{"id":433,"date":"2019-08-03T23:11:41","date_gmt":"2019-08-03T14:11:41","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/log-rank-test-in-r\/"},"modified":"2024-10-07T12:43:35","modified_gmt":"2024-10-07T03:43:35","slug":"log-rank-test-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/log-rank-test-in-r\/","title":{"rendered":"R \u3067\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u884c\u3046\u65b9\u6cd5"},"content":{"rendered":"\n

\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3068\u306f\u3001\u751f\u5b58\u6642\u9593\u89e3\u6790\u3067\u3001\u4e8c\u7fa4\u4ee5\u4e0a\u306e\u30b0\u30eb\u30fc\u30d7\u304c\u3042\u308b\u5834\u5408\u306b\u3001\u30b0\u30eb\u30fc\u30d7\u9593\u3067\u7d71\u8a08\u5b66\u7684\u306b\u5dee\u304c\u3042\u308b\u304b\u3092\u691c\u8a0e\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n

R \u3067\u306e\u65b9\u6cd5\u3092\u89e3\u8aac\u3002<\/p>\n\n\n\n\n\n\n\n

R \u3067\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u3059\u308b\u5834\u5408\u306e\u95a2\u6570\u306f\uff1f<\/h2>\n\n\n\n

R \u3067\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u3059\u308b\u5834\u5408\u3001survival \u30d1\u30c3\u30b1\u30fc\u30b8\u306esurvdiff()\u95a2\u6570\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n

survival \u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u6700\u521d\u304b\u3089\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b\u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u3001\u4f7f\u3046\u3068\u304d\u306blibrary()\u3067\u547c\u3073\u51fa\u3059\u3002<\/p>\n\n\n\n

library<\/span>(<\/span>survival)<\/span>\n<\/code><\/pre>\n\n\n\n
survdiff()\u306f\u3069\u3046\u3084\u3063\u3066\u4f7f\u3046\uff1f<\/h2>\n\n\n\n
survdiff()\u306f\u3001Surv()\u3068\u7d44\u307f\u5408\u308f\u305b\u3066\u4f7f\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
Surv()\u306f\u3001\u751f\u5b58\u6642\u9593\u30c7\u30fc\u30bf\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u3001\u751f\u5b58\u6642\u9593\u89e3\u6790\u306b\u4f7f\u3048\u308b\u30c7\u30fc\u30bf\u306b\u5909\u63db\u3059\u308b\u95a2\u6570\u3002<\/p>\n\n\n\n
Surv()\u306b\u3064\u3044\u3066\u306f\u3001\u3053\u3061\u3089\u3082\u53c2\u7167\u3002<\/p>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u3067\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u30b0\u30eb\u30fc\u30d7\u3054\u3068\u306b\u66f8\u304f\u65b9\u6cd5<\/a>\n\t\t\t\t\t\tR\u3067\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u66f8\u304f\u65b9\u6cd5\u306e\u7d39\u4ecb\u3002 survfit \u3092\u4f7f\u3063\u305f\u30b0\u30eb\u30fc\u30d7\u3054\u3068\u306e\u66f2\u7dda\u306e\u66f8\u304d\u65b9\u3002 R\u3067\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u66f8\u304f\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf \u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n
survdiff(Surv(\u6642\u9593\u30c7\u30fc\u30bf, \u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf) ~ \u30b0\u30eb\u30fc\u30d7\u5909\u6570)<\/p>\n\n\n\n
\u3068\u3044\u3046\u5f62\u304c\u57fa\u672c\u5f62\u3002<\/p>\n\n\n\n
survival \u30d1\u30c3\u30b1\u30fc\u30b8\u306e ovarian \u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u3001\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
