{"id":7375,"date":"2025-10-30T09:47:18","date_gmt":"2025-10-30T00:47:18","guid":{"rendered":"https:\/\/blog.since2020.jp\/?p=7375"},"modified":"2025-10-30T09:47:18","modified_gmt":"2025-10-30T00:47:18","slug":"regression_analysis_etc","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/regression_analysis_etc\/","title":{"rendered":"\u56de\u5e30\u5206\u6790\u3092\u6975\u3081\u308b(4\/4)\uff1a\u56de\u5e30\u5206\u6790\u305d\u306e\u4ed6"},"content":{"rendered":"\n<p>\u56de\u5e30\u5206\u6790\u30b7\u30ea\u30fc\u30ba\u306e\u6700\u7d42\u56de\u3068\u306a\u308b\u4eca\u56de\u306f\u3001\u7279\u6b8a\u306a\u5fdc\u7528\u5206\u91ce\u306b\u304a\u3051\u308b\u56de\u5e30\u624b\u6cd5\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002\u5236\u9650\u4ed8\u304d\u5f93\u5c5e\u5909\u6570\u3092\u6271\u3046\u30c8\u30fc\u30d3\u30c3\u30c8\u30e2\u30c7\u30eb\u3001\u6642\u9593\u8ef8\u3092\u8003\u616e\u3057\u305f\u751f\u5b58\u6642\u9593\u5206\u6790\u3001\u305d\u3057\u3066\u73fe\u4ee3\u306e\u6a5f\u68b0\u5b66\u7fd2\u306e\u4ee3\u8868\u683c\u3067\u3042\u308b\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30e2\u30c7\u30eb\u307e\u3067\u3001\u5e45\u5e83\u3044\u56de\u5e30\u5206\u6790\u306e\u5fdc\u7528\u3092\u5b66\u3073\u307e\u3059\u3002<\/p>\n\n\n<h2>\u30c8\u30fc\u30d3\u30c3\u30c8\u30e2\u30c7\u30eb<\/h2>\n<p><strong>\u30c8\u30fc\u30d3\u30c3\u30c8\u30e2\u30c7\u30eb\uff08Tobit Model\uff09<\/strong>\u306f\u3001\u76ee\u7684\u5909\u6570\u304c\u7279\u5b9a\u306e\u5024\u3067\u5207\u65ad\u3055\u308c\u308b\uff08censored\uff09\u30c7\u30fc\u30bf\u3092\u6271\u3046\u56de\u5e30\u30e2\u30c7\u30eb\u3067\u3059\u30021958\u5e74\u306bJames Tobin\u306b\u3088\u3063\u3066\u63d0\u6848\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\r\n<b>\u30e2\u30c7\u30eb\u306e\u5b9a\u5f0f\u5316<\/b>\r\n<p>\u6f5c\u5728\u5909\u6570\\(y_i^*\\)\u304c\u3042\u308a\u3001\u5b9f\u969b\u306b\u89b3\u6e2c\u3055\u308c\u308b\\(y_i\\)\u306f\uff1a<\/p>\r\n<p>\\[y_i = \\begin{cases} y_i^* &amp; \\text{if } y_i^* &gt; 0 \\\\ 0 &amp; \\text{if } y_i^* \\leq 0 \\end{cases}\\]<\/p>\r\n<p>\u6f5c\u5728\u5909\u6570\u306f\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306b\u5f93\u3044\u307e\u3059\uff1a<\/p>\r\n<p>\\[y_i^* = \\boldsymbol{x}_i^T\\boldsymbol{\\beta} + \\varepsilon_i, \\quad \\varepsilon_i \\sim N(0, \\sigma^2)\\]<\/p>\r\n<b>\u5fdc\u7528\u4f8b<\/b>\r\n<ul>\r\n\t<li><strong>\u6d88\u8cbb\u652f\u51fa<\/strong>: \u8ca0\u306e\u652f\u51fa\u306f\u89b3\u6e2c\u3055\u308c\u306a\u3044<\/li>\r\n\t<li><strong>\u52b4\u50cd\u6642\u9593<\/strong>: 0\u6642\u9593\u672a\u6e80\u306f\u89b3\u6e2c\u3055\u308c\u306a\u3044<\/li>\r\n\t<li><strong>\u6295\u8cc7\u984d<\/strong>: \u8ca0\u306e\u6295\u8cc7\u306f\u89b3\u6e2c\u3055\u308c\u306a\u3044<\/li>\r\n<\/ul>\r\n<b>\u63a8\u5b9a\u65b9\u6cd5<\/b>\r\n<p>\u6700\u5c24\u63a8\u5b9a\u3092\u7528\u3044\u307e\u3059\u3002\u5c24\u5ea6\u95a2\u6570\u306f\uff1a<\/p>\r\n<p>\\[L = \\prod_{y_i=0} P(y_i^* \\leq 