"), \n            aes(x = delta, y = estimate), size = 1) +\n  geom_hline(yintercept = 0, linetype = \"dashed\", color = \"black\") +\n  # x\u8ef8\u306e\u30e9\u30d9\u30eb\u3092\u8abf\u6574\uff08-1 \u306e\u4f4d\u7f6e\u3092 \"MAR\" \u3068\u8868\u793a\uff09\n  scale_x_continuous(breaks = c(-1, 0, 2, 5, 8), \n                     labels = c(\"MAR\", \"0\", \"2\", \"5\", \"8\")) +\n  labs(\n    title = \"Comparison of Treatment Effects: MAR vs MNAR\",\n    subtitle = \"Sensitivity analysis showing robustness of treatment estimates\",\n    x = \"Assumed Delta (MNAR) compared to standard MAR\",\n    y = \"Treatment Effect Estimate (95% CI)\",\n    color = \"Model Type\"\n  ) +\n  theme_minimal() +\n  theme(legend.position = \"bottom\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"963\" height=\"709\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-4.png\" alt=\"\" class=\"wp-image-4550\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-4.png 963w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-4-300x221.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-4-768x565.png 768w\" sizes=\"(max-width: 963px) 100vw, 963px\" \/><\/figure>\n\n\n\n<p>\u56f3\u306f\u3001MAR \u3068 MNAR <code>delta=0<\/code> \u304c\u540c\u3058\u504f\u56de\u5e30\u4fc2\u6570\u306e\u63a8\u5b9a\u5024\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u304a\u308a\u3001<code>delta<\/code> \u304c 2, 5, 8 \u3068\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3001\u82e5\u5e72\u70b9\u63a8\u5b9a\u5024\u306f\u5927\u304d\u304f\u306a\u308b\u3082\u3001\u5927\u304d\u306a\u5909\u5316\u306f\u306a\u304b\u3063\u305f\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u7d50\u679c\u3001MNAR \u3092\u60f3\u5b9a\u3057\u3066\u3001<code>qol_followup<\/code> \u304c\u5927\u304d\u3044\u75c7\u4f8b\u304c\u8131\u843d\u3057\u3084\u3059\u304b\u3063\u305f\u3068\u4eee\u5b9a\u3057\u305f\u5834\u5408\u3067\u3082\u3001\u7d50\u679c\u306b\u5927\u304d\u306a\u9055\u3044\u306f\u306a\u304f\u3001\u7d50\u8ad6\u306f\u3001\u6b20\u6e2c\u304cMAR\u3068\u60f3\u5b9a\u3057\u305f\u591a\u91cd\u4ee3\u5165\u3067\u3042\u3063\u3066\u3082\u554f\u984c\u306a\u304b\u3063\u305f\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>mice\u3092\u7528\u3044\u305f\u591a\u91cd\u4ee3\u5165\u306b\u304a\u3051\u308bMNAR\u611f\u5ea6\u5206\u6790\u306f\u3001\u6b20\u6e2c\u30c7\u30fc\u30bf\u304cMNAR\u3067\u3042\u308b\u53ef\u80fd\u6027\u3092\u8003\u616e\u3057\u3001\u5206\u6790\u7d50\u679c\u306e\u30ed\u30d0\u30b9\u30c8\u6027\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u4e0a\u8a18\u306e\u3088\u3046\u306b\u3001\u6b20\u6e2c\u5024\u3068\u89b3\u6e2c\u5024\u306e\u9593\u306b\u4eee\u5b9a\u3055\u308c\u308b\u5dee\uff08\u30c7\u30eb\u30bf\uff09\u3092\u5909\u5316\u3055\u305b\u308b<strong>\u30c7\u30eb\u30bf\u8abf\u6574\u6cd5<\/strong>\u306f\u3001\u6bd4\u8f03\u7684\u76f4\u611f\u7684\u306b\u611f\u5ea6\u5206\u6790\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u611f\u5ea6\u5206\u6790\u3092\u901a\u3058\u3066\u3001\u6211\u3005\u306f\u5358\u306b\u300c\u6b20\u6e2c\u306b\u5bfe\u51e6\u3057\u305f\u300d\u3068\u3044\u3046\u3060\u3051\u3067\u306a\u304f\u3001\u300c\u6b20\u6e2c\u30e1\u30ab\u30cb\u30ba\u30e0\u306e\u4e0d\u78ba\u5b9f\u6027\u304c\u7d50\u679c\u306b\u3069\u306e\u7a0b\u5ea6\u5f71\u97ff\u3059\u308b\u304b\u300d\u3068\u3044\u3046\u91cd\u8981\u306a\u554f\u3044\u306b\u7b54\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u3088\u308a\u900f\u660e\u6027\u306e\u9ad8\u3044\u3001\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u7814\u7a76\u7d50\u679c\u306e\u5831\u544a\u304c\u53ef\u80fd\u3068\u306a\u308a\u3001\u3072\u3044\u3066\u306f\u79d1\u5b66\u7684\u77e5\u898b\u306e\u78ba\u5b9f\u6027\u3092\u9ad8\u3081\u308b\u3053\u3068\u306b\u7e4b\u304c\u308b\u3002\u6b20\u6e2c\u30c7\u30fc\u30bf\u306e\u591a\u3044\u7814\u7a76\u306b\u304a\u3044\u3066\u306f\u3001\u7a4d\u6975\u7684\u306bMNAR\u611f\u5ea6\u5206\u6790\u3092\u691c\u8a0e\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3059\u308b\u3002<\/p>\n\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\">\u95a2\u9023\u66f8\u7c4d<\/h2>\n\n\n\n<p><a href=\"https:\/\/amzn.to\/3Lnye10\">\u6b20\u6e2c\u30c7\u30fc\u30bf\u306e\u7d71\u8a08\u79d1\u5b66\u2015\u2015\u533b\u5b66\u3068\u793e\u4f1a\u79d1\u5b66\u3078\u306e\u5fdc\u7528<\/a><\/p>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u7d71\u8a08\u89e3\u6790\u306b\u304a\u3044\u3066\u3001\u6b20\u6e2c\u30c7\u30fc\u30bf\u306f\u5e38\u306b\u60a9\u307e\u3057\u3044\u554f\u984c\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u6b20\u6e2c\u304c\u30e9\u30f3\u30c0\u30e0\u3067\u306f\u306a\u3044\uff08Missing Not At Random; MNAR\uff09\u5834\u5408\u3001\u591a\u91cd\u4ee3\u5165\uff08Multiple Imputation; MI\uff09\u306e\u3088\u3046\u306a\u6a19\u6e96\u7684\u306a [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4550,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[149],"tags":[],"class_list":["post-4116","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-149"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-4.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4116","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=4116"}],"version-history":[{"count":4,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4116\/revisions"}],"predecessor-version":[{"id":4552,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4116\/revisions\/4552"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4550"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}