{"id":508,"date":"2018-08-24T20:21:52","date_gmt":"2018-08-24T11:21:52","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-for-inter-rater-reliability-icc-case2\/"},"modified":"2025-05-06T21:33:42","modified_gmt":"2025-05-06T12:33:42","slug":"how-to-determine-sample-size-for-inter-rater-reliability-icc-case2","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-for-inter-rater-reliability-icc-case2\/","title":{"rendered":"R \u3067\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(2,1) \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3068\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC Case2 \u306e\u8a08\u7b97\u3068\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092 R \u3067\u3084\u3063\u3066\u307f\u305f<\/p>\n\n\n\n\n\n\n\n

\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(2,1) \u306e\u8a08\u7b97\u4f8b<\/h2>\n\n\n\n

\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 Intra-class Correlation Coefficient Case2 ICC Case2 \u306f\u691c\u8005\u9593\u4fe1\u983c\u6027\u306e\u6307\u6a19\u3002<\/p>\n\n\n\n

\u60a3\u8005\u3055\u3093\u3092\u6570\u540d\u306e\u691c\u67fb\u8005\uff08\u307e\u305f\u306f\u8a55\u4fa1\u8005\uff09\u3067\u691c\u67fb\uff08\u307e\u305f\u306f\u8a55\u4fa1\uff09\u3057\u3066\u3001\u305d\u306e\u6e2c\u5b9a\u5024\u306e\u4e00\u81f4\u6027\u3092\u898b\u308b\u306e\u304c\u4e3b\u76ee\u7684\u3002<\/p>\n\n\n\n

\u8907\u6570\u306e\u691c\u67fb\u8005\u304c\u5404\u60a3\u8005\u3055\u3093 1 \u56de\u305a\u3064\u691c\u67fb\u30fb\u8a55\u4fa1\u3057\u305f\u5834\u5408\u306e ICC(2,1) \u304c\u826f\u304f\u7528\u3044\u3089\u308c\u308b\u3002<\/p>\n\n\n\n

9\u4eba\u306e\u60a3\u8005\u3055\u3093\u3092A\uff5eE\u306e5\u4eba\u306e\u691c\u67fb\u8005\u30671\u56de\u305a\u3064\u691c\u67fb\u3057\u305f\u6642<\/h3>\n\n\n\n

irr\u30d1\u30c3\u30b1\u30fc\u30b8\u306eicc()\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n

\u6700\u521d\u4e00\u56de\u3060\u3051\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u3002<\/p>\n\n\n\n