0) \\prod_{y_i&gt;0} f(y_i)\\]<\/p>\r\n<p>\u3053\u3053\u3067\u3001\\(P(y_i^* \\leq 0) = \\Phi(-\\boldsymbol{x}_i^T\\boldsymbol{\\beta}\/\\sigma)\\)\u3001\\(f(y_i)\\)\u306f\u5207\u65ad\u3055\u308c\u3066\u3044\u306a\u3044\u89b3\u6e2c\u5024\u306e\u5bc6\u5ea6\u95a2\u6570\u3067\u3059\u3002<\/p>\n\n<h2>\u751f\u5b58\u6642\u9593\u5206\u6790<\/h2>\n<p><strong>\u751f\u5b58\u6642\u9593\u5206\u6790<\/strong>\uff08Survival Analysis\uff09\u306f\u3001\u3042\u308b\u4e8b\u8c61\uff08\u6b7b\u4ea1\u3001\u518d\u767a\u3001\u6545\u969c\u306a\u3069\uff09\u304c\u767a\u751f\u3059\u308b\u307e\u3067\u306e\u6642\u9593\u3092\u5206\u6790\u3059\u308b\u7d71\u8a08\u624b\u6cd5\u3067\u3059\u3002<\/p>\r\n<b>\u57fa\u672c\u6982\u5ff5<\/b>\r\n<b>\u751f\u5b58\u6642\u9593<\/b>\r\n<p>\u4e8b\u8c61\u767a\u751f\u307e\u3067\u306e\u6642\u9593\\(T\\)\u3002\u901a\u5e38\u306f\u975e\u8ca0\u306e\u9023\u7d9a\u5909\u6570\u3067\u3059\u3002<\/p>\r\n<b>\u6253\u3061\u5207\u308a\uff08Censoring\uff09<\/b>\r\n<p>\u89b3\u5bdf\u671f\u9593\u4e2d\u306b\u4e8b\u8c61\u304c\u767a\u751f\u3057\u306a\u3044\u5834\u5408\u3001\u771f\u306e\u751f\u5b58\u6642\u9593\u306f\u672a\u77e5\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3092<strong>\u6253\u3061\u5207\u308a<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\r\n<p>\u4e3b\u306a\u6253\u3061\u5207\u308a\u306e\u7a2e\u985e\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u53f3\u6253\u3061\u5207\u308a<\/strong>: \u89b3\u5bdf\u7d42\u4e86\u6642\u70b9\u3067\u4e8b\u8c61\u672a\u767a\u751f<\/li>\r\n\t<li><strong>\u5de6\u6253\u3061\u5207\u308a<\/strong>: \u89b3\u5bdf\u958b\u59cb\u524d\u306b\u4e8b\u8c61\u767a\u751f\u306e\u53ef\u80fd\u6027<\/li>\r\n\t<li><strong>\u533a\u9593\u6253\u3061\u5207\u308a<\/strong>: \u4e8b\u8c61\u767a\u751f\u6642\u523b\u304c\u533a\u9593\u5185\u3067\u4e0d\u660e<\/li>\r\n<\/ul>\r\n<b>\u751f\u5b58\u95a2\u6570<\/b>\r\n<p><strong>\u751f\u5b58\u95a2\u6570<\/strong>\\(S(t)\\)\u306f\u3001\u6642\u523b\\(t\\)\u307e\u3067\u4e8b\u8c61\u304c\u767a\u751f\u3057\u306a\u3044\u78ba\u7387\u3067\u3059\uff1a<\/p>\r\n<p>\\[S(t) = P(T &gt; t) = 1 &#8211; F(t)\\]<\/p>\r\n<p>\u3053\u3053\u3067\u3001\\(F(t)\\)\u306f\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3067\u3059\u3002<\/p>\r\n<p>\u751f\u5b58\u95a2\u6570\u306e\u6027\u8cea\uff1a<\/p>\r\n<ul>\r\n\t<li>\\(S(0) = 1\\)<\/li>\r\n\t<li>\\(S(\\infty) = 0\\)<\/li>\r\n\t<li>\u5358\u8abf\u975e\u5897\u52a0\u95a2\u6570<\/li>\r\n<\/ul>\r\n<b>\u30cf\u30b6\u30fc\u30c9\u95a2\u6570<\/b>\r\n<p><strong>\u30cf\u30b6\u30fc\u30c9\u95a2\u6570<\/strong>\\(h(t)\\)\u306f\u3001\u6642\u523b\\(t\\)\u307e\u3067\u751f\u5b58\u3057\u305f\u6761\u4ef6\u4e0b\u3067\u306e\u77ac\u9593\u6b7b\u4ea1\u7387\u3067\u3059\uff1a<\/p>\r\n<p>\\[h(t) = \\lim_{\\Delta t \\to 0} \\frac{P(t \\leq T &lt; t + \\Delta t | T \\geq t)}{\\Delta t}\\]<\/p>\r\n<p>\u3053\u308c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3082\u8868\u73fe\u3055\u308c\u307e\u3059\uff1a<\/p>\r\n<p>\\[h(t) = \\frac{f(t)}{S(t)} = -\\frac{d}{dt}\\log