ovarian \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f\u3001\u5375\u5de3\u304c\u3093\u306e\u6cbb\u7642\u3092\u3001\u4e8c\u7a2e\u985e\u306e\u6cbb\u7642\u6cd5\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u632f\u308a\u5206\u3051\u305f\u6642\u306e\u8a66\u9a13\u7d50\u679c\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n
futime\u304c\u751f\u5b58\u6642\u9593\u30c7\u30fc\u30bf\u3001fustat\u304c\u6253\u3061\u5207\u308a\u304b\u3001\u6b7b\u4ea1\u304b\u3001rx\u306f\u4e8c\u3064\u306e\u6cbb\u7642\u6cd5\u306e\u3069\u3061\u3089\u3092\u53d7\u3051\u305f\u304b\u3092\u8868\u3059\u5909\u6570\u3002<\/p>\n\n\n\n
ovarian \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5185\u5bb9<\/h3>\n\n\n\n
ovarian \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5148\u982d\u90e8\u5206\u3092\u8868\u793a\u3057\u3066\u307f\u308b\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002futime\u306f\u65e5\u6570\u3002<\/p>\n\n\n\n
><\/span> head<\/span>(<\/span>ovarian)<\/span>\nfutime fustat     age resid.ds rx ecog.ps\n1<\/span>     59<\/span>      1<\/span> 72.3315<\/span>        2<\/span>  1<\/span>       1<\/span>\n2<\/span>    115<\/span>      1<\/span> 74.4932<\/span>        2<\/span>  1<\/span>       1<\/span>\n3<\/span>    156<\/span>      1<\/span> 66.4658<\/span>        2<\/span>  1<\/span>       2<\/span>\n4<\/span>    421<\/span>      0<\/span> 53.3644<\/span>        2<\/span>  2<\/span>       1<\/span>\n5<\/span>    431<\/span>      1<\/span> 50.3397<\/span>        2<\/span>  1<\/span>       1<\/span>\n6<\/span>    448<\/span>      0<\/span> 56.4301<\/span>        1<\/span>  1<\/span>       2<\/span>\n<\/code><\/pre>\n\n\n\n
\u751f\u5b58\u6642\u9593\u30c7\u30fc\u30bf\u3068\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u3092Surv()\u3057\u3066\u307f\u308b<\/h3>\n\n\n\n
\u307e\u305aSurv()\u3092\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
><\/span> Surv<\/span>(<\/span>ovarian$<\/span>futime,<\/span>ovarian$<\/span>fustat)<\/span>\n[<\/span>1<\/span>]<\/span>   59<\/span>   115<\/span>   156<\/span>   421<\/span>+<\/span>  431<\/span>   448<\/span>+<\/span>  464<\/span>   475<\/span>   477<\/span>+<\/span>  563<\/span>\n[<\/span>11<\/span>]<\/span>  638<\/span>   744<\/span>+<\/span>  769<\/span>+<\/span>  770<\/span>+<\/span>  803<\/span>+<\/span>  855<\/span>+<\/span> 1040<\/span>+<\/span> 1106<\/span>+<\/span> 1129<\/span>+<\/span> 1206<\/span>+<\/span>\n[<\/span>21<\/span>]<\/span> 1227<\/span>+<\/span>  268<\/span>   329<\/span>   353<\/span>   365<\/span>   377<\/span>+<\/span>\n<\/code><\/pre>\n\n\n\n
\u6570\u5024\u306f\u751f\u5b58\u65e5\u6570\u3067\u3001\uff0b\u304c\u3064\u3044\u3066\u3044\u308b\u65e5\u6570\u306f\u89b3\u5bdf\u6253\u3061\u5207\u308a\u306e\u65e5\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u305d\u306e\u65e5\u6570\u307e\u3067\u306f\u751f\u304d\u3066\u3044\u305f\u3053\u3068\u306f\u308f\u304b\u308b\u304c\u3001\u305d\u308c\u4ee5\u964d\u306e\u60c5\u5831\u304c\u306a\u3044\u3068\u3044\u3046\u610f\u5473\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u3053\u308c\u3092\u6253\u3061\u5207\u308a\uff08censoring\u3001censored\u3001\u30bb\u30f3\u30b5\u30ea\u30f3\u30b0\u3001\u30bb\u30f3\u30b5\u30fc\u30c9\uff09\u30c7\u30fc\u30bf\u3068\u547c\u3076\u3002<\/p>\n\n\n\n