install.packages<\/span>(<\/span>\"irr\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u30c7\u30fc\u30bf\u62dd\u501f\u5143\uff1a\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570\uff5c\u7d71\u8a08\u89e3\u6790\u30bd\u30d5\u30c8 \u30a8\u30af\u30bb\u30eb\u7d71\u8a08<\/a><\/p>\n\n\n\n
A <-<\/span> c<\/span>(<\/span>0<\/span>,<\/span>2<\/span>,<\/span>2<\/span>,<\/span>1<\/span>,<\/span>3<\/span>,<\/span>0<\/span>,<\/span>4<\/span>,<\/span>4<\/span>,<\/span>6<\/span>)<\/span>\nB <-<\/span> c<\/span>(<\/span>0<\/span>,<\/span>4<\/span>,<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>1<\/span>,<\/span>5<\/span>,<\/span>4<\/span>,<\/span>6<\/span>)<\/span>\nC <-<\/span> c<\/span>(<\/span>0<\/span>,<\/span>2<\/span>,<\/span>0<\/span>,<\/span>0<\/span>,<\/span>3<\/span>,<\/span>0<\/span>,<\/span>4<\/span>,<\/span>4<\/span>,<\/span>6<\/span>)<\/span>\nD <-<\/span> c<\/span>(<\/span>0<\/span>,<\/span>2<\/span>,<\/span>2<\/span>,<\/span>1<\/span>,<\/span>3<\/span>,<\/span>0<\/span>,<\/span>4<\/span>,<\/span>5<\/span>,<\/span>4<\/span>)<\/span>\nE <-<\/span> c<\/span>(<\/span>0<\/span>,<\/span>3<\/span>,<\/span>2<\/span>,<\/span>1<\/span>,<\/span>3<\/span>,<\/span>0<\/span>,<\/span>4<\/span>,<\/span>4<\/span>,<\/span>6<\/span>)<\/span>\ndat.twoway <-<\/span> cbind<\/span>(<\/span>A,<\/span>B,<\/span>C,<\/span>D,<\/span>E)<\/span>\nrownames<\/span>(<\/span>dat.twoway)<\/span> <-<\/span> c<\/span>(<\/span>1<\/span>:<\/span>9<\/span>)<\/span>\nprint(dat.twoway)\nlibrary<\/span>(<\/span>irr)<\/span>\nicc<\/span>(<\/span>dat.twoway,<\/span> model=<\/span>\"twoway\"<\/span>,<\/span> type=<\/span>\"agreement\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u8aad\u307f\u8fbc\u3093\u3060\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b<\/p>\n\n\n\n
> print(dat.twoway)\n  A B C D E\n1 0 0 0 0 0\n2 2 4 2 2 3\n3 2 1 0 2 2\n4 1 2 0 1 1\n5 3 3 3 3 3\n6 0 1 0 0 0\n7 4 5 4 4 4\n8 4 4 4 5 4\n9 6 6 6 4 6<\/code><\/pre>\n\n\n\n
ICC(2,1) \u306e\u8a08\u7b97\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
> icc(dat.twoway, model=\"twoway\", type=\"agreement\")\n Single Score Intraclass Correlation\n\n   Model: twoway \n   Type : agreement \n\n   Subjects = 9 \n     Raters = 5 \n   ICC(A,1) = 0.906\n\n F-Test, H0: r0 = 0 ; H1: r0 > 0 \n  F(8,32.8) = 55.6 , p = 6.98e-17 \n\n 95%-Confidence Interval for ICC Population Values:\n  0.783 < ICC < 0.974<\/code><\/pre>\n\n\n\n
ICC(2,1)\u306f\u30010.906\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
\u9ad8\u3044\u4e00\u81f4\u5ea6\u3060\u3002<\/p>\n\n\n\n
\u60a3\u8005\u3055\u309310\u4eba\u3092A\uff5eD\u306e4\u4eba\u306e\u691c\u67fb\u8005\u3067\u819d\u95a2\u7bc0\u5c48\u66f2\u53ef\u52d5\u57df\u3092\u691c\u67fb\u3057\u305f\u6642<\/h3>\n\n\n\n
\u5225\u306e\u30c7\u30fc\u30bf\u3067ICC(2,1)\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u60a3\u8005\u3055\u309310\u4eba\u3001A\uff5eD\u306e4\u4eba\u306e\u691c\u67fb\u8005\u3067\u3001\u819d\u95a2\u7bc0\u5c48\u66f2\u53ef\u52d5\u57df\u3092\u691c\u67fb\u3057\u305f\u30c7\u30fc\u30bf\u3060\u3002<\/p>\n\n\n\n
\u30c7\u30fc\u30bf\u62dd\u501f\u5143\uff1a\u4fe1\u983c\u6027\u6307\u6a19\u3068\u3057\u3066\u306e\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570<\/a><\/p>\n\n\n\n
