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14px;\">\u4e0e\u4f20\u7edf\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u76f8\u6bd4\uff0cpbkrtest\u5305\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u80fd\u591f\u8003\u8651\u5230\u6df7\u5408\u6548\u5e94\u6a21\u578b\u7684\u7279\u6b8a\u7ed3\u6784\uff0c\u5e76\u63d0\u4f9b\u4e86\u66f4\u51c6\u786e\u7684\u5047\u8bbe\u68c0\u9a8c\u7ed3\u679c\u3002\u4f20\u7edf\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u901a\u5e38\u5047\u8bbe\u6570\u636e\u72ec\u7acb\u540c\u5206\u5e03\uff0c\u800c\u6df7\u5408\u6548\u5e94\u6a21\u578b\u5219\u80fd\u591f\u5904\u7406\u6570\u636e\u4e2d\u5b58\u5728\u7684\u5c42\u7ea7\u7ed3\u6784\u548c\u76f8\u5173\u6027\u3002\u6b64\u5916\uff0cpbkrtest\u5305\u8fd8\u63d0\u4f9b\u4e86\u6a21\u578b\u8bca\u65ad\u7684\u529f\u80fd\uff0c\u53ef\u4ee5\u5e2e\u52a9\u7528\u6237\u8bc4\u4f30\u6a21\u578b\u7684\u62df\u5408\u7a0b\u5ea6\u548c\u5047\u8bbe\u7684\u5408\u7406\u6027\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">pbkrtest\u5305\u7684\u5e94\u7528\u8303\u56f4\u975e\u5e38\u5e7f\u6cdb\uff0c\u9002\u7528\u4e8e\u8bb8\u591a\u9886\u57df\u7684\u6570\u636e\u5206\u6790\u548c\u7814\u7a76\u3002\u4f8b\u5982\uff0c\u5728\u793e\u4f1a\u79d1\u5b66\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u4f7f\u7528\u6df7\u5408\u6548\u5e94\u6a21\u578b\u6765\u5206\u6790\u5bb6\u5ead\u3001\u793e\u533a\u6216\u5b66\u6821\u4e4b\u95f4\u7684\u5dee\u5f02\u5bf9\u4e2a\u4f53\u884c\u4e3a\u7684\u5f71\u54cd\u3002\u5728\u751f\u7269\u533b\u5b66\u7814\u7a76\u4e2d\uff0c\u6df7\u5408\u6548\u5e94\u6a21\u578b\u53ef\u4ee5\u7528\u4e8e\u8003\u8651\u5b9e\u9a8c\u8bbe\u8ba1\u7684\u91cd\u590d\u6027\uff0c\u4ece\u800c\u66f4\u51c6\u786e\u5730\u8bc4\u4f30\u6cbb\u7597\u6548\u679c\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">\u8981\u4f7f\u7528pbkrtest\u5305\uff0c\u53ef\u4ee5\u5728R\u4e2d\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\u548c\u52a0\u8f7d\uff1a<\/span><\/p>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\">> install.packages(\"pbkrtest\") #\u5b89\u88c5pbkrtest\u8bed\u8a00\u5305<\/span><\/code><code><span class=\"code-snippet_outer\">> library(pbkrtest) #\u52a0\u8f7d\u8bed\u8a00\u5305<\/span><\/code><\/pre>\n<\/section>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u4e0b\u9762\u662f\u4e00\u4e2a\u4f7f\u7528pbkrtest\u5305\u8fdb\u884c\u751f\u7269\u4fe1\u606f\u76f8\u5173\u5b9e\u9645\u6570\u636e\u5206\u6790\u7684\u793a\u4f8b\uff1a<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u5047\u8bbe\u6211\u4eec\u6b63\u5728\u7814\u7a76\u4e00\u79cd\u65b0\u836f\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u3002\u6211\u4eec\u6709\u4e00\u4e2a\u5b9e\u9a8c\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u4e8610\u4e2a\u75c5\u4eba\uff0c\u5728\u7ed9\u4e88\u836f\u7269\u6cbb\u7597\u524d\u540e\uff0c\u6d4b\u91cf\u4e86\u4ed6\u4eec\u7684\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\u3002\u6b64\u5916\uff0c\u6bcf\u4e2a\u75c5\u4eba\u8fd8\u6709\u4e00\u4e9b\u57fa\u672c\u4fe1\u606f\uff0c\u5982\u6027\u522b\u548c\u5e74\u9f84\u3002\u6211\u4eec\u60f3\u8981\u786e\u5b9a\u836f\u7269\u662f\u5426\u5bf9\u57fa\u56e0\u8868\u8fbe\u4ea7\u751f\u663e\u8457\u5f71\u54cd\uff0c\u5e76\u4e14\u662f\u5426\u5b58\u5728\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u52a0\u8f7d\u6240\u9700\u7684\u5305\uff0c\u5e76\u5bfc\u5165\u6570\u636e\u96c6\u3002\u5047\u8bbe\u6211\u4eec\u7684\u6570\u636e\u96c6\u547d\u540d\u4e3a”gene_expression.csv”\uff0c\u5176\u4e2d\u5305\u542b\u4e86”PatientID”\uff08\u75c5\u4ebaID\uff09\u3001”Treatment”\uff08\u6cbb\u7597\u524d\u540e\uff09\u3001”GeneExpression”\uff08\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\uff09\u3001”Gender”\uff08\u6027\u522b\uff09\u548c”Age”\uff08\u5e74\u9f84\uff09\u7b49\u53d8\u91cf\u3002<\/span><span style=\"color: rgb(51, 51, 51);font-family: "Open Sans";font-size: 12pt;letter-spacing: 0.034em;\"><\/span><\/p>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\"># \u52a0\u8f7d\u6240\u9700\u7684\u5305<\/span><\/code><code><span class=\"code-snippet_outer\">> library(lme4)<\/span><\/code><code><span class=\"code-snippet_outer\">> library(pbkrtest)<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\"># \u5bfc\u5165\u6570\u636e\u96c6<\/span><\/code><code><span class=\"code-snippet_outer\">> data <- read.csv(\"gene_expression.csv\")<\/span><\/code><\/pre>\n<\/section>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<p><br \/><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u5176\u4e2d\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\u662f\u56e0\u53d8\u91cf\uff0c\u6cbb\u7597\u548c\u75c5\u4eba\u662f\u56fa\u5b9a\u6548\u5e94\uff0c\u800c\u75c5\u4eba\u662f\u968f\u673a\u6548\u5e94\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528lmer()\u51fd\u6570\u6765\u62df\u5408\u8be5\u6a21\u578b\u3002<\/span><\/p>\n<\/section>\n<section powered-by=\"xiumi.us\">\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"powershell\"><code><span class=\"code-snippet_outer\"># \u6784\u5efa\u6df7\u5408\u6548\u5e94\u6a21\u578b<\/span><\/code><code><span class=\"code-snippet_outer\">> model <- lmer(GeneExpression ~ Treatment + (1 | PatientID), data = data)<\/span><\/code><\/pre>\n<\/section>\n<p><br \/><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528pbkrtest\u5305\u63d0\u4f9b\u7684summary()\u51fd\u6570\u6765\u67e5\u770b\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\uff0c\u5305\u62ec\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u3002<\/span><\/p>\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\"># \u67e5\u770b\u6a21\u578b\u6458\u8981\u4fe1\u606f<\/span><\/code><code><span class=\"code-snippet_outer\">> summary(model)<\/span><\/code><\/pre>\n<\/section>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u8f93\u51fa\u7684\u6458\u8981\u4fe1\u606f\u5c06\u63d0\u4f9b\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u7b49\u7edf\u8ba1\u91cf\u3002\u901a\u8fc7\u68c0\u67e5\u56fa\u5b9a\u6548\u5e94\u7684p\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u6cbb\u7597\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u662f\u5426\u663e\u8457\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528anova()\u51fd\u6570\u6765\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002\u5047\u8bbe\u6211\u4eec\u8fd8\u60f3\u8003\u8651\u6027\u522b\u548c\u5e74\u9f84\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u5305\u542b\u8fd9\u4e9b\u53d8\u91cf\u7684\u6a21\u578b\uff0c\u5e76\u4f7f\u7528anova()\u51fd\u6570\u8fdb\u884c\u6bd4\u8f83\u3002<\/span><span style=\"mso-spacerun:'yes';font-family:Calibri;mso-fareast-font-family:\u5b8b\u4f53;mso-bidi-font-family:'Times New Roman';\"><o:p><\/o:p><\/span><\/p>\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\"># \u6784\u5efa\u5305\u542b\u6027\u522b\u548c\u5e74\u9f84\u7684\u6a21\u578b<\/span><\/code><code><span class=\"code-snippet_outer\">> model_full <- lmer(GeneExpression ~ Treatment + Gender + Age + (1 | PatientID), data = data)<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\"># \u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\u7684\u663e\u8457\u6027\u5dee\u5f02<\/span><\/code><code><span class=\"code-snippet_outer\">> anova(model, model_full)<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\">\u901a\u8fc7\u6bd4\u8f83\u6a21\u578b\u7684\u663e\u8457\u6027\u5dee\u5f02\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u662f\u5426\u6709\u5fc5\u8981\u5c06\u6027\u522b\u548c\u5e74\u9f84\u8003\u8651\u5728\u5185\u3002<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\">\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528pbkrtest\u5305\u6765\u5206\u6790\u751f\u7269\u4fe1\u606f\u76f8\u5173\u7684\u5b9e\u9645\u6570\u636e\u3002\u6211\u4eec\u6784\u5efa\u4e86\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u8003\u8651\u4e86\u6cbb\u7597\u548c\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\uff0c\u5e76\u4f7f\u7528summary()\u51fd\u6570\u67e5\u770b\u4e86\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u4f7f\u7528anova()\u51fd\u6570\u6bd4\u8f83\u4e86\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002\u901a\u8fc7\u8fd9\u4e9b\u5206\u6790\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u5173\u4e8e\u836f\u7269\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u4ee5\u53ca\u5176\u4ed6\u56e0\u7d20\u7684\u7ed3\u8bba\u3002<\/span><\/code><\/pre>\n<\/section>\n<p><br \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.5904486251808972\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/2_aI02Snqic1JnZGPAomXtPa3csaPnWw.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEmaOa5eqyuqaiarEhSggFLgIaEjaI02Snqic1JnZGPAomXtPa3csaPnWw\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"691\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.7147192716236722\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/3_iauibcz0Z6srzhhBfhanO360hPKQ5g.