survfit()\u3067\u30b0\u30eb\u30fc\u30d7\u3054\u3068\u306e\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u63cf\u3044\u3066\u307f\u308b<\/h3>\n\n\n\n
\u691c\u5b9a\u306e\u524d\u306b\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3067\u56f3\u793a\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u4e8c\u7a2e\u985e\u306e\u6cbb\u7642\u3067\u3069\u306e\u304f\u3089\u3044\u7570\u306a\u308b\u306e\u304b\u3001\u751f\u5b58\u66f2\u7dda\u3092\u66f8\u3044\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
survfit1 <-<\/span> survfit<\/span>(<\/span>Surv<\/span>(<\/span>futime,<\/span>fustat)<\/span>~<\/span>rx,<\/span> data=<\/span>ovarian)<\/span>\nplot<\/span>(<\/span>survfit1,<\/span>las=<\/span>1<\/span>,<\/span>xlab=<\/span>\"Survival Time (days)\"<\/span>,<\/span> ylab=<\/span>\"Overall Survival\"<\/span>,<\/span> col=<\/span>2<\/span>:<\/span>3<\/span>)<\/span>\nlegend<\/span>(<\/span>\"topright\"<\/span>,<\/span> paste<\/span>(<\/span>\"Treatment=\"<\/span>,<\/span>1<\/span>:<\/span>2<\/span>,<\/span>sep=<\/span>\"\"<\/span>),<\/span> lty=<\/span>1<\/span>,<\/span> col=<\/span>2<\/span>:<\/span>3<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
Treatment1\u3088\u308a\u30822\u306e\u307b\u3046\u304c\u751f\u5b58\u78ba\u7387\u304c\u9ad8\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u7d71\u8a08\u5b66\u7684\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u306e\u304b\u3069\u3046\u304b\u6c17\u306b\u306a\u308b\u3068\u3053\u308d\u3060\u3002<\/p>\n\n\n\n
survdiff()\u3067\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u3057\u3066\u307f\u308b<\/h3>\n\n\n\n
survdiff()\u3092\u4f7f\u3063\u3066\u3001\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
><\/span> survdiff<\/span>(<\/span>Surv<\/span>(<\/span>futime,<\/span>fustat)<\/span> ~<\/span> rx,<\/span> data=<\/span>ovarian)<\/span>\nCall:<\/span>\nsurvdiff<\/span>(<\/span>formula =<\/span> Surv<\/span>(<\/span>futime,<\/span> fustat)<\/span> ~<\/span> rx,<\/span> data =<\/span> ovarian)<\/span>\nN Observed Expected <\/span>(<\/span>O-<\/span>E)<\/span>^<\/span>2<\/span>\/<\/span>E <\/span>(<\/span>O-<\/span>E)<\/span>^<\/span>2<\/span>\/<\/span>V\nrx=<\/span>1<\/span> 13<\/span>        7<\/span>     5.23<\/span>     0.596<\/span>      1.06<\/span>\nrx=<\/span>2<\/span> 13<\/span>        5<\/span>     6.77<\/span>     0.461<\/span>      1.06<\/span>\nChisq=<\/span> 1.1<\/span>  on 1<\/span> degrees of freedom,<\/span> p=<\/span> 0.3<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u3068\u3057\u3066\u3001p=0.3\u3067\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u306f\u306a\u3044\u3002<\/p>\n\n\n\n
\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306e\u554f\u984c\u304b\u3001effect size\u306e\u554f\u984c\u304b\u306f\u4e0d\u660e\u3060\u304c\u3001\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3067\u306f\u5dee\u304c\u3042\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3060\u3051\u306b\u60dc\u3057\u3044\u6c17\u304c\u3059\u308b\u3002<\/p>\n\n\n\n
\u4e09\u7fa4\u4ee5\u4e0a\u306e\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a<\/h3>\n\n\n\n