S(t)\\]<\/p>\r\n<b>\u7d2f\u7a4d\u30cf\u30b6\u30fc\u30c9\u95a2\u6570<\/b>\r\n<p><strong>\u7d2f\u7a4d\u30cf\u30b6\u30fc\u30c9\u95a2\u6570<\/strong>\\(H(t)\\)\u306f\u3001\u30cf\u30b6\u30fc\u30c9\u95a2\u6570\u306e\u7a4d\u5206\u3067\u3059\uff1a<\/p>\r\n<p>\\[H(t) = \\int_0^t h(u) du = -\\log S(t)\\]<\/p>\r\n<p>\u3053\u308c\u306b\u3088\u308a\u3001\u751f\u5b58\u95a2\u6570\u306f\uff1a<\/p>\r\n<p>\\[S(t) = \\exp(-H(t))\\]<\/p>\n\n<h2>\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u6cd5<\/h2>\n<p><strong>\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u6cd5<\/strong>\uff08Kaplan-Meier method\uff09\u306f\u3001\u6253\u3061\u5207\u308a\u30c7\u30fc\u30bf\u304c\u3042\u308b\u5834\u5408\u306e\u751f\u5b58\u95a2\u6570\u306e\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u63a8\u5b9a\u6cd5\u3067\u3059\u3002<\/p>\r\n<b>\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u63a8\u5b9a\u91cf<\/b>\r\n<p>\u4e8b\u8c61\u767a\u751f\u6642\u523b\u3092\\(t_1 &lt; t_2 &lt; \\cdots &lt; t_k\\)\u3068\u3059\u308b\u3068\u304d\u3001\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u63a8\u5b9a\u91cf\u306f\uff1a<\/p>\r\n<p>\\[\\hat{S}(t) = \\prod_{t_i \\leq t} \\left(1 &#8211; \\frac{d_i}{n_i}\\right)\\]<\/p>\r\n<p>\u3053\u3053\u3067\uff1a<\/p>\r\n<ul>\r\n\t<li>\\(d_i\\): \u6642\u523b\\(t_i\\)\u3067\u306e\u4e8b\u8c61\u767a\u751f\u6570<\/li>\r\n\t<li>\\(n_i\\): \u6642\u523b\\(t_i\\)\u76f4\u524d\u306e\u30ea\u30b9\u30af\u96c6\u5408\u306e\u5927\u304d\u3055<\/li>\r\n<\/ul>\r\n<b>\u30b0\u30ea\u30fc\u30f3\u30a6\u30c3\u30c9\u306e\u516c\u5f0f<\/b>\r\n<p>\u5206\u6563\u306e\u63a8\u5b9a\u306b\u306f<strong>\u30b0\u30ea\u30fc\u30f3\u30a6\u30c3\u30c9\u306e\u516c\u5f0f<\/strong>\u3092\u7528\u3044\u307e\u3059\uff1a<\/p>\r\n<p>\\[\\text{Var}[\\hat{S}(t)] = [\\hat{S}(t)]^2 \\sum_{t_i \\leq t} \\frac{d_i}{n_i(n_i &#8211; d_i)}\\]<\/p>\n\n<h2>Cox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb<\/h2>\n<p><strong>Cox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb<\/strong>\u306f\u3001\u5171\u5909\u91cf\u3092\u8003\u616e\u3057\u305f\u751f\u5b58\u6642\u9593\u5206\u6790\u306e\u4ee3\u8868\u7684\u306a\u624b\u6cd5\u3067\u3059\u3002<\/p>\r\n<b>\u30e2\u30c7\u30eb\u306e\u5b9a\u5f0f\u5316<\/b>\r\n<p>\u30cf\u30b6\u30fc\u30c9\u95a2\u6570\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u89e3\u3057\u307e\u3059\uff1a<\/p>\r\n<p>\\[h(t|\\boldsymbol{x}) = h_0(t) \\exp(\\boldsymbol{x}^T\\boldsymbol{\\beta})\\]<\/p>\r\n<p>\u3053\u3053\u3067\uff1a<\/p>\r\n<ul>\r\n\t<li>\\(h_0(t)\\): \u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u30cf\u30b6\u30fc\u30c9\u95a2\u6570<\/li>\r\n\t<li>\\(\\exp(\\boldsymbol{x}^T\\boldsymbol{\\beta})\\): \u76f8\u5bfe\u30ea\u30b9\u30af<\/li>\r\n<\/ul>\r\n<b>\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u306e\u4eee\u5b9a<\/b>\r\n<p>\u7570\u306a\u308b\u5171\u5909\u91cf\u3092\u6301\u3064\u500b\u4f53\u306e\u30cf\u30b6\u30fc\u30c9\u6bd4\u304c\u6642\u9593\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b\u4eee\u5b9a\uff1a<\/p>\r\n<p>\\[\\frac{h(t|\\boldsymbol{x}_1)}{h(t|\\boldsymbol{x}_2)} = \\exp[(\\boldsymbol{x}_1 &#8211; \\boldsymbol{x}_2)^T\\boldsymbol{\\beta}]\\]<\/p>\r\n<b>\u504f\u5c24\u5ea6<\/b>\r\n<p>Cox\u30e2\u30c7\u30eb\u3067\u306f<strong>\u504f\u5c24\u5ea6<\/strong>\uff08partial likelihood\uff09\u3092\u7528\u3044\u3066\\(\\boldsymbol{\\beta}\\)\u3092\u63a8\u5b9a\u3057\u307e\u3059\uff1a<\/p>\r\n<p>\\[L(\\boldsymbol{\\beta}) = \\prod_{i \\in D} \\frac{\\exp(\\boldsymbol{x}_i^T\\boldsymbol{\\beta})}{\\sum_{j \\in R_i} \\exp(\\boldsymbol{x}_j^T\\boldsymbol{\\beta})}\\]<\/p>\r\n<p>\u3053\u3053\u3067\u3001\\(D\\)\u306f\u4e8b\u8c61\u767a\u751f\u3057\u305f\u500b\u4f53\u306e\u96c6\u5408\u3001\\(R_i\\)\u306f\u6642\u523b\\(t_i\\)\u3067\u306e\u30ea\u30b9\u30af\u96c6\u5408\u3067\u3059\u3002<\/p>\n\n<h2>\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30e2\u30c7\u30eb<\/h2>\n<p><strong>\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30e2\u30c7\u30eb<\/strong>\u306f\u3001\u4eba\u9593\u306e\u8133\u795e\u7d4c\u7cfb\u3092\u6a21\u5023\u3057\u305f\u6a5f\u68b0\u5b66\u7fd2\u624b\u6cd5\u3067\u3001\u73fe\u4ee3\u306e\u6df1\u5c64\u5b66\u7fd2\u306e\u57fa\u76e4\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\r\n<b>\u57fa\u672c\u69cb\u9020<\/b>\r\n<b>\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3<\/b>\r\n<p>\u6700\u3082\u57fa\u672c\u7684\u306a\u69cb\u6210\u5358\u4f4d\u3067\u3001\u5165\u529b\u306e\u91cd\u307f\u4ed8\u304d\u548c\u3092\u6d3b\u6027\u5316\u95a2\u6570\u306b\u901a\u3057\u307e\u3059\uff1a<\/p>\r\n<p>\\[y = f\\left(\\sum_{i=1}^{p} w_i x_i + b\\right)\\]<\/p>\r\n<p>\u3053\u3053\u3067\u3001\\(w_i\\)\u306f\u91cd\u307f\u3001\\(b\\)\u306f\u30d0\u30a4\u30a2\u30b9\u3001\\(f(\\cdot)\\)\u306f\u6d3b\u6027\u5316\u95a2\u6570\u3067\u3059\u3002<\/p>\r\n<b>\u591a\u5c64\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3<\/b>\r\n<p>\u8907\u6570\u306e\u5c64\u3092\u91cd\u306d\u305f\u69cb\u9020\uff1a<\/p>\r\n<p>\\[\\boldsymbol{h}^{(1)} = f^{(1)}(\\boldsymbol{W}^{(1)}\\boldsymbol{x} + \\boldsymbol{b}^{(1)})\\]<\/p>\r\n<p>\\[\\boldsymbol{h}^{(2)} = f^{(2)}(\\boldsymbol{W}^{(2)}\\boldsymbol{h}^{(1)} + \\boldsymbol{b}^{(2)})\\]<\/p>\r\n<p>\\[\\vdots\\]<\/p>\r\n<p>\\[\\boldsymbol{y} = f^{(L)}(\\boldsymbol{W}^{(L)}\\boldsymbol{h}^{(L-1)} + \\boldsymbol{b}^{(L)})\\]<\/p>\r\n<b>\u6d3b\u6027\u5316\u95a2\u6570<\/b>\r\n<p>\u4e3b\u306a\u6d3b\u6027\u5316\u95a2\u6570\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u30b7\u30b0\u30e2\u30a4\u30c9<\/strong>: \\(\\sigma(x) = \\frac{1}{1 + e^{-x}}\\)<\/li>\r\n\t<li><strong>\u53cc\u66f2\u7dda\u6b63\u63a5<\/strong>: \\(\\tanh(x) = \\frac{e^x &#8211; e^{-x}}{e^x + e^{-x}}\\)<\/li>\r\n\t<li><strong>ReLU<\/strong>: \\(\\text{ReLU}(x) = \\max(0, x)\\)<\/li>\r\n\t<li><strong>Leaky ReLU<\/strong>: \\(\\text{LeakyReLU}(x) = \\max(\\alpha