A <-<\/span> c<\/span>(<\/span>126<\/span>,<\/span>137<\/span>,<\/span>113<\/span>,<\/span>153<\/span>,<\/span>146<\/span>,<\/span>161<\/span>,<\/span>110<\/span>,<\/span>145<\/span>,<\/span>126<\/span>,<\/span>114<\/span>)<\/span>\nB <-<\/span> c<\/span>(<\/span>122<\/span>,<\/span>143<\/span>,<\/span>119<\/span>,<\/span>143<\/span>,<\/span>157<\/span>,<\/span>157<\/span>,<\/span>109<\/span>,<\/span>151<\/span>,<\/span>141<\/span>,<\/span>126<\/span>)<\/span>\nC <-<\/span> c<\/span>(<\/span>131<\/span>,<\/span>141<\/span>,<\/span>115<\/span>,<\/span>135<\/span>,<\/span>150<\/span>,<\/span>160<\/span>,<\/span>105<\/span>,<\/span>152<\/span>,<\/span>132<\/span>,<\/span>130<\/span>)<\/span>\nD <-<\/span> c<\/span>(<\/span>125<\/span>,<\/span>141<\/span>,<\/span>105<\/span>,<\/span>144<\/span>,<\/span>149<\/span>,<\/span>160<\/span>,<\/span>113<\/span>,<\/span>156<\/span>,<\/span>122<\/span>,<\/span>125<\/span>)<\/span>\ndat.twoway <-<\/span> cbind<\/span>(<\/span>A,<\/span>B,<\/span>C,<\/span>D)<\/span>\nrownames<\/span>(<\/span>dat.twoway)<\/span> <-<\/span> c<\/span>(<\/span>1<\/span>:<\/span>10<\/span>)<\/span>\nprint(dat.twoway)\nicc<\/span>(<\/span>dat.twoway,<\/span> model=<\/span>\"twoway\"<\/span>,<\/span> type=<\/span>\"agreement\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u611f\u3058\u306b\u306a\u308b<\/p>\n\n\n\n
> print(dat.twoway)\n     A   B   C   D\n1  126 122 131 125\n2  137 143 141 141\n3  113 119 115 105\n4  153 143 135 144\n5  146 157 150 149\n6  161 157 160 160\n7  110 109 105 113\n8  145 151 152 156\n9  126 141 132 122\n10 114 126 130 125<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
> icc(dat.twoway, model=\"twoway\", type=\"agreement\")\n Single Score Intraclass Correlation\n\n   Model: twoway \n   Type : agreement \n\n   Subjects = 10 \n     Raters = 4 \n   ICC(A,1) = 0.909\n\n F-Test, H0: r0 = 0 ; H1: r0 > 0 \n    F(9,30) = 40.4 , p = 2.46e-14 \n\n 95%-Confidence Interval for ICC Population Values:\n  0.788 < ICC < 0.973<\/code><\/pre>\n\n\n\n
ICC(2,1)\u306f0.909\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
\u3053\u3061\u3089\u3082\u4e00\u81f4\u5ea6\u304c\u9ad8\u3044\u3002<\/p>\n\n\n\n
irr\u30d1\u30c3\u30b1\u30fc\u30b8\u306eanxiety\u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u305f\u4f8b<\/h3>\n\n\n\n
20\u4eba\u306e\u60a3\u8005\u3055\u3093\u30923\u4eba\u306e\u8a55\u4fa1\u8005\u304c\u8a55\u4fa1\u3057\u305f\u7d50\u679c\u306eICC\u3002<\/p>\n\n\n\n
data(<\/span>anxiety)<\/span>\nprint(anxiety)\nicc(<\/span>anxiety,<\/span> model=\"twoway\",<\/span> type=\"agreement\")<\/span>\n<\/code><\/pre>\n\n\n\n
anxiety \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a<\/p>\n\n\n\n
> print(anxiety)\n   rater1 rater2 rater3\n1       3      3      2\n2       3      6      1\n3       3      4      4\n4       4      6      4\n5       5      2      3\n6       5      4      2\n7       2      2      1\n8       3      4      6\n9       5      3      1\n10      2      3      1\n11      2      2      1\n12      6      3      2\n13      1      3      3\n14      5      3      3\n15      2      2      1\n16      2      2      1\n17      1      1      3\n18      2      3      3\n19      4      3      2\n20      3      4      2<\/code><\/pre>\n\n\n\n
ICC(2,1)\u306f0.198\u3068\u304b\u306a\u308a\u4f4e\u3044\u4e00\u81f4\u5ea6\u3002<\/p>\n\n\n\n
> icc(anxiety, model=\"twoway\", type=\"agreement\")\n Single Score Intraclass Correlation\n\n   Model: twoway \n   Type : agreement \n\n   Subjects = 20 \n     Raters = 3 \n   ICC(A,1) = 0.198\n\n F-Test, H0: r0 = 0 ; H1: r0 > 0 \n F(19,39.7) = 1.83 , p = 0.0543 \n\n 95%-Confidence Interval for ICC Population Values:\n  -0.039 < ICC 8< 0.494<\/code><\/pre>\n\n\n\n
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(2,1) \u306e\u89e3\u91c8<\/h2>\n\n\n\n