\u3068\u3053\u308d\u3067\u3001survival \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u80ba\u304c\u3093\u30c7\u30fc\u30bf\u3067ECOG performance score\uff08\u56db\u7fa4\uff09\u306e\u5dee\u3092\u691c\u5b9a\u3057\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u80ba\u304c\u3093\u30c7\u30fc\u30bf\u306e\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u306b\u3064\u3044\u3066\u306f\u3053\u3061\u3089\u3092\u53c2\u7167\u3002<\/p>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u3067\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u30b0\u30eb\u30fc\u30d7\u3054\u3068\u306b\u66f8\u304f\u65b9\u6cd5<\/a>\n\t\t\t\t\t\tR\u3067\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u66f8\u304f\u65b9\u6cd5\u306e\u7d39\u4ecb\u3002 survfit \u3092\u4f7f\u3063\u305f\u30b0\u30eb\u30fc\u30d7\u3054\u3068\u306e\u66f2\u7dda\u306e\u66f8\u304d\u65b9\u3002 R\u3067\u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda\u3092\u66f8\u304f\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf \u30ab\u30d7\u30e9\u30f3\u30de\u30a4\u30e4\u30fc\u66f2\u7dda…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n
><\/span> survdiff<\/span>(<\/span>Surv<\/span>(<\/span>time,<\/span>status)<\/span>~<\/span>ph.ecog,<\/span> data=<\/span>lung)<\/span>\nCall:<\/span>\nsurvdiff<\/span>(<\/span>formula =<\/span> Surv<\/span>(<\/span>time,<\/span> status)<\/span> ~<\/span> ph.ecog,<\/span> data =<\/span> lung)<\/span>\nn=<\/span>227<\/span>,<\/span> 1<\/span> observation deleted due to missingness.\nN Observed Expected <\/span>(<\/span>O-<\/span>E)<\/span>^<\/span>2<\/span>\/<\/span>E <\/span>(<\/span>O-<\/span>E)<\/span>^<\/span>2<\/span>\/<\/span>V\nph.ecog=<\/span>0<\/span>  63<\/span>       37<\/span>   54.153<\/span>    5.4331<\/span>    8.2119<\/span>\nph.ecog=<\/span>1<\/span> 113<\/span>       82<\/span>   83.528<\/span>    0.0279<\/span>    0.0573<\/span>\nph.ecog=<\/span>2<\/span>  50<\/span>       44<\/span>   26.147<\/span>   12.1893<\/span>   14.6491<\/span>\nph.ecog=<\/span>3<\/span>   1<\/span>        1<\/span>    0.172<\/span>    3.9733<\/span>    4.0040<\/span>\nChisq=<\/span> 22<\/span>  on 3<\/span> degrees of freedom,<\/span> p=<\/span> 7e-05<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u3068\u3057\u3066\u3001$ p = 7 \\times 10^{-5} = 0.00007 $ \u306a\u306e\u3067\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u30b0\u30eb\u30fc\u30d7\u9593\u3067\u7570\u306a\u3063\u3066\u3044\u305f\u3002<\/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>
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092Step by step\u3067\u3084\u3063\u3066\u307f\u308b<\/h2>\n\n\n\n
survdiff() \u95a2\u6570\u3092\u4f7f\u308f\u305a\u306b\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u3057\u3066\u307f\u308b\u3068\u3069\u3046\u306a\u308b\u304b\uff1f<\/p>\n\n\n\n
\u4e0a\u8ff0\u306e ovarian \u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u3084\u3063\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
ovarian \u30c7\u30fc\u30bf\u3092\u52a0\u5de5\u3059\u308b<\/h3>\n\n\n\n
\u751f\u5b58\u6642\u9593\u30c7\u30fc\u30bf\u3001\u30a4\u30d9\u30f3\u30c8\u30c7\u30fc\u30bf\u3001\u6cbb\u7642\u7fa4\u30c7\u30fc\u30bf\u306e\u4e09\u5909\u6570\u306b\u7d5e\u308a\u3001\u751f\u5b58\u6642\u9593\u304c\u77ed\u3044\u9806\u306b\u4e26\u3079\u66ff\u3048\u308b\u3002<\/p>\n\n\n\n