x, x)\\)<\/li>\r\n<\/ul>\r\n<b>\u5b66\u7fd2\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/b>\r\n<b>\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5<\/b>\r\n<p>\u52fe\u914d\u964d\u4e0b\u6cd5\u3068\u9023\u9396\u5f8b\u3092\u7528\u3044\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\uff1a<\/p>\r\n<p>\\[w_{ij}^{(l)} \\leftarrow w_{ij}^{(l)} &#8211; \\eta \\frac{\\partial L}{\\partial w_{ij}^{(l)}}\\]<\/p>\r\n<b>\u6b63\u5247\u5316<\/b>\r\n<p>\u904e\u5b66\u7fd2\u3092\u9632\u3050\u305f\u3081\u306e\u624b\u6cd5\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>L1\/L2\u6b63\u5247\u5316<\/strong>: \u91cd\u307f\u306b\u30da\u30ca\u30eb\u30c6\u30a3\u3092\u8ab2\u3059<\/li>\r\n\t<li><strong>\u30c9\u30ed\u30c3\u30d7\u30a2\u30a6\u30c8<\/strong>: \u5b66\u7fd2\u6642\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u30ce\u30fc\u30c9\u3092\u7121\u52b9\u5316<\/li>\r\n\t<li><strong>\u30d0\u30c3\u30c1\u6b63\u898f\u5316<\/strong>: \u5404\u5c64\u306e\u5165\u529b\u3092\u6b63\u898f\u5316<\/li>\r\n<\/ul>\n\n<h2>R\u306b\u3088\u308b\u5b9f\u88c5\uff1a\u751f\u5b58\u6642\u9593\u5206\u6790\u3068\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u6cd5<\/h2>\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u6cbb\u7642\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u751f\u5b58\u30c7\u30fc\u30bf\u3092\u7528\u3044\u3066\u3001\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u6cd5\u306b\u3088\u308b\u751f\u5b58\u95a2\u6570\u306e\u63a8\u5b9a\u30682\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>\r\n<div class=\"hcb_wrap\">\r\n<pre><code class=\"language-r\"># \u5fc5\u8981\u306a\u30e9\u30a4\u30d6\u30e9\u30ea\r\nlibrary(survival)\r\n\r\n# \u30c7\u30fc\u30bf\u751f\u6210\r\nset.seed(123)\r\nn &lt;- 200\r\n\r\n# \u6cbb\u7642\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u751f\u5b58\u6642\u9593\u3092\u751f\u6210\r\ntreatment_times &lt;- rweibull(n\/2, shape = 1.5, scale = 100)\r\ncontrol_times &lt;- rweibull(n\/2, shape = 1.2, scale = 60)\r\n\r\n# \u6253\u3061\u5207\u308a\u6642\u9593\r\ncensoring_time &lt;- 120\r\ntreatment_observed &lt;- pmin(treatment_times, censoring_time)\r\ncontrol_observed &lt;- pmin(control_times, censoring_time)\r\n\r\n# \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u4f5c\u6210\r\nsurvival_data &lt;- data.frame(\r\n  time = c(treatment_observed, control_observed),\r\n  status = c(treatment_times &lt;= censoring_time, control_times &lt;= censoring_time),\r\n  group = factor(c(rep(\"Treatment\", n\/2), rep(\"Control\", n\/2)))\r\n)\r\n\r\n# \u30c7\u30fc\u30bf\u6982\u8981\r\ntable(survival_data$group, survival_data$status)\r\n\r\n# \u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u63a8\u5b9a\r\nkm_fit &lt;- survfit(Surv(time, status) ~ group, data = survival_data)\r\nprint(km_fit)\r\n\r\n# \u751f\u5b58\u66f2\u7dda\u306e\u53ef\u8996\u5316\r\npar(mfrow = c(1, 2))\r\n\r\n# 1. \u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u751f\u5b58\u66f2\u7dda\r\nplot(km_fit, col = c(\"blue\", \"red\"), lwd = 2,\r\n     main = \"Kaplan-Meier Curves\",\r\n     xlab = \"Time\", ylab = \"Survival Probability\")\r\nlegend(\"topright\", legend = c(\"Control\", \"Treatment\"),\r\n       col = c(\"blue\", \"red\"), lwd = 2)\r\n\r\n# 2. 