\u4e00\u3064\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u57fa\u6e96\u304c\u3042\u308b\u306e\u3067\u53c2\u7167\u3055\u308c\u305f\u3044<\/p>\n\n\n\n
ICC<\/td>\u89e3\u91c8<\/td><\/tr>
< 0.5<\/td>Poor<\/td><\/tr>
0.5 – < 0.75<\/td>Moderate<\/td><\/tr>
0.75 – < 0.9<\/td>Good<\/td><\/tr>
>= 0.9<\/td>Excellent<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u51fa\u5178\uff1aA Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research<\/a><\/p>\n\n\n\n
\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>\r\n
\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(2,1) \u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97<\/h2>\n\n\n\n
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(2,1) \u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3069\u3046\u3084\u308b\u306e\u3060\u308d\u3046\u304b\uff1f<\/p>\n\n\n\n
\u53c2\u8003\u6587\u732e\u3000Doros G. and Lew R. Design Based on Intra-Class Correlation Coefficients. Am J Biostatistics 2010: 1 (1); 1-8.<\/a>\u306b\u8a08\u7b97\u7d50\u679c\u304c\u63b2\u8f09\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u691c\u67fb\u8005\u304c3\u4eba\u30015\u4eba\u30017\u4eba\u300110\u4eba\u306e\u3068\u304d\u3001\u4fe1\u983c\u533a\u9593\u5168\u4f53\u306e\u5e73\u5747\u5e45 $ \\Delta $ \u304c0.2\u30010.3\u30010.4\u306e\u3068\u304d\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u4fe1\u983c\u533a\u9593\u306e\u6709\u610f\u6c34\u6e96\u304c10%\uff08$ \\alpha $ = 0.1\uff09\u306e\u3068\u304d\u30685%\uff08$ \\alpha $ = 0.05\uff09\u306e\u6642\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
ICC(2,1)\u306e\u63a8\u5b9a\u5024 $ \\rho $ \u304c0.6\u30010.7\u30010.8\u306e\u3068\u304d\u304c\u305d\u308c\u305e\u308c\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u4f8b\u3048\u3070\u3001\u691c\u67fb\u8005\u304c3\u4eba(k=3)\u3067\u3001\u4fe1\u983c\u533a\u9593\u5e45\u304c0.4\u3067\u63a8\u5b9a\u3057\u305f\u3044\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u6709\u610f\u6c34\u6e965%\u3064\u307e\u308a95%\u4fe1\u983c\u533a\u9593\u3067\u63a8\u5b9a\u3059\u308b\u3068\u3057\u3066\u3001$ \\rho $ \u304c 0.8 \u3068\u63a8\u5b9a\u3055\u308c\u308b\u3068\u3059\u308b\u3068\u3001\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff08\u60a3\u8005\u3055\u3093\u306e\u4eba\u6570\uff09\u306f14\u4eba\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n\n\n\n\n
\u53c2\u8003\u6587\u732e\u306b\u306f\u30b9\u30af\u30ea\u30d7\u30c8\u306e\u8acb\u6c42\u304c\u53ef\u80fd\u3068\u66f8\u3044\u3066\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
\u8ad6\u6587\u306b\u63b2\u8f09\u3055\u308c\u3066\u3044\u306a\u3044\u6570\u5024\u306b\u95a2\u3057\u3066\u306f\u3001\u5404\u81ea\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u53d6\u308a\u5bc4\u305b\u3066\u3001\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u78ba\u8a8d\u306e\u4e0a\u3001\u8a08\u7b97\u3057\u3066\u3082\u3089\u3044\u305f\u3044\u3002<\/p>\n\n\n\n
\u8a08\u7b97\u306b\u304a\u3051\u308b\u6ce8\u610f\u70b9<\/h3>\n\n\n\n
\u5b9f\u969b\u306e\u8a08\u7b97\u306b\u306f\u3001variance ratio $ \\sigma_T^2 \/ \\sigma_E^2 $ \u3001\u60f3\u5b9a\u3059\u308b ICC(2,1) \u306e\u5024 $ \\rho $ \u304c\u5fc5\u8981\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
$ \\rho $ \u3068 variance ratio \u306b\u306f\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
$$ \\rho = \\frac{\\sigma_T^2 \/ \\sigma_E^2} {\\sigma_T^2 \/ \\sigma_E^2 + \\sigma_J^2 \/ \\sigma_E^2 + 1} $$<\/p>\n\n\n\n\n\n\n\n
\u3053\u3053\u3067\u3001<\/p>\n\n\n\n