\u6cbb\u7642\u7fa41\u30682\u306b\u308f\u3051\u305f\u30c7\u30fc\u30bf\u3082\u4f5c\u6210\u3059\u308b\u3002<\/p>\n\n\n\n
dat <-<\/span> ovarian[,<\/span>c<\/span>(<\/span>1<\/span>,<\/span>2<\/span>,<\/span>5<\/span>)]<\/span>\ndat0 <-<\/span> dat[<\/span>order<\/span>(<\/span>dat$<\/span>futime),<\/span> ]<\/span>\ndat1 <-<\/span> subset<\/span>(<\/span>dat0,<\/span> dat0$<\/span>rx==<\/span>1<\/span>)<\/span>\ndat2 <-<\/span> subset<\/span>(<\/span>dat0,<\/span> dat0$<\/span>rx==<\/span>2<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u89b3\u5bdf\u30fb\u671f\u5f85\u30fbat risk\u4eba\u6570\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n\n\n\n
\u5404\u7fa4\u306e\u30a4\u30d9\u30f3\u30c8\u89b3\u5bdf\u30c7\u30fc\u30bf\uff08\u4eba\u6570\uff09\u3092O1j\u3001O2j\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u5404\u7fa4\u306e\u300c\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u305f\u6642\u70b9\u300d\u306e\u300c\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u3046\u308b(at risk)\u300d\u4eba\u6570\u3092N1j\u3001N2j\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u5404\u7fa4\u306e\u300c\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u305f\u6642\u70b9\u300d\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u671f\u5f85\u5024\u3092E1j\u3001E2j\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u30a4\u30d9\u30f3\u30c8\u89b3\u5bdf\u30c7\u30fc\u30bf\uff08O\uff09\u306e\u52a0\u5de5<\/h4>\n\n\n\n
O1j\u3068O2j\u306e\u305d\u308c\u305e\u308c\u306e\u5408\u8a08\u3092O1\u3001O2\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
O1\u306f\u6cbb\u7642\u7fa41\u306e\u30a4\u30d9\u30f3\u30c8\u767a\u73fe\u4eba\u6570\u30677\u4eba\u3001O2\u306f\u6cbb\u7642\u7fa42\u306e\u30a4\u30d9\u30f3\u30c8\u767a\u73fe\u4eba\u6570\u30675\u4eba\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
O1j <-<\/span> ifelse<\/span>(<\/span>dat0$<\/span>fustat==<\/span>1<\/span> &<\/span> dat0$<\/span>rx==<\/span>1<\/span>,<\/span>1<\/span>,<\/span>0<\/span>)<\/span>\nO2j <-<\/span> ifelse<\/span>(<\/span>dat0$<\/span>fustat==<\/span>1<\/span> &<\/span> dat0$<\/span>rx==<\/span>2<\/span>,<\/span>1<\/span>,<\/span>0<\/span>)<\/span>\nO1 <-<\/span> sum<\/span>(<\/span>O1j)<\/span>\nO2 <-<\/span> sum<\/span>(<\/span>O2j)<\/span>\n<\/code><\/pre>\n\n\n\n
At risk \u4eba\u6570\u30c7\u30fc\u30bf\uff08N\uff09\u306e\u52a0\u5de5<\/h4>\n\n\n\n
At risk\u306e\u4eba\u6570\u306f\u3001\u6700\u521d\u306f\u5168\u54e1\u3060\u304c\u3001\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u73fe\u3057\u305f\u5f8c\u306f\u3001\u30a4\u30d9\u30f3\u30c8\u767a\u73fe\u8005\u306f\u9664\u304b\u308c\u3066\u3044\u304f\u3002<\/p>\n\n\n\n
\u4eba\u6570\u306f\u3060\u3093\u3060\u3093\u6e1b\u3063\u3066\u3044\u304f\u3002<\/p>\n\n\n\n
