{"id":4368,"date":"2025-08-03T09:10:39","date_gmt":"2025-08-03T00:10:39","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4368"},"modified":"2025-08-03T09:10:41","modified_gmt":"2025-08-03T00:10:41","slug":"unlocking-causal-effects-a-practical-guide-to-inverse-probability-treatment-weighting-iptw","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/unlocking-causal-effects-a-practical-guide-to-inverse-probability-treatment-weighting-iptw\/","title":{"rendered":"\u9006\u78ba\u7387\u91cd\u307f\u4ed8\u3051\uff08IPTW\uff09\u3092\u7528\u3044\u305f\u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a\uff1a\u56e0\u679c\u63a8\u8ad6\u306e\u57fa\u672c\u3068\u5b9f\u8df5"},"content":{"rendered":"\n<p>\u300c\u3042\u306e\u6cbb\u7642\u3092\u53d7\u3051\u3066\u3044\u305f\u3089\u3001\u3069\u3046\u306a\u3063\u3066\u3044\u305f\u306e\u3060\u308d\u3046\uff1f\u300d\u591a\u304f\u306e\u4eba\u304c\u4e00\u5ea6\u306f\u62b1\u304f\u7591\u554f\u3060\u308d\u3046\u3002\u533b\u5b66\u7814\u7a76\u3084\u793e\u4f1a\u79d1\u5b66\u306b\u304a\u3044\u3066\u3001\u7279\u5b9a\u306e\u4ecb\u5165\uff08\u6cbb\u7642\u3001\u653f\u7b56\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306a\u3069\uff09\u304c\u3082\u305f\u3089\u3059\u52b9\u679c\u3092\u6b63\u78ba\u306b\u77e5\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u91cd\u8981\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u73fe\u5b9f\u306e\u4e16\u754c\u3067\u306f\u3001\u8ab0\u304c\u3069\u306e\u4ecb\u5165\u3092\u53d7\u3051\u308b\u304b\u306f\u5076\u7136\u3067\u306f\u306a\u304f\u3001\u69d8\u3005\u306a\u8981\u56e0\u306b\u5f71\u97ff\u3055\u308c\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u300c\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u300d\u304c\u3042\u308b\u72b6\u6cc1\u3067\u3001\u771f\u306e\u6cbb\u7642\u52b9\u679c\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3068\u306a\u308b\u306e\u304c\u300c\u56e0\u679c\u63a8\u8ad6\u300d\u306e\u624b\u6cd5\u3067\u3042\u308b\u3002\u4eca\u56de\u306f\u305d\u306e\u4e2d\u3067\u3082\u3001\u7279\u306b\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u300c<strong>\u9006\u78ba\u7387\u91cd\u307f\u4ed8\u3051\uff08IPTW: Inverse Probability Treatment Weighting\uff09<\/strong>\u300d\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u305d\u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u304b\u3089\u5177\u4f53\u7684\u306a\u8a08\u7b97\u65b9\u6cd5\u307e\u3067\u3092\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u56e0\u679c\u63a8\u8ad6\u306b\u304a\u3051\u308b\u6cbb\u7642\u52b9\u679c\u63a8\u5b9a<\/h2>\n\n\n\n<p>\u79c1\u305f\u3061\u304c\u77e5\u308a\u305f\u3044\u306e\u306f\u3001\u300c\u3082\u3057\u5168\u54e1\u304c\u6cbb\u7642\u3092\u53d7\u3051\u3066\u3044\u305f\u3089\u3069\u3046\u306a\u3063\u305f\u304b\u300d\u3068\u