2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\r\nkm_summary &lt;- summary(km_fit)\r\nkm_data &lt;- data.frame(\r\n  time = km_summary$time,\r\n  surv = km_summary$surv,\r\n  group = km_summary$strata\r\n)\r\n\r\n# log(-log(S(t))) vs log(t) \u306e\u8a08\u7b97\r\nkm_data$log_neg_log_surv &lt;- log(-log(km_data$surv))\r\nkm_data$log_time &lt;- log(km_data$time)\r\n\r\n# \u7121\u9650\u5927\u5024\u3092\u9664\u53bb\r\nkm_data &lt;- km_data[is.finite(km_data$log_neg_log_surv), ]\r\n\r\n# \u6cbb\u7642\u7fa4\u3068\u5bfe\u7167\u7fa4\u306b\u5206\u5272\r\ntreatment_data &lt;- km_data[grepl(\"Treatment\", km_data$group), ]\r\ncontrol_data &lt;- km_data[grepl(\"Control\", km_data$group), ]\r\n\r\n# 2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\r\nplot(control_data$log_time, control_data$log_neg_log_surv,\r\n     type = \"l\", col = \"blue\", lwd = 2,\r\n     main = \"Log-Log Plot\",\r\n     xlab = \"log(Time)\", ylab = \"log(-log(S(t)))\")\r\nlines(treatment_data$log_time, treatment_data$log_neg_log_surv,\r\n      col = \"red\", lwd = 2)\r\nlegend(\"topleft\", legend = c(\"Control\", \"Treatment\"),\r\n       col = c(\"blue\", \"red\"), lwd = 2)\r\n\r\n# \u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\r\nlogrank_test &lt;- survdiff(Surv(time, status) ~ group, data = survival_data)\r\np_value &lt;- 1 - pchisq(logrank_test$chisq, df = 1)\r\n\r\ncat(sprintf(\"\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a p\u5024: %.4f\\\\n\", p_value))\r\nif(p_value &lt; 0.05) {\r\n  cat(\"\u7d50\u8ad6: 2\u7fa4\u9593\u306b\u6709\u610f\u5dee\u3042\u308a\\\\n\")\r\n} else {\r\n  cat(\"\u7d50\u8ad6: 2\u7fa4\u9593\u306b\u6709\u610f\u5dee\u306a\u3057\\\\n\")\r\n}\r\n\r\n# 2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u306e\u89e3\u91c8\r\nif(nrow(treatment_data) &gt; 1 &amp;&amp; nrow(control_data) &gt; 1) {\r\n  # \u5404\u7fa4\u306e\u76f4\u7dda\u6027\uff08\u30ef\u30a4\u30d6\u30eb\u5206\u5e03\u306e\u78ba\u8a8d\uff09\r\n  lm_treatment &lt;- lm(log_neg_log_surv ~ log_time, data = treatment_data)\r\n  lm_control &lt;- lm(log_neg_log_surv ~ log_time, data = control_data)\r\n\r\n  cat(sprintf(\"\\\\n2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u306e\u50be\u304d:\\\\n\"))\r\n  cat(sprintf(\"\u6cbb\u7642\u7fa4: %.3f\\\\n\", coef(lm_treatment)[2]))\r\n  cat(sprintf(\"\u5bfe\u7167\u7fa4: %.3f\\\\n\", coef(lm_control)[2]))\r\n\r\n  # 2\u7fa4\u9593\u306e\u8ddd\u96e2\uff08\u6cbb\u7642\u52b9\u679c\u306e\u5927\u304d\u3055\uff09\r\n  common_times &lt;- seq(min(km_data$log_time), max(km_data$log_time), length.out = 20)\r\n  treatment_interp &lt;- approx(treatment_data$log_time, treatment_data$log_neg_log_surv,\r\n                            xout = common_times, rule = 2)$y\r\n  control_interp &lt;- approx(control_data$log_time, control_data$log_neg_log_surv,\r\n                          xout = common_times, rule = 2)$y\r\n\r\n  mean_distance &lt;- mean(abs(treatment_interp - control_interp), na.rm = TRUE)\r\n  cat(sprintf(\"\u5e73\u5747\u8ddd\u96e2: %.3f\\\\n\", mean_distance))\r\n\r\n  if(mean_distance &gt; 0.5) {\r\n    cat(\"\u2192 \u5927\u304d\u306a\u6cbb\u7642\u52b9\u679c\\\\n\")\r\n  } else if(mean_distance &gt; 0.2) {\r\n    cat(\"\u2192 \u4e2d\u7a0b\u5ea6\u306e\u6cbb\u7642\u52b9\u679c\\\\n\")\r\n  } else {\r\n    cat(\"\u2192 \u5c0f\u3055\u306a\u6cbb\u7642\u52b9\u679c\\\\n\")\r\n  }\r\n}<\/code><\/pre>\r\n<\/div>\r\n<b>\u51fa\u529b\u7d50\u679c<\/b>\r\n<div class=\"hcb_wrap\">\r\n<pre class=\"prism line-numbers lang-plain\" data-lang=\"Plain Text\">=== \u30c7\u30fc\u30bf\u6982\u8981 ===<code>            FALSE TRUE\r\n  Control       4   96\r\n  Treatment    27   73\r\n\r\n=== \u4e2d\u592e\u751f\u5b58\u6642\u9593 ===\r\nCall: survfit(formula = Surv(time, status) ~ group, data = survival_data)\r\n\r\n                  n events median 0.95LCL 0.95UCL\r\ngroup=Control   100     96   44.2    36.0    54.9\r\ngroup=Treatment 100     73   83.5    67.7    92.8\r\n\r\n=== \u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a ===\r\np\u5024: 0.0000\r\n\u7d50\u8ad6: 2\u7fa4\u9593\u306b\u6709\u610f\u5dee\u3042\u308a\r\n\r\n=== 2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u306e\u50be\u304d ===\r\n\u6cbb\u7642\u7fa4: 1.460\r\n\u5bfe\u7167\u7fa4: 1.250\r\n\u5e73\u5747\u8ddd\u96e2: 1.031\r\n\u2192 \u5927\u304d\u306a\u6cbb\u7642\u52b9\u679c\r\n<\/code><\/pre>\r\n<\/div>\r\n<p><img decoding=\"async\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/10\/ra4.png\" alt=\"\" width=\"419\" height=\"404\" class=\"alignnone size-full wp-image-7376 aligncenter\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/10\/ra4.png 419w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/10\/ra4-300x289.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\r\n<pre><\/pre>\r\n<p><!-- notionvc: b133d30c-4acb-49a8-b129-e0f15b780719 --><\/p>\n\n<h2>\u51fa\u529b\u7d50\u679c\u306e\u89e3\u91c8<\/h2>\n<b>\u751f\u5b58\u6642\u9593\u306e\u6bd4\u8f03<\/b>\r\n<p>\u5206\u6790\u7d50\u679c\u304b\u3089\u4ee5\u4e0b\u306e\u77e5\u898b\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\r\n<p><strong>\u57fa\u672c\u7d71\u8a08<\/strong>\uff1a<\/p>\r\n<ul>\r\n\t<li>\u5bfe\u7167\u7fa4\u306e\u4e2d\u592e\u751f\u5b58\u6642\u9593\uff1a\u7d0444.2\u6642\u9593<\/li>\r\n\t<li>\u6cbb\u7642\u7fa4\u306e\u4e2d\u592e\u751f\u5b58\u6642\u9593\uff1a\u7d0483.5\u6642\u9593<\/li>\r\n\t<li>\u6cbb\u7642\u306b\u3088\u308a\u751f\u5b58\u6642\u9593\u304c\u7d042\u500d\u306b\u5ef6\u9577<\/li>\r\n<\/ul>\r\n<p><strong>\u7d71\u8a08\u7684\u691c\u5b9a<\/strong>\uff1a<\/p>\r\n<ul>\r\n\t<li>\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306ep\u5024 &lt; 