N1j <-<\/span> rep<\/span>(<\/span>0<\/span>,<\/span>length<\/span>(<\/span>dat0$<\/span>fustat))<\/span>\nN2j <-<\/span> rep<\/span>(<\/span>0<\/span>,<\/span>length<\/span>(<\/span>dat0$<\/span>fustat))<\/span>\nN1j[<\/span>1<\/span>]<\/span> <-<\/span> length<\/span>(<\/span>dat1$<\/span>fustat)<\/span>\nN2j[<\/span>1<\/span>]<\/span> <-<\/span> length<\/span>(<\/span>dat2$<\/span>fustat)<\/span>\nfor<\/span> (<\/span>j in<\/span> 2<\/span>:<\/span>length<\/span>(<\/span>dat0$<\/span>fustat)){<\/span>\nifelse<\/span>(<\/span>dat0$<\/span>rx[<\/span>j-<\/span>1<\/span>]<\/span>==<\/span>1<\/span>,<\/span> N1j[<\/span>j]<\/span> <-<\/span> N1j[<\/span>j-<\/span>1<\/span>]<\/span>-<\/span>1<\/span>,<\/span> N1j[<\/span>j]<\/span> <-<\/span> N1j[<\/span>j-<\/span>1<\/span>])<\/span>\nifelse<\/span>(<\/span>dat0$<\/span>rx[<\/span>j-<\/span>1<\/span>]<\/span>==<\/span>2<\/span>,<\/span> N2j[<\/span>j]<\/span> <-<\/span> N2j[<\/span>j-<\/span>1<\/span>]<\/span>-<\/span>1<\/span>,<\/span> N2j[<\/span>j]<\/span> <-<\/span> N2j[<\/span>j-<\/span>1<\/span>])<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u30a4\u30d9\u30f3\u30c8\u671f\u5f85\u5024\u30c7\u30fc\u30bf\uff08E\uff09\u306e\u8a08\u7b97<\/h4>\n\n\n\n
\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u73fe\u3057\u305f\u6642\u70b9\u306b\u304a\u3051\u308b\u3001\u5404\u7fa4\u306eat risk \u4eba\u6570\u306e\u3001\u5168\u4f53 at risk \u4eba\u6570\u306b\u5bfe\u3059\u308b\u5272\u5408\u306b\u5408\u308f\u305b\u3066\u3001\u671f\u5f85\u3055\u308c\u308b\u30a4\u30d9\u30f3\u30c8\u6570\u304c\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
Oj <-<\/span> O1j +<\/span> O2j\nNj <-<\/span> N1j +<\/span> N2j\nE1j <-<\/span> Oj*<\/span>N1j\/<\/span>Nj\nE2j <-<\/span> Oj*<\/span>N2j\/<\/span>Nj\nE1 <-<\/span> sum<\/span>(<\/span>E1j)<\/span>\nE2 <-<\/span> sum<\/span>(<\/span>E2j)<\/span>\n<\/code><\/pre>\n\n\n\n
\u671f\u5f85\u5024\u306e\u5408\u8a08\u306f\u6cbb\u7642\u7fa41\u30675.23\u4eba\u3001\u6cbb\u7642\u7fa42\u30676.77\u4eba\u3068\u8a08\u7b97\u3055\u308c\u3001survdiff()\u306e\u7d50\u679c\u3068\u4e00\u81f4\u3059\u308b\u3002<\/p>\n\n\n\n
\u6cbb\u7642\u7fa41\u306e\u89b3\u5bdf\u5024O1\u304c7\u4eba\u3001\u6cbb\u7642\u7fa42\u306e\u89b3\u5bdf\u5024O2\u304c5\u4eba\u3067\u3042\u308b\u306e\u3067\u3001\u5c11\u3057\u305a\u3064\u305a\u308c\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
><\/span> E1\n[<\/span>1<\/span>]<\/span> 5.233531<\/span>\n><\/span> E2\n[<\/span>1<\/span>]<\/span> 6.766469<\/span>\n<\/code><\/pre>\n\n\n\n
\u52a0\u5de5\u30fb\u8a08\u7b97\u3057\u305f\u51fa\u6765\u4e0a\u304c\u308a\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8<\/h4>\n\n\n\n
\u4e0a\u8a18\u3067\u4f5c\u6210\u3057\u305f\u30c7\u30fc\u30bf\u3092\u4e26\u3079\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> cbind<\/span>(<\/span>dat0,<\/span>O1j,<\/span>O2j,<\/span>Oj,<\/span>N1j,<\/span>N2j,<\/span>Nj,<\/span>E1j,<\/span>E2j)<\/span>\nfutime fustat rx O1j O2j Oj N1j N2j Nj       E1j       E2j\n1<\/span>      59<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>  13<\/span>  13<\/span> 26<\/span> 0.5000000<\/span> 0.5000000<\/span>\n2<\/span>     115<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>  12<\/span>  13<\/span> 25<\/span> 0.4800000<\/span> 0.5200000<\/span>\n3<\/span>     156<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>  11<\/span>  13<\/span> 24<\/span> 0.4583333<\/span> 0.5416667<\/span>\n22<\/span>    268<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>  10<\/span>  13<\/span> 23<\/span> 0.4347826<\/span> 