300c\u3082\u3057\u5168\u54e1\u304c\u6cbb\u7642\u3092\u53d7\u3051\u306a\u304b\u3063\u305f\u3089\u3069\u3046\u306a\u3063\u305f\u304b\u300d\u3068\u3044\u3046\u4eee\u60f3\u7684\u306a\u72b6\u6cc1\u9593\u306e\u6bd4\u8f03\u3067\u3042\u308b\u3002\u3053\u308c\u3092\u300c<strong>\u53cd\u4e8b\u5b9f\uff08Counterfactual\uff09<\/strong>\u300d\u3068\u547c\u3076\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\u500b\u3005\u306e\u5bfe\u8c61\u8005 $i$ \u306b\u3064\u3044\u3066\u3001\u6cbb\u7642\u3092\u53d7\u3051\u305f\u5834\u5408\u306e\u6f5c\u5728\u7684\u7d50\u679c $Y_i(1)$ \u3068\u3001\u6cbb\u7642\u3092\u53d7\u3051\u306a\u304b\u3063\u305f\u5834\u5408\u306e\u6f5c\u5728\u7684\u7d50\u679c $Y_i(0)$ \u306e\u4e21\u65b9\u3092\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3057\u304b\u3057\u3001\u73fe\u5b9f\u306b\u306f\u5404\u5bfe\u8c61\u8005\u306f\u3069\u3061\u3089\u304b\u4e00\u65b9\u306e\u6cbb\u7642\u72b6\u614b\u3057\u304b\u89b3\u5bdf\u3067\u304d\u306a\u3044\u3002\u4f8b\u3048\u3070\u3001\u6cbb\u7642\u3092\u53d7\u3051\u305f\u4eba\u306f $Y_i(1)$ \u306f\u89b3\u6e2c\u3067\u304d\u308b\u304c $Y_i(0)$ \u306f\u89b3\u6e2c\u3067\u304d\u306a\u3044\u3002\u3053\u306e\u300c\u89b3\u6e2c\u3067\u304d\u306a\u3044\u53cd\u4e8b\u5b9f\u300d\u304c\u56e0\u679c\u63a8\u8ad6\u306e\u6700\u5927\u306e\u8ab2\u984c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a\u76ee\u6a19\u306f\u3001\u901a\u5e38\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a**\u5e73\u5747\u6cbb\u7642\u52b9\u679c\uff08ATE: Average Treatment Effect\uff09**\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<p>$$ATE = E[Y(1) &#8211; Y(0)]$$<\/p>\n\n\n\n<p>\u3042\u308b\u3044\u306f\u3001\u6cbb\u7642\u3092\u53d7\u3051\u305f\u7fa4\u306b\u304a\u3051\u308b\u5e73\u5747\u6cbb\u7642\u52b9\u679c\uff08ATT: Average Treatment Effect on the Treated\uff09\u3082\u3088\u304f\u7528\u3044\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p>$$ATT = E[Y(1) &#8211; Y(0) | T=1]$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067 $T$ \u306f\u6cbb\u7642\u5272\u308a\u5f53\u3066\u3092\u793a\u3059\u5909\u6570\uff08$T=1$ \u304c\u6cbb\u7642\u7fa4\u3001$T=0$ \u304c\u5bfe\u7167\u7fa4\uff09\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u72b6\u6cc1\u3067\u306f\u3001\u5358\u7d14\u306b\u6cbb\u7642\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u5e73\u5747\u30a2\u30a6\u30c8\u30ab\u30e0\u3092\u6bd4\u8f03\u3057\u3066\u3082\u3001\u305d\u308c\u306f\u771f\u306e\u6cbb\u7642\u52b9\u679c\u3092\u53cd\u6620\u3057\u306a\u3044\u3002\u4f8b\u3048\u3070\u3001\u5065\u5eb7\u306a\u4eba\u307b\u3069\u6cbb\u7642\u3092\u53d7\u3051\u308b\u50be\u5411\u304c\u3042\u308b\u5834\u5408\u3001\u6cbb\u7642\u7fa4\u306e\u30a2\u30a6\u30c8\u30ab\u30e0\u304c\u9ad8\u304f\u3066\u3082\u3001\u305d\u308c\u306f\u6cbb\u7642