0.001<\/li>\r\n\t<li>2\u7fa4\u9593\u306b\u7d71\u8a08\u7684\u306b\u6709\u610f\u306a\u5dee\u304c\u5b58\u5728<\/li>\r\n<\/ul>\r\n<b>\u30b0\u30e9\u30d5\u304b\u3089\u8aad\u307f\u53d6\u308c\u308b\u5177\u4f53\u7684\u306a\u60c5\u5831<\/b>\r\n<p><strong>\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u751f\u5b58\u66f2\u7dda<\/strong>\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u5bfe\u7167\u7fa4\uff08\u9752\u7dda\uff09<\/strong>: \u6025\u6fc0\u306a\u4e0b\u964d\u3067\u3001\u6642\u959350\u4ed8\u8fd1\u3067\u751f\u5b58\u78ba\u73870.5\u3092\u4e0b\u56de\u308b<\/li>\r\n\t<li><strong>\u6cbb\u7642\u7fa4\uff08\u8d64\u7dda\uff09<\/strong>: \u7de9\u3084\u304b\u306a\u4e0b\u964d\u3067\u3001\u6642\u959380\u4ed8\u8fd1\u3067\u751f\u5b58\u78ba\u73870.5\u306b\u5230\u9054<\/li>\r\n\t<li>\u89b3\u5bdf\u671f\u9593\u5168\u4f53\u3092\u901a\u3058\u3066\u6cbb\u7642\u7fa4\u304c\u5e38\u306b\u4e0a\u4f4d\u306b\u4f4d\u7f6e\u3057\u3001\u6301\u7d9a\u7684\u306a\u6cbb\u7642\u52b9\u679c\u3092\u793a\u3059<\/li>\r\n<\/ul>\r\n<p><strong>2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8<\/strong>\uff1a<\/p>\r\n<ul>\r\n\t<li>\u4e21\u7fa4\u3068\u3082\u307b\u307c\u76f4\u7dda\u95a2\u4fc2\u3092\u793a\u3057\u3001\u30ef\u30a4\u30d6\u30eb\u5206\u5e03\u3078\u306e\u9069\u5408\u3092\u793a\u5506<\/li>\r\n\t<li>2\u3064\u306e\u76f4\u7dda\u304c\u307b\u307c\u5e73\u884c\uff08\u50be\u304d\u5dee0.21\uff09\u3067\u3001\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u306e\u4eee\u5b9a\u304c\u6210\u7acb<\/li>\r\n\t<li>\u5e73\u5747\u5782\u76f4\u8ddd\u96e21.031\u306f\u5927\u304d\u306a\u6cbb\u7642\u52b9\u679c\u3092\u793a\u3057\u3001\u7d042.8\u500d\u306e\u30cf\u30b6\u30fc\u30c9\u6bd4\u6539\u5584\u3092\u793a\u5506<\/li>\r\n<\/ul>\r\n<p><!-- notionvc: 887cb7db-a7f8-4190-8242-d840d47c7d16 --><\/p>\n\n<h2>\u307e\u3068\u3081<\/h2>\n<p>\u672c\u30b7\u30ea\u30fc\u30ba\u3092\u901a\u3058\u3066\u3001\u56de\u5e30\u5206\u6790\u306e\u5e45\u5e83\u3044\u5fdc\u7528\u3092\u5b66\u3073\u307e\u3057\u305f\u3002\u6700\u7d42\u56de\u306e\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\r\n<ol>\r\n\t<li><strong>\u30c8\u30fc\u30d3\u30c3\u30c8\u30e2\u30c7\u30eb<\/strong>: \u5236\u9650\u4ed8\u304d\u5f93\u5c5e\u5909\u6570\u3078\u306e\u5bfe\u5fdc<\/li>\r\n\t<li><strong>\u751f\u5b58\u6642\u9593\u5206\u6790<\/strong>: \u6642\u9593\u8ef8\u3068\u6253\u3061\u5207\u308a\u3092\u8003\u616e\u3057\u305f\u5206\u6790<\/li>\r\n\t<li><strong>\u30ab\u30d7\u30e9\u30f3\u30fb\u30de\u30a4\u30e4\u30fc\u6cd5<\/strong>: \u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u751f\u5b58\u95a2\u6570\u63a8\u5b9a<\/li>\r\n\t<li><strong>Cox\u56de\u5e30<\/strong>: \u30bb\u30df\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u56de\u5e30\u624b\u6cd5<\/li>\r\n\t<li><strong>2\u91cd\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8<\/strong>: \u5206\u5e03\u306e\u6027\u8cea\u3068\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u306e\u78ba\u8a8d<\/li>\r\n\t<li><strong>\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af<\/strong>: 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