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEKkk460Eule1qPw8JXHw5cTQibP9iauibcz0Z6srzhhBfhanO360hPKQ5g\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"659\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"1\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/4_buRNUhOh9UMhFqcsvW3LPphfJSZZKw.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEuRYzyw57mPEmiaUFuCs6TD4YJbuRNUhOh9UMhFqcsvW3LPphfJSZZKw\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"667\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.7484177215189873\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/5_htZvVNPkiclibkcCDsMf1CwPK769rA.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEylWk3zYaOlVzvHwvDgleibvzxI1htZvVNPkiclibkcCDsMf1CwPK769rA\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"632\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.7514450867052023\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/6_OZ4Gqf3sYqib9h4nPO6mlmMtHXBDgQ.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkErC9cAlwK1rD1sawEQCJ24wvpgOZ4Gqf3sYqib9h4nPO6mlmMtHXBDgQ\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"692\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p><br \/><\/p>\n<p><span style=\"font-size: 14px;\">\u4ee5\u4e0a\u5c31\u662f\u5bf9R\u8bed\u8a00\u5305pbkrtest\u7684\u7b80\u5355\u4ecb\u7ecd\u5566\uff0cpbkrtest\u5305\u4e3a\u7814\u7a76\u4eba\u5458\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u7528\u4e8e\u5728\u6df7\u5408\u6548\u5e94\u6a21\u578b\u4e2d\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u548c\u53c2\u6570\u4f30\u8ba1\u3002\u5b83\u80fd\u591f\u5904\u7406\u590d\u6742\u7684\u6570\u636e\u7ed3\u6784\u548c\u76f8\u5173\u6027\uff0c\u63d0\u4f9b\u51c6\u786e\u7684\u7edf\u8ba1\u63a8\u65ad\u7ed3\u679c\u3002\u901a\u8fc7\u4f7f\u7528pbkrtest\u5305\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u6570\u636e\uff0c\u5e76\u5f97\u51fa\u66f4\u53ef\u9760\u7684\u7ed3\u8bba\u3002<\/span><\/p>\n<p style=\"text-align: center;\"><br \/><\/p>\n<\/section>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><span style=\"font-size: 14px;color: rgb(0, 0, 0);\"><span style=\"font-size: 14px;\">\u5c0f\u4f19\u4f34\u4eec\uff0c\u4eca\u5929\u6709\u6ca1\u6709\u5b66\u5230\u65b0\u77e5\u8bc6\u5462\uff0c\u60f3\u8981\u7ee7\u7eed\u4e86\u89e3<\/span>R<span style=\"font-size: 14px;\">\u8bed\u8a00\u5185\u5bb9\u53ef\u4ee5\u6301\u7eed\u5173\u6ce8\u5c0f\u679c\u54e6\uff5e\uff5e\u6216\u8005\u4e5f\u53ef\u4ee5\u5173\u6ce8\u6211\u4eec\u7684\u5b98\u7f51\u4e5f\u4f1a\u6301\u7eed\u66f4\u65b0<\/span><\/span><span style=\"font-size: 14px;color: rgb(0, 0, 0);\"><span style=\"font-size: 14px;\">\u7684\u54e6\uff5e<\/span> <\/span><\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">http:\/\/www.biocloudservice.com\/home.html<\/span><span style=\"color: rgb(0, 0, 0);font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><br \/><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">References:<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">1.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/ourcodingclub.github.io\/tutorials\/mixed-models\/<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">2.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/terpconnect.umd.edu\/~egurarie\/teaching\/Biol709\/Topic3\/Lecture16_MixedEffectsModels.html<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">3.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/stackoverflow.com\/questions\/40546716\/plotting-mixed-models-regression-coefficients-in-r<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">4.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">http:\/\/www.analyticsforfun.com\/2014\/06\/performing-anova-test-in-r-results-and.html<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">5.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/www.scribbr.com\/statistics\/anova-in-r\/<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"letter-spacing: 0.034em;text-align: left;\"><\/span><\/p>\n<section powered-by=\"xiumi.us\">\n<p><span style=\"color: rgb(217, 33, 66);font-size: 10.5pt;font-family: \u5fae\u8f6f\u96c5\u9ed1;\">\u5176\u4ed6\u76f8\u5173\u5206\u6790\u5185\u5bb9\uff0c\u4f8b\u5982\u9884\u6d4b\u80bf\u7624\u6837\u672c\u836f\u7269\u654f\u611f\u6027\u5206\u6790(http:\/\/www.biocloudservice.com\/712\/712.php),\u9884\u6d4b\u67d0\u6837\u672c\u4e9a\u578b\u5bf9\u514d\u75ab\u6cbb\u7597\u7684\u53cd\u5e94(http:\/\/www.biocloudservice.com\/292\/292.php)\uff0c\u5355\u6837\u672c\u5bcc\u96c6\u7b97\u6cd5\u5206\u6790\u514d\u75ab\u6d78\u6da6\u4e30\u5ea6(http:\/\/www.biocloudservice.com\/106\/106.php)\uff0c\u8ba1\u7b9764\u79cd\u514d\u75ab\u7ec6\u80de\u76f8\u5bf9\u542b\u91cf(http:\/\/www.biocloudservice.com\/107\/107.php)\u7b49\u90fd\u53ef\u4ee5\u7528\u672c\u516c\u53f8\u65b0\u5f00\u53d1\u7684\u96f6\u4ee3\u7801\u4e91\u5e73\u53f0\u751f\u4fe1\u5206\u6790\u5c0f\u5de5\u5177\uff0c\u4e00\u952e\u5b8c\u6210\u8be5\u5206\u6790\u5965\uff0c\u611f\u5174\u8da3\u7684\u5c0f\u4f19\u4f34\u6b22\u8fce\u6765\u5c1d\u8bd5\u5965\uff0c\u7f51\u5740\uff1ahttp:\/\/www.biocloudservice.com\/home.html\u3002<\/span><span 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0px;display: inline-block;width: 647px;vertical-align: top;align-self: flex-start;flex: 0 0 auto;border-style: solid;border-width: 1px;border-color: rgb(217, 217, 217);\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 15px;outline: 0px;justify-content: flex-start;display: flex;flex-flow: row nowrap;\">\n<section style=\"padding-left: 9px;outline: 0px;display: inline-block;width: 625px;vertical-align: top;align-self: flex-start;flex: 0 0 auto;border-style: solid;border-width: 0px 0px 0px 12px;border-left-color: rgb(212, 32, 2);\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;text-align: justify;font-size: 17px;color: rgb(62, 62, 62);\">\n<p style=\"outline: 0px;\"><strong style=\"outline: 0px;\">\u5c0f\u679c\u53cb\u60c5\u63a8\u8350<\/strong><\/p>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 3px;outline: 0px;\">\n<section style=\"outline: 0px;background-color: rgb(217, 217, 217);height: 1px;\"><svg viewbox=\"0 0 1 1\" 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\/><\/span><\/a><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p><span style=\"mso-spacerun:"yes";font-family:\u5fae\u8f6f\u96c5\u9ed1;font-size:10.5000pt;mso-font-kerning:1.0000pt;\"><o:p><\/o:p><\/span><\/p>\n<section style=\"margin-bottom: 0px;letter-spacing: 0.578px;white-space: normal;caret-color: rgba(0, 0, 0, 0);font-size: 16px;\">\n<section>\n<section style=\"margin-top: 0.5em;\">\n<section style=\"padding: 0.5em;border-width: 1px;border-style: solid;box-shadow: rgb(226, 226, 226) 0px 16px 1px -13px;border-color: rgb(0, 150, 136);\">\n<section style=\"text-align: left;\">\n<section style=\"color: rgb(255, 129, 36);text-align: justify;\">\n<section style=\"margin-bottom: 8px;\">\n<p style=\"text-indent: 0em;line-height: 1.75em;\"><span style=\"letter-spacing: 0.5px;\">\u70b9\u51fb<strong><span style=\"color: rgb(0, 150, 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\/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section powered-by=\"xiumi.us\">\n<section style=\"display: contents;\" powered-by=\"xiumi.us\">\n<section style=\"display: contents;\">\n<section style=\"display: contents;\">\n<section style=\"height: 0px;overflow: hidden;\"><span style=\"font-size: 14px;letter-spacing: 0.578px;caret-color: red;\"> <\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<p><br \/><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;letter-spacing: 0.034em;\">pbkrtest\u5305\u7684\u4e3b\u8981\u529f\u80fd\u662f\u63d0\u4f9b\u6709\u6548\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\uff0c\u7528\u4e8e\u8bc4\u4f30\u6df7\u5408\u6548\u5e94\u6a21\u578b\u4e2d\u56fa\u5b9a\u6548\u5e94\u7684\u663e\u8457\u6027\u3002\u5b83\u901a\u8fc7\u8ba1\u7b97\u8fd1\u4f3c\u7684p\u503c\uff0c\u5229\u7528\u53c2\u6570\u4f30\u8ba1\u7684\u6e10\u8fd1\u5206\u5e03\uff0c\u6765\u8fdb\u884c\u7edf\u8ba1\u63a8\u65ad\u3002\u8fd9\u79cd\u8fd1\u4f3c\u65b9\u6cd5\u5bf9\u4e8e\u5927\u578b\u6570\u636e\u96c6\u548c\u590d\u6742\u7684\u6a21\u578b\u7ed3\u6784\u5c24\u5176\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u663e\u8457\u964d\u4f4e\u8ba1\u7b97\u7684\u590d\u6742\u6027\u3002<\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;letter-spacing: 0.034em;\"><br \/><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">\u5728\u4f7f\u7528pbkrtest\u5305\u65f6\uff0c\u7528\u6237\u53ef\u4ee5\u6307\u5b9a\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u5e76\u4f7f\u7528\u9002\u5f53\u7684\u51fd\u6570\u8fdb\u884c\u62df\u5408\u3002\u7136\u540e\uff0c\u53ef\u4ee5\u4f7f\u7528summary()\u51fd\u6570\u6765\u67e5\u770b\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\uff0c\u5305\u62ec\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u3002\u540c\u65f6\uff0cpbkrtest\u5305\u8fd8\u63d0\u4f9b\u4e86anova()\u51fd\u6570\uff0c\u7528\u4e8e\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">\u4e0e\u4f20\u7edf\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u76f8\u6bd4\uff0cpbkrtest\u5305\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u80fd\u591f\u8003\u8651\u5230\u6df7\u5408\u6548\u5e94\u6a21\u578b\u7684\u7279\u6b8a\u7ed3\u6784\uff0c\u5e76\u63d0\u4f9b\u4e86\u66f4\u51c6\u786e\u7684\u5047\u8bbe\u68c0\u9a8c\u7ed3\u679c\u3002\u4f20\u7edf\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u901a\u5e38\u5047\u8bbe\u6570\u636e\u72ec\u7acb\u540c\u5206\u5e03\uff0c\u800c\u6df7\u5408\u6548\u5e94\u6a21\u578b\u5219\u80fd\u591f\u5904\u7406\u6570\u636e\u4e2d\u5b58\u5728\u7684\u5c42\u7ea7\u7ed3\u6784\u548c\u76f8\u5173\u6027\u3002\u6b64\u5916\uff0cpbkrtest\u5305\u8fd8\u63d0\u4f9b\u4e86\u6a21\u578b\u8bca\u65ad\u7684\u529f\u80fd\uff0c\u53ef\u4ee5\u5e2e\u52a9\u7528\u6237\u8bc4\u4f30\u6a21\u578b\u7684\u62df\u5408\u7a0b\u5ea6\u548c\u5047\u8bbe\u7684\u5408\u7406\u6027\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">pbkrtest\u5305\u7684\u5e94\u7528\u8303\u56f4\u975e\u5e38\u5e7f\u6cdb\uff0c\u9002\u7528\u4e8e\u8bb8\u591a\u9886\u57df\u7684\u6570\u636e\u5206\u6790\u548c\u7814\u7a76\u3002\u4f8b\u5982\uff0c\u5728\u793e\u4f1a\u79d1\u5b66\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u4f7f\u7528\u6df7\u5408\u6548\u5e94\u6a21\u578b\u6765\u5206\u6790\u5bb6\u5ead\u3001\u793e\u533a\u6216\u5b66\u6821\u4e4b\u95f4\u7684\u5dee\u5f02\u5bf9\u4e2a\u4f53\u884c\u4e3a\u7684\u5f71\u54cd\u3002\u5728\u751f\u7269\u533b\u5b66\u7814\u7a76\u4e2d\uff0c\u6df7\u5408\u6548\u5e94\u6a21\u578b\u53ef\u4ee5\u7528\u4e8e\u8003\u8651\u5b9e\u9a8c\u8bbe\u8ba1\u7684\u91cd\u590d\u6027\uff0c\u4ece\u800c\u66f4\u51c6\u786e\u5730\u8bc4\u4f30\u6cbb\u7597\u6548\u679c\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">\u8981\u4f7f\u7528pbkrtest\u5305\uff0c\u53ef\u4ee5\u5728R\u4e2d\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\u548c\u52a0\u8f7d\uff1a<\/span><\/p>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\">> install.packages(\"pbkrtest\") #\u5b89\u88c5pbkrtest\u8bed\u8a00\u5305<\/span><\/code><code><span class=\"code-snippet_outer\">> library(pbkrtest) #\u52a0\u8f7d\u8bed\u8a00\u5305<\/span><\/code><\/pre>\n<\/section>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u4e0b\u9762\u662f\u4e00\u4e2a\u4f7f\u7528pbkrtest\u5305\u8fdb\u884c\u751f\u7269\u4fe1\u606f\u76f8\u5173\u5b9e\u9645\u6570\u636e\u5206\u6790\u7684\u793a\u4f8b\uff1a<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u5047\u8bbe\u6211\u4eec\u6b63\u5728\u7814\u7a76\u4e00\u79cd\u65b0\u836f\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u3002\u6211\u4eec\u6709\u4e00\u4e2a\u5b9e\u9a8c\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u4e8610\u4e2a\u75c5\u4eba\uff0c\u5728\u7ed9\u4e88\u836f\u7269\u6cbb\u7597\u524d\u540e\uff0c\u6d4b\u91cf\u4e86\u4ed6\u4eec\u7684\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\u3002\u6b64\u5916\uff0c\u6bcf\u4e2a\u75c5\u4eba\u8fd8\u6709\u4e00\u4e9b\u57fa\u672c\u4fe1\u606f\uff0c\u5982\u6027\u522b\u548c\u5e74\u9f84\u3002\u6211\u4eec\u60f3\u8981\u786e\u5b9a\u836f\u7269\u662f\u5426\u5bf9\u57fa\u56e0\u8868\u8fbe\u4ea7\u751f\u663e\u8457\u5f71\u54cd\uff0c\u5e76\u4e14\u662f\u5426\u5b58\u5728\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u52a0\u8f7d\u6240\u9700\u7684\u5305\uff0c\u5e76\u5bfc\u5165\u6570\u636e\u96c6\u3002\u5047\u8bbe\u6211\u4eec\u7684\u6570\u636e\u96c6\u547d\u540d\u4e3a”gene_expression.csv”\uff0c\u5176\u4e2d\u5305\u542b\u4e86”PatientID”\uff08\u75c5\u4ebaID\uff09\u3001”Treatment”\uff08\u6cbb\u7597\u524d\u540e\uff09\u3001”GeneExpression”\uff08\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\uff09\u3001”Gender”\uff08\u6027\u522b\uff09\u548c”Age”\uff08\u5e74\u9f84\uff09\u7b49\u53d8\u91cf\u3002<\/span><span style=\"color: rgb(51, 51, 51);font-family: "Open Sans";font-size: 12pt;letter-spacing: 0.034em;\"><\/span><\/p>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\"># \u52a0\u8f7d\u6240\u9700\u7684\u5305<\/span><\/code><code><span class=\"code-snippet_outer\">> library(lme4)<\/span><\/code><code><span class=\"code-snippet_outer\">> library(pbkrtest)<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\"># \u5bfc\u5165\u6570\u636e\u96c6<\/span><\/code><code><span class=\"code-snippet_outer\">> data <- read.csv(\"gene_expression.csv\")<\/span><\/code><\/pre>\n<\/section>\n<\/section>\n<section style=\"text-align: justify;\" powered-by=\"xiumi.us\">\n<p><br \/><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u5176\u4e2d\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\u662f\u56e0\u53d8\u91cf\uff0c\u6cbb\u7597\u548c\u75c5\u4eba\u662f\u56fa\u5b9a\u6548\u5e94\uff0c\u800c\u75c5\u4eba\u662f\u968f\u673a\u6548\u5e94\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528lmer()\u51fd\u6570\u6765\u62df\u5408\u8be5\u6a21\u578b\u3002<\/span><\/p>\n<\/section>\n<section powered-by=\"xiumi.us\">\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"powershell\"><code><span class=\"code-snippet_outer\"># \u6784\u5efa\u6df7\u5408\u6548\u5e94\u6a21\u578b<\/span><\/code><code><span class=\"code-snippet_outer\">> model <- lmer(GeneExpression ~ Treatment + (1 | PatientID), data = data)<\/span><\/code><\/pre>\n<\/section>\n<p><br \/><\/p>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\">\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528pbkrtest\u5305\u63d0\u4f9b\u7684summary()\u51fd\u6570\u6765\u67e5\u770b\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\uff0c\u5305\u62ec\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u3002<\/span><\/p>\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\"># \u67e5\u770b\u6a21\u578b\u6458\u8981\u4fe1\u606f<\/span><\/code><code><span class=\"code-snippet_outer\">> summary(model)<\/span><\/code><\/pre>\n<\/section>\n<p><span style=\"font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;font-size: 14px;\"><br \/><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u8f93\u51fa\u7684\u6458\u8981\u4fe1\u606f\u5c06\u63d0\u4f9b\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u7b49\u7edf\u8ba1\u91cf\u3002\u901a\u8fc7\u68c0\u67e5\u56fa\u5b9a\u6548\u5e94\u7684p\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u6cbb\u7597\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u662f\u5426\u663e\u8457\u3002<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528anova()\u51fd\u6570\u6765\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002\u5047\u8bbe\u6211\u4eec\u8fd8\u60f3\u8003\u8651\u6027\u522b\u548c\u5e74\u9f84\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u5305\u542b\u8fd9\u4e9b\u53d8\u91cf\u7684\u6a21\u578b\uff0c\u5e76\u4f7f\u7528anova()\u51fd\u6570\u8fdb\u884c\u6bd4\u8f83\u3002<\/span><span style=\"mso-spacerun:'yes';font-family:Calibri;mso-fareast-font-family:\u5b8b\u4f53;mso-bidi-font-family:'Times New Roman';\"><o:p><\/o:p><\/span><\/p>\n<section class=\"code-snippet__fix code-snippet__js\">\n<ul class=\"code-snippet__line-index code-snippet__js\">\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<li><\/li>\n<\/ul>\n<pre class=\"code-snippet__js\" data-lang=\"shell\"><code><span class=\"code-snippet_outer\"># \u6784\u5efa\u5305\u542b\u6027\u522b\u548c\u5e74\u9f84\u7684\u6a21\u578b<\/span><\/code><code><span class=\"code-snippet_outer\">> model_full <- lmer(GeneExpression ~ Treatment + Gender + Age + (1 | PatientID), data = data)<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\"># \u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\u7684\u663e\u8457\u6027\u5dee\u5f02<\/span><\/code><code><span class=\"code-snippet_outer\">> anova(model, model_full)<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\">\u901a\u8fc7\u6bd4\u8f83\u6a21\u578b\u7684\u663e\u8457\u6027\u5dee\u5f02\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u662f\u5426\u6709\u5fc5\u8981\u5c06\u6027\u522b\u548c\u5e74\u9f84\u8003\u8651\u5728\u5185\u3002<\/span><\/code><code><span class=\"code-snippet_outer\"><br \/><\/span><\/code><code><span class=\"code-snippet_outer\">\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528pbkrtest\u5305\u6765\u5206\u6790\u751f\u7269\u4fe1\u606f\u76f8\u5173\u7684\u5b9e\u9645\u6570\u636e\u3002\u6211\u4eec\u6784\u5efa\u4e86\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u8003\u8651\u4e86\u6cbb\u7597\u548c\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\uff0c\u5e76\u4f7f\u7528summary()\u51fd\u6570\u67e5\u770b\u4e86\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u4f7f\u7528anova()\u51fd\u6570\u6bd4\u8f83\u4e86\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002\u901a\u8fc7\u8fd9\u4e9b\u5206\u6790\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u5173\u4e8e\u836f\u7269\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u4ee5\u53ca\u5176\u4ed6\u56e0\u7d20\u7684\u7ed3\u8bba\u3002<\/span><\/code><\/pre>\n<\/section>\n<p><br \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.5904486251808972\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/2_aI02Snqic1JnZGPAomXtPa3csaPnWw.