0.5652174<\/span>\n23<\/span>    329<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>   9<\/span>  13<\/span> 22<\/span> 0.4090909<\/span> 0.5909091<\/span>\n24<\/span>    353<\/span>      1<\/span>  2<\/span>   0<\/span>   1<\/span>  1<\/span>   8<\/span>  13<\/span> 21<\/span> 0.3809524<\/span> 0.6190476<\/span>\n25<\/span>    365<\/span>      1<\/span>  2<\/span>   0<\/span>   1<\/span>  1<\/span>   8<\/span>  12<\/span> 20<\/span> 0.4000000<\/span> 0.6000000<\/span>\n26<\/span>    377<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   8<\/span>  11<\/span> 19<\/span> 0.0000000<\/span> 0.0000000<\/span>\n4<\/span>     421<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   8<\/span>  10<\/span> 18<\/span> 0.0000000<\/span> 0.0000000<\/span>\n5<\/span>     431<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>   8<\/span>   9<\/span> 17<\/span> 0.4705882<\/span> 0.5294118<\/span>\n6<\/span>     448<\/span>      0<\/span>  1<\/span>   0<\/span>   0<\/span>  0<\/span>   7<\/span>   9<\/span> 16<\/span> 0.0000000<\/span> 0.0000000<\/span>\n7<\/span>     464<\/span>      1<\/span>  2<\/span>   0<\/span>   1<\/span>  1<\/span>   6<\/span>   9<\/span> 15<\/span> 0.4000000<\/span> 0.6000000<\/span>\n8<\/span>     475<\/span>      1<\/span>  2<\/span>   0<\/span>   1<\/span>  1<\/span>   6<\/span>   8<\/span> 14<\/span> 0.4285714<\/span> 0.5714286<\/span>\n9<\/span>     477<\/span>      0<\/span>  1<\/span>   0<\/span>   0<\/span>  0<\/span>   6<\/span>   7<\/span> 13<\/span> 0.0000000<\/span> 0.0000000<\/span>\n10<\/span>    563<\/span>      1<\/span>  2<\/span>   0<\/span>   1<\/span>  1<\/span>   5<\/span>   7<\/span> 12<\/span> 0.4166667<\/span> 0.5833333<\/span>\n11<\/span>    638<\/span>      1<\/span>  1<\/span>   1<\/span>   0<\/span>  1<\/span>   5<\/span>   6<\/span> 11<\/span> 0.4545455<\/span> 0.5454545<\/span>\n12<\/span>    744<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   4<\/span>   6<\/span> 10<\/span> 0.0000000<\/span> 0.0000000<\/span>\n13<\/span>    769<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   4<\/span>   5<\/span>  9<\/span> 0.0000000<\/span> 0.0000000<\/span>\n14<\/span>    770<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   4<\/span>   4<\/span>  8<\/span> 0.0000000<\/span> 0.0000000<\/span>\n15<\/span>    803<\/span>      0<\/span>  1<\/span>   0<\/span>   0<\/span>  0<\/span>   4<\/span>   3<\/span>  7<\/span> 0.0000000<\/span> 0.0000000<\/span>\n16<\/span>    855<\/span>      0<\/span>  1<\/span>   0<\/span>   0<\/span>  0<\/span>   3<\/span>   3<\/span>  6<\/span> 0.0000000<\/span> 0.0000000<\/span>\n17<\/span>   1040<\/span>      0<\/span>  1<\/span>   0<\/span>   0<\/span>  0<\/span>   2<\/span>   3<\/span>  5<\/span> 0.0000000<\/span> 0.0000000<\/span>\n18<\/span>   1106<\/span>      0<\/span>  1<\/span>   0<\/span>   0<\/span>  0<\/span>   1<\/span>   3<\/span>  4<\/span> 0.0000000<\/span> 0.0000000<\/span>\n19<\/span>   1129<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   0<\/span>   3<\/span>  3<\/span> 0.0000000<\/span> 0.0000000<\/span>\n20<\/span>   1206<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   0<\/span>   2<\/span>  2<\/span> 0.0000000<\/span> 0.0000000<\/span>\n21<\/span>   1227<\/span>      0<\/span>  2<\/span>   0<\/span>   0<\/span>  0<\/span>   0<\/span>   1<\/span>  1<\/span> 0.0000000<\/span> 0.0000000<\/span>\n<\/code><\/pre>\n\n\n\n