\u306e\u52b9\u679c\u3067\u306f\u306a\u304f\u3001\u5143\u3005\u306e\u5065\u5eb7\u72b6\u614b\u306e\u9055\u3044\u306b\u3088\u308b\u3082\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u56e0\u679c\u63a8\u8ad6\u3067\u306f\u3001\u3053\u306e\u3088\u3046\u306a\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u3092\u53d6\u308a\u9664\u304f\u305f\u3081\u306b\u69d8\u3005\u306a\u624b\u6cd5\u304c\u958b\u767a\u3055\u308c\u3066\u3044\u308b\u3002\u305d\u306e\u4e00\u3064\u304cIPTW\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">IPTW\u306b\u3088\u308b\u6cbb\u7642\u52b9\u679c\u63a8\u5b9a\u6982\u8981<\/h2>\n\n\n\n<p>IPTW\u306f\u3001\u5404\u5bfe\u8c61\u8005\u304c\u5b9f\u969b\u306b\u53d7\u3051\u305f\u6cbb\u7642\uff08\u307e\u305f\u306f\u53d7\u3051\u306a\u304b\u3063\u305f\u6cbb\u7642\uff09\u3092\u53d7\u3051\u308b\u78ba\u7387\u306e\u9006\u6570\u3067\u91cd\u307f\u4ed8\u3051\u3092\u3059\u308b\u3053\u3068\u3067\u3001\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u3092\u88dc\u6b63\u3057\u3001\u3042\u305f\u304b\u3082\u30e9\u30f3\u30c0\u30e0\u5316\u6bd4\u8f03\u8a66\u9a13\uff08RCT\uff09\u306e\u3088\u3046\u306b\u6cbb\u7642\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u80cc\u666f\u56e0\u5b50\u304c\u5747\u7b49\u306b\u5206\u5e03\u3059\u308b\u3088\u3046\u306b\u8abf\u6574\u3059\u308b\u624b\u6cd5\u3067\u3042\u308b\u3002\u305f\u3060\u3057\u3001\u6e2c\u5b9a\u3057\u3066\u3044\u306a\u3044\u80cc\u666f\u56e0\u5b50\u3092\u6f5c\u5728\u7684\u5747\u7b49\u306b\u306f\u3067\u304d\u306a\u3044\u70b9\u304cRCT\u3068\u306f\u7570\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u50be\u5411\u30b9\u30b3\u30a2\u306e\u63a8\u5b9a<\/strong>: \u307e\u305a\u3001\u5404\u5bfe\u8c61\u8005\u304c\u6cbb\u7642\u3092\u53d7\u3051\u308b\u78ba\u7387\uff08\u3053\u308c\u3092\u300c<strong>\u50be\u5411\u30b9\u30b3\u30a2<\/strong>\u300d\u3068\u547c\u3076\uff09\u3092\u63a8\u5b9a\u3059\u308b\u3002\u50be\u5411\u30b9\u30b3\u30a2\u306f\u3001\u5171\u5909\u91cf $X$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u4e0b\u3067\u306e\u6cbb\u7642\u5272\u308a\u5f53\u3066\u306e\u6761\u4ef6\u4ed8\u304d\u78ba\u7387 $e(X) = P(T=1 | X)$ \u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30e2\u30c7\u30eb\u306a\u3069\u3092\u7528\u3044\u3066\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u91cd\u307f\u306e\u8a08\u7b97<\/strong>: \u63a8\u5b9a\u3055\u308c\u305f\u50be\u5411\u30b9\u30b3\u30a2\u3092\u7528\u3044\u3066\u3001\u5404\u5bfe\u8c61\u8005\u306b\u4ee5\u4e0b\u306e\u91cd\u307f\u3092\u4ed8\u4e0e\u3059\u308b\u3002<ul><li><strong>\u6cbb\u7642\u7fa4\uff08$T=1$\uff09\u306e\u5834\u5408<\/strong>: $w_i = \\frac{1}{e(X_i)}$<\/li><\/ul> <ul><li><strong>\u5bfe\u7167\u7fa4\uff08$T=0$\uff09\u306e\u5834\u5408<\/strong>: $w_i = \\frac{1}{1 &#8211; e(X_i)}$<\/li><\/ul>\u3053\u306e\u91cd\u307f\u306f\u300c<strong>\u9006\u78ba\u7387\u91cd\u307f<\/strong>\u300d\u3068\u547c\u3070\u308c\u308b\u3002\u76f4\u611f\u7684\u306b\u8a00\u3046\u3068\u3001\u6cbb\u7642\u3092\u53d7\u3051\u308b\u78ba\u7387\u304c\u4f4e\u3044\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u6cbb\u7642\u3092\u53d7\u3051\u305f\u4eba\uff08\u3042\u308b\u3044\u306f\u3001\u6cbb\u7642\u3092\u53d7\u3051\u306a\u3044\u78ba\u7387\u304c\u4f4e\u3044\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u6cbb\u7642\u3092\u53d7\u3051\u306a\u304b\u3063\u305f\u4eba\uff09\u306b\u306f\u3001\u3088\u308a\u5927\u304d\u306a\u91cd\u307f\u304c\u4e0e\u3048\u3089\u308c\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7a00\u306a\u7d44\u307f\u5408\u308f\u305b\u306e\u30c7\u30fc\u30bf\u30dd\u30a4\u30f3\u30c8\u306e\u300c\u91cd\u8981\u6027\u300d\u3092\u5897\u5e45\u3055\u305b\u3001\u5168\u4f53\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u8abf\u6574\u3059\u308b\u52b9\u679c\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747\u306e\u8a08\u7b97<\/strong>: \u5404\u7fa4\u306e\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747\u30a2\u30a6\u30c8\u30ab\u30e0\u3092\u8a08\u7b97\u3059\u308b\u3002\n<ul class=\"wp-block-list\">\n<li>\u6cbb\u7642\u7fa4\u306e\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747: $E[Y(1)] \\approx \\frac{\\sum_{i=1}^N Y_i \\cdot T_i \\cdot w_i}{\\sum_{i=1}^N T_i \\cdot w_i}$<\/li>\n\n\n\n<li>\u5bfe\u7167\u7fa4\u306e\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747: $E[Y(0)] \\approx \\frac{\\sum_{i=1}^N Y_i \\cdot (1-T_i) \\cdot w_i}{\\sum_{i=1}^N (1-T_i) \\cdot w_i}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a<\/strong>: \u6700\u5f8c\u306b\u3001\u3053\u308c\u3089\u306e\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747\u30a2\u30a6\u30c8\u30ab\u30e0\u306e\u5dee\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3001ATE\u3092\u63a8\u5b9a\u3059\u308b\u3002 $ATE_{IPTW} = \\hat{E}[Y(1)] &#8211; \\hat{E}[Y(0)]$<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306eIPTW\u306e\u6709\u52b9\u6027\u306f\u3001\u300c<strong>\u5f37\u304f\u7121\u8996\u3067\u304d\u308b\u5272\u308a\u5f53\u3066\uff08Strongly Ignorable Treatment Assignment\uff09<\/strong>\u300d\u3068\u3044\u3046\u4eee\u5b9a\u306b\u57fa\u3065\u3044\u3066\u3044\u308b\u3002\u3053\u308c\u306f\u3001\u300c\u3059\u3079\u3066\u306e\u95a2\u9023\u3059\u308b\u5171\u5909\u91cf $X$ \u3092\u6761\u4ef6\u4ed8\u3051\u308c\u3070\u3001\u6cbb\u7642\u5272\u308a\u5f53\u3066\u306f\u30a2\u30a6\u30c8\u30ab\u30e0\u3068\u306f\u72ec\u7acb\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u4eee\u5b9a\u3067\u3042\u308b\u3002\u7c21\u5358\u306b\u8a00\u3048\u3070\u3001\u300c\u89b3\u6e2c\u3055\u308c\u305f\u5171\u5909\u91cf $X$ \u3092\u3059\u3079\u3066\u8003\u616e\u3059\u308c\u3070\u3001\u6cbb\u7642\u3092\u53d7\u3051\u305f\u304b\u5426\u304b\u306f\u5b8c\u5168\u306b\u30e9\u30f3\u30c0\u30e0\u3067\u3042\u308b\u300d\u3068\u4eee\u5b9a\u3067\u304d\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u4eee\u5b9a\u304c\u6e80\u305f\u3055\u308c\u306a\u3044\u5834\u5408\uff08\u672a\u6e2c\u5b9a\u306e\u4ea4\u7d61\u56e0\u5b50\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306a\u3069\uff09\u3001IPTW\u306f\u771f\u306e\u56e0\u679c\u52b9\u679c\u3092\u63a8\u5b9a\u3067\u304d\u306a\u3044\u3002\u3064\u307e\u308a\u3001\u672a\u6e2c\u5b9a\u306e\u4ea4\u7d61\u56e0\u5b50\u306f\u5fc5\u305a\u5b58\u5728\u3059\u308b\u305f\u3081\u3001IPTW\u304cRCT\u306b\u7f6e\u304d\u63db\u308f\u308b\u3053\u3068\u306f\u306a\u3044\u3053\u3068\u306f\u7559\u610f\u3057\u305f\u3044\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-1966922223\" 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\u3068R\u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u3092\u7528\u3044\u3066IPTW\u306b\u3088\u308b\u6cbb\u7642\u52b9\u679c\u63a8\u5b9a\u306e\u5177\u4f53\u4f8b\u3092R\u3067\u793a\u3059\u3002<\/p>\n\n\n\n<p><strong>\u30b7\u30ca\u30ea\u30aa<\/strong>: \u3042\u308b\u85ac\uff08\u6cbb\u7642\uff09\u304c\u8840\u5727\uff08\u30a2\u30a6\u30c8\u30ab\u30e0\uff09\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u8a55\u4fa1\u3057\u305f\u3044\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u85ac\u306f\u3001\u5e74\u9f62\u3084\u65e2\u5b58\u306e\u5065\u5eb7\u72b6\u614b\u304c\u826f\u3044\u4eba\u306b\u51e6\u65b9\u3055\u308c\u308b\u50be\u5411\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30c7\u30fc\u30bf\u306e\u751f\u6210 (\u4f8b\u793a\u7528)\nset.seed(123)\nN &lt;- 500 # \u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\n\n# \u5171\u5909\u91cf: \u5e74\u9f62 (age) \u3068\u65e2\u5b58\u306e\u5065\u5eb7\u72b6\u614b\u30b9\u30b3\u30a2 (health_score)\nage &lt;- round(rnorm(N, 50, 10))\nhealth_score &lt;- round(rnorm(N, 70, 15))\n\n# \u6cbb\u7642\u5272\u308a\u5f53\u3066 (treatment): \u5e74\u9f62\u304c\u82e5\u304f\u3001\u5065\u5eb7\u72b6\u614b\u304c\u826f\u3044\u307b\u3069\u6cbb\u7642\u3092\u53d7\u3051\u308b\u78ba\u7387\u304c\u9ad8\u3044\n# \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306e\u7dda\u5f62\u4e88\u6e2c\u5b50\nlinear_predictor_t &lt;- -2 + 0.05 * (80 - age) + 0.03 * health_score\nprob_treatment &lt;- 1 \/ (1 + exp(-linear_predictor_t))\ntreatment &lt;- rbinom(N, 1, prob_treatment)\n\n# \u30a2\u30a6\u30c8\u30ab\u30e0 (blood_pressure): \u6cbb\u7642\u304c\u8840\u5727\u3092\u4e0b\u3052\u3001\u5e74\u9f62\u304c\u9ad8\u3044\u3068\u8840\u5727\u304c\u9ad8\u304f\u3001\u5065\u5eb7\u72b6\u614b\u304c\u826f\u3044\u3068\u8840\u5727\u304c\u4f4e\u3044\n# \u771f\u306e\u6cbb\u7642\u52b9\u679c\u306f -5 \u3068\u3059\u308b\nblood_pressure &lt;- round(130 - 5 * treatment + 0.5 * age - 0.2 * health_score + rnorm(N, 0, 5))\n\n# \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306b\u307e\u3068\u3081\u308b\ndf &lt;- data.frame(age, health_score, treatment, blood_pressure)\n\n# 1. \u50be\u5411\u30b9\u30b3\u30a2\u306e\u63a8\u5b9a\n# \u5171\u5909\u91cf (age, health_score) \u3092\u7528\u3044\u3066 treatment \u3092\u4e88\u6e2c\u3059\u308b\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30e2\u30c7\u30eb\npropensity_model &lt;- glm(treatment ~ age + health_score, data = df, family = binomial)\ndf$propensity_score &lt;- predict(propensity_model, type = \"response\")\n\n# \u50be\u5411\u30b9\u30b3\u30a2\u306e\u7bc4\u56f2\u3092\u78ba\u8a8d (0\u30681\u306b\u8fd1\u3059\u304e\u308b\u5024\u304c\u306a\u3044\u304b)\nsummary(df$propensity_score)\n\n# 2. \u91cd\u307f\u306e\u8a08\u7b97\ndf$weight &lt;- ifelse(df$treatment == 1, 1 \/ df$propensity_score, 1 \/ (1 - df$propensity_score))\n\n# \u91cd\u307f\u306e\u5206\u5e03\u3092\u78ba\u8a8d (\u6975\u7aef\u306b\u5927\u304d\u306a\u91cd\u307f\u304c\u306a\u3044\u304b)\nsummary(df$weight)\n\n# 3. \u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747\u306e\u8a08\u7b97\n# \u6cbb\u7642\u7fa4\u306e\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747\u30a2\u30a6\u30c8\u30ab\u30e0\nweighted_mean_treated &lt;- sum(df$blood_pressure&#91;df$treatment == 1] * df$weight&#91;df$treatment == 1]) \/ sum(df$weight&#91;df$treatment == 1])\n\n# \u5bfe\u7167\u7fa4\u306e\u91cd\u307f\u4ed8\u3051\u3055\u308c\u305f\u5e73\u5747\u30a2\u30a6\u30c8\u30ab\u30e0\nweighted_mean_control &lt;- sum(df$blood_pressure&#91;df$treatment == 0] * df$weight&#91;df$treatment == 0]) \/ sum(df$weight&#91;df$treatment == 0])\n\n# 4. \u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a (ATE)\nate_iptw &lt;- weighted_mean_treated - weighted_mean_control\nprint(paste(\"IPTW\u306b\u3088\u308b\u5e73\u5747\u6cbb\u7642\u52b9\u679c (ATE):\", round(ate_iptw, 2)))\n\n# \u53c2\u8003: \u5358\u7d14\u306a\u5e73\u5747\u6bd4\u8f03 (\u30d0\u30a4\u30a2\u30b9\u3042\u308a)\nnaive_mean_treated &lt;- mean(df$blood_pressure&#91;df$treatment == 1])\nnaive_mean_control &lt;- mean(df$blood_pressure&#91;df$treatment == 0])\nnaive_diff &lt;- naive_mean_treated - naive_mean_control\nprint(paste(\"\u5358\u7d14\u306a\u5e73\u5747\u5dee:\", round(naive_diff, 2)))\n<\/code><\/pre>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001IPTW\u306b\u3088\u308b\u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a\u5024\u3068\u3001\u5358\u7d14\u306a\u5e73\u5747\u6bd4\u8f03\u306b\u3088\u308b\u63a8\u5b9a\u5024\u304c\u8868\u793a\u3055\u308c\u308b\u3002\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u304c\u3042\u308b\u72b6\u6cc1\u3067\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u4e21\u8005\u306e\u5024\u306f\u7570\u306a\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u679c\u89e3\u91c8\u4f8b<\/h3>\n\n\n\n<p>\u5b9f\u884c\u7d50\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> # 