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEmaOa5eqyuqaiarEhSggFLgIaEjaI02Snqic1JnZGPAomXtPa3csaPnWw\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"691\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.7147192716236722\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/3_iauibcz0Z6srzhhBfhanO360hPKQ5g.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEKkk460Eule1qPw8JXHw5cTQibP9iauibcz0Z6srzhhBfhanO360hPKQ5g\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"659\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"1\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/4_buRNUhOh9UMhFqcsvW3LPphfJSZZKw.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEuRYzyw57mPEmiaUFuCs6TD4YJbuRNUhOh9UMhFqcsvW3LPphfJSZZKw\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"667\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.7484177215189873\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/5_htZvVNPkiclibkcCDsMf1CwPK769rA.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkEylWk3zYaOlVzvHwvDgleibvzxI1htZvVNPkiclibkcCDsMf1CwPK769rA\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"632\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"rich_pages wxw-img\" data-galleryid=\"\" data-ratio=\"0.7514450867052023\" data-s=\"300,640\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/06\/6_OZ4Gqf3sYqib9h4nPO6mlmMtHXBDgQ.png?w=640\" onerror=\"this.src='https:\/\/mmbiz.qpic.cn\/sz_mmbiz_png\/zcicibWZessAztctFDciaTgXQTByLub6rkErC9cAlwK1rD1sawEQCJ24wvpgOZ4Gqf3sYqib9h4nPO6mlmMtHXBDgQ\/640?wx_fmt=png'\" data-type=\"png\" data-w=\"692\" style=\"\" data-recalc-dims=\"1\" \/><\/p>\n<p><br \/><\/p>\n<p><span style=\"font-size: 14px;\">\u4ee5\u4e0a\u5c31\u662f\u5bf9R\u8bed\u8a00\u5305pbkrtest\u7684\u7b80\u5355\u4ecb\u7ecd\u5566\uff0cpbkrtest\u5305\u4e3a\u7814\u7a76\u4eba\u5458\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u7528\u4e8e\u5728\u6df7\u5408\u6548\u5e94\u6a21\u578b\u4e2d\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u548c\u53c2\u6570\u4f30\u8ba1\u3002\u5b83\u80fd\u591f\u5904\u7406\u590d\u6742\u7684\u6570\u636e\u7ed3\u6784\u548c\u76f8\u5173\u6027\uff0c\u63d0\u4f9b\u51c6\u786e\u7684\u7edf\u8ba1\u63a8\u65ad\u7ed3\u679c\u3002\u901a\u8fc7\u4f7f\u7528pbkrtest\u5305\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u6570\u636e\uff0c\u5e76\u5f97\u51fa\u66f4\u53ef\u9760\u7684\u7ed3\u8bba\u3002<\/span><\/p>\n<p style=\"text-align: center;\"><br \/><\/p>\n<\/section>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><span style=\"font-size: 14px;color: rgb(0, 0, 0);\"><span style=\"font-size: 14px;\">\u5c0f\u4f19\u4f34\u4eec\uff0c\u4eca\u5929\u6709\u6ca1\u6709\u5b66\u5230\u65b0\u77e5\u8bc6\u5462\uff0c\u60f3\u8981\u7ee7\u7eed\u4e86\u89e3<\/span>R<span style=\"font-size: 14px;\">\u8bed\u8a00\u5185\u5bb9\u53ef\u4ee5\u6301\u7eed\u5173\u6ce8\u5c0f\u679c\u54e6\uff5e\uff5e\u6216\u8005\u4e5f\u53ef\u4ee5\u5173\u6ce8\u6211\u4eec\u7684\u5b98\u7f51\u4e5f\u4f1a\u6301\u7eed\u66f4\u65b0<\/span><\/span><span style=\"font-size: 14px;color: rgb(0, 0, 0);\"><span style=\"font-size: 14px;\">\u7684\u54e6\uff5e<\/span> <\/span><\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">http:\/\/www.biocloudservice.com\/home.html<\/span><span style=\"color: rgb(0, 0, 0);font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><br \/><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">References:<o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">1.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/ourcodingclub.github.io\/tutorials\/mixed-models\/<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">2.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/terpconnect.umd.edu\/~egurarie\/teaching\/Biol709\/Topic3\/Lecture16_MixedEffectsModels.html<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">3.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/stackoverflow.com\/questions\/40546716\/plotting-mixed-models-regression-coefficients-in-r<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">4.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">http:\/\/www.analyticsforfun.com\/2014\/06\/performing-anova-test-in-r-results-and.html<\/span><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\"><o:p><\/o:p><\/span><\/p>\n<p><span style=\"font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">5.