\u691c\u5b9a\u7d71\u8a08\u91cf \u30ab\u30a4\u4e8c\u4e57\u5024\u3068\u6709\u610f\u78ba\u7387\u306e\u8a08\u7b97<\/h3>\n\n\n\n
\u691c\u5b9a\u7d71\u8a08\u91cf\u306f\u3001\u89b3\u5bdf\u5024\u3068\u671f\u5f85\u5024\u306e\u5dee\u306e2\u4e57\u3092\u671f\u5f85\u5024\u3067\u5272\u3063\u305f\u5024\u3092\u5404\u7fa4\u3067\u6c42\u3081\u3001\u5408\u8a08\u3059\u308b\u3002<\/p>\n\n\n\n
(<\/span>O1-<\/span>E1)<\/span>^<\/span>2<\/span>\/<\/span>E1 +<\/span> (<\/span>O2-<\/span>E2)<\/span>^<\/span>2<\/span>\/<\/span>E2\n<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306e\u30ab\u30a4\u4e8c\u4e57 $ \\chi^2 $ \u306fsurvdiff()\u306e\u7d50\u679c\u3068\u4e00\u81f4\u3057\u3066\u7d041.1\u3068\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> (<\/span>O1-<\/span>E1)<\/span>^<\/span>2<\/span>\/<\/span>E1 +<\/span> (<\/span>O2-<\/span>E2)<\/span>^<\/span>2<\/span>\/<\/span>E2\n[<\/span>1<\/span>]<\/span> 1.057393<\/span>\n<\/code><\/pre>\n\n\n\n
\u81ea\u7531\u5ea61\u3067\u691c\u5b9a\u3059\u308b\u3068\u3001\u4e0a\u5074\u6709\u610f\u78ba\u7387\u306f\u7d040.3\u3068\u306a\u308b\u3002\u3053\u308c\u3082survdiff()\u306e\u7d50\u679c\u3068\u4e00\u81f4\u3057\u305f\u3002<\/p>\n\n\n\n
><\/span> pchisq<\/span>(<\/span>1.057393<\/span>,<\/span>1<\/span>,<\/span>lower.tail=<\/span>FALSE<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> 0.3038105<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
R\u3067\u3001\u4e8c\u7fa4\u4ee5\u4e0a\u306e\u751f\u5b58\u306b\u3064\u3044\u3066\u7d71\u8a08\u5b66\u7684\u306b\u7570\u306a\u308b\u304b\u3069\u3046\u304b\u3092\u691c\u5b9a\u3059\u308b\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u884c\u3063\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306f\u3001\u30ab\u30a4\u4e8c\u4e57\u5024\u3092\u4f7f\u3063\u305f\u691c\u5b9a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092survdiff()\u3092\u4f7f\u308f\u305a\u306bStep by step\u3067\u3084\u3063\u3066\u307f\u308b\u3068\u3001\u5b9f\u969b\u306b\u3069\u3093\u306a\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u304b\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u305f\u6642\u70b9\u306e\u89b3\u5bdf\u5024\u3001at risk \u4eba\u6570\u304b\u3089\u3001\u30a4\u30d9\u30f3\u30c8\u306e\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3057\u3001$ \\chi^2 $ \u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
\u691c\u5b9a\u306f\u81ea\u7531\u5ea61\u306e $ \\chi^2 $ \u691c\u5b9a\u3060\u3002<\/p>\n\n\n\n
\u89b3\u5bdf\u5024\u304c\u671f\u5f85\u5024\u306b\u6bd4\u3079\u3066\u5927\u304d\u304f\u96e2\u308c\u305f\u5834\u5408\u3001$ \\chi^2 $ \u5024\u304c\u5927\u304d\u304f\u306a\u308a\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3068\u5224\u65ad\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u3064\u307e\u308a\u3001\u7fa4\u9593\u306b\u7d71\u8a08\u5b66\u7684\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u3068\u3044\u3046\u7d50\u8ad6\u306b\u306a\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
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