4. \u6cbb\u7642\u52b9\u679c\u306e\u63a8\u5b9a (ATE)\n> ate_iptw &lt;- weighted_mean_treated - weighted_mean_control\n> print(paste(\"IPTW\u306b\u3088\u308b\u5e73\u5747\u6cbb\u7642\u52b9\u679c (ATE):\", round(ate_iptw, 2)))\n&#91;1] \"IPTW\u306b\u3088\u308b\u5e73\u5747\u6cbb\u7642\u52b9\u679c (ATE): -4.04\"\n> # \u53c2\u8003: \u5358\u7d14\u306a\u5e73\u5747\u6bd4\u8f03 (\u30d0\u30a4\u30a2\u30b9\u3042\u308a)\n> naive_mean_treated &lt;- mean(df$blood_pressure&#91;df$treatment == 1])\n> naive_mean_control &lt;- mean(df$blood_pressure&#91;df$treatment == 0])\n> naive_diff &lt;- naive_mean_treated - naive_mean_control\n> print(paste(\"\u5358\u7d14\u306a\u5e73\u5747\u5dee:\", round(naive_diff, 2)))\n&#91;1] \"\u5358\u7d14\u306a\u5e73\u5747\u5dee: -6.59\"<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u5358\u7d14\u306a\u5e73\u5747\u5dee\u304c -6.59 \u3068\u306a\u3063\u3066\u3044\u308b\u306e\u306b\u5bfe\u3057\u3001IPTW\u306b\u3088\u308b\u63a8\u5b9a\u5024\u306f -4.04 \u3068\u306a\u3063\u305f\u3002\u3053\u308c\u306f\u3001\u6cbb\u7642\u3092\u53d7\u3051\u308b\u4eba\u304c\u5143\u3005\u5065\u5eb7\u3067\u8840\u5727\u304c\u4f4e\u3044\u50be\u5411\u304c\u3042\u3063\u305f\u305f\u3081\u3001\u5358\u7d14\u306a\u6bd4\u8f03\u3067\u306f\u6cbb\u7642\u52b9\u679c\u304c\u904e\u5927\u8a55\u4fa1\u3055\u308c\u3066\u3044\u305f\u53ef\u80fd\u6027\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002IPTW\u306b\u3088\u3063\u3066\u3001\u3053\u308c\u3089\u306e\u9078\u629e\u30d0\u30a4\u30a2\u30b9\u304c\u8abf\u6574\u3055\u308c\u3001\u3088\u308a\u771f\u306e\u6cbb\u7642\u52b9\u679c\u306b\u8fd1\u3044\u5024\uff08\u3053\u306e\u4f8b\u3067\u306f\u771f\u306e\u5024\u304c-5\uff09\u304c\u63a8\u5b9a\u3055\u308c\u305f\u3068\u8003\u3048\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u7d50\u679c\u3092\u89e3\u91c8\u3059\u308b\u969b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u70b9\u306b\u7559\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u50be\u5411\u30b9\u30b3\u30a2\u306e\u59a5\u5f53\u6027<\/strong>: \u50be\u5411\u30b9\u30b3\u30a2\u306e\u30e2\u30c7\u30eb\u304c\u9069\u5207\u3067\u3042\u3063\u305f\u304b\uff08\u3059\u3079\u3066\u306e\u91cd\u8981\u306a\u4ea4\u7d61\u56e0\u5b50\u3092\u7db2\u7f85\u3057\u3066\u3044\u305f\u304b\u3001\u30e2\u30c7\u30eb\u306e\u9069\u5408\u5ea6\u306f\u9ad8\u304b\u3063\u305f\u304b\uff09\u3002<\/li>\n\n\n\n<li><strong>\u5171\u901a\u30b5\u30dd\u30fc\u30c8\u306e\u78ba\u8a8d<\/strong>: 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