<\/span><span style=\"color: rgb(0, 0, 255);text-decoration: underline;font-size: 14px;font-family: "Helvetica Neue", Helvetica, "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif;\">https:\/\/www.scribbr.com\/statistics\/anova-in-r\/<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"letter-spacing: 0.034em;text-align: left;\"><\/span><\/p>\n<section powered-by=\"xiumi.us\">\n<p><span style=\"color: rgb(217, 33, 66);font-size: 10.5pt;font-family: \u5fae\u8f6f\u96c5\u9ed1;\">\u5176\u4ed6\u76f8\u5173\u5206\u6790\u5185\u5bb9\uff0c\u4f8b\u5982\u9884\u6d4b\u80bf\u7624\u6837\u672c\u836f\u7269\u654f\u611f\u6027\u5206\u6790(http:\/\/www.biocloudservice.com\/712\/712.php),\u9884\u6d4b\u67d0\u6837\u672c\u4e9a\u578b\u5bf9\u514d\u75ab\u6cbb\u7597\u7684\u53cd\u5e94(http:\/\/www.biocloudservice.com\/292\/292.php)\uff0c\u5355\u6837\u672c\u5bcc\u96c6\u7b97\u6cd5\u5206\u6790\u514d\u75ab\u6d78\u6da6\u4e30\u5ea6(http:\/\/www.biocloudservice.com\/106\/106.php)\uff0c\u8ba1\u7b9764\u79cd\u514d\u75ab\u7ec6\u80de\u76f8\u5bf9\u542b\u91cf(http:\/\/www.biocloudservice.com\/107\/107.php)\u7b49\u90fd\u53ef\u4ee5\u7528\u672c\u516c\u53f8\u65b0\u5f00\u53d1\u7684\u96f6\u4ee3\u7801\u4e91\u5e73\u53f0\u751f\u4fe1\u5206\u6790\u5c0f\u5de5\u5177\uff0c\u4e00\u952e\u5b8c\u6210\u8be5\u5206\u6790\u5965\uff0c\u611f\u5174\u8da3\u7684\u5c0f\u4f19\u4f34\u6b22\u8fce\u6765\u5c1d\u8bd5\u5965\uff0c\u7f51\u5740\uff1ahttp:\/\/www.biocloudservice.com\/home.html\u3002<\/span><span style=\"mso-spacerun:"yes";font-family:\u5fae\u8f6f\u96c5\u9ed1;font-size:10.5000pt;mso-font-kerning:1.0000pt;\">\u4eca\u5929\u5c0f\u679c\u7684\u5206\u4eab\u5c31\u5230\u8fd9\u91cc\uff0c\u4e0b\u671f\u5728\u89c1\u5965\u3002<\/span><\/p>\n<p style=\"margin-bottom: 0px;outline: 0px;white-space: normal;\"><span style=\"outline: 0px;font-size: var(--articleFontsize);letter-spacing: 0.034em;\"><\/span><\/p>\n<section data-mpa-powered-by=\"yiban.io\" style=\"margin-bottom: 0px;outline: 0px;letter-spacing: 0.578px;visibility: visible;\">\n<section style=\"outline: 0px;visibility: visible;\">\n<section style=\"outline: 0px;visibility: visible;\">\n<section style=\"outline: 0px;visibility: visible;\">\n<section style=\"outline: 0px;visibility: visible;\">\n<section style=\"outline: 0px;visibility: visible;\">\n<section data-role=\"list\" style=\"outline: 0px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;visibility: visible;\">\n<section style=\"outline: 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style=\"outline: 0px;text-align: justify;\">\n<p style=\"outline: 0px;\"><br style=\"outline: 0px;\" \/><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"outline: 0px;display: inline-block;vertical-align: top;width: auto;align-self: flex-start;flex: 0 0 auto;min-width: 5%;height: auto;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;text-align: center;\">\n<section style=\"outline: 0px;display: inline-block;width: 6px;height: 6px;vertical-align: top;overflow: hidden;border-radius: 230px;background-color: rgb(217, 217, 217);\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;text-align: justify;\">\n<p style=\"outline: 0px;\"><br style=\"outline: 0px;\" \/><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-bottom: 10px;outline: 0px;text-align: left;justify-content: flex-start;display: flex;flex-flow: row nowrap;\">\n<section style=\"padding: 14px 10px;outline: 0px;display: inline-block;width: 647px;vertical-align: top;align-self: flex-start;flex: 0 0 auto;border-style: solid;border-width: 1px;border-color: rgb(217, 217, 217);\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 15px;outline: 0px;justify-content: flex-start;display: flex;flex-flow: row nowrap;\">\n<section style=\"padding-left: 9px;outline: 0px;display: inline-block;width: 625px;vertical-align: top;align-self: flex-start;flex: 0 0 auto;border-style: solid;border-width: 0px 0px 0px 12px;border-left-color: rgb(212, 32, 2);\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;text-align: justify;font-size: 17px;color: rgb(62, 62, 62);\">\n<p style=\"outline: 0px;\"><strong style=\"outline: 0px;\">\u5c0f\u679c\u53cb\u60c5\u63a8\u8350<\/strong><\/p>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 3px;outline: 0px;\">\n<section style=\"outline: 0px;background-color: rgb(217, 217, 217);height: 1px;\"><svg viewbox=\"0 0 1 1\" 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