{"id":507,"date":"2018-08-25T12:42:29","date_gmt":"2018-08-25T03:42:29","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-for-log-rank-test\/"},"modified":"2024-10-13T15:14:07","modified_gmt":"2024-10-13T06:14:07","slug":"how-to-determine-sample-size-for-log-rank-test","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-for-log-rank-test\/","title":{"rendered":"R \u3067\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092 R \u3067\u884c\u3046\u65b9\u6cd5<\/p>\n\n\n\n\n\n\n\n

\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306f\u3069\u3046\u3084\u308b\u304b\uff1f<\/h2>\n\n\n\n

\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306f\u3001\u6642\u9593\u7d4c\u904e\u3068\u3068\u3082\u306b\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u3066\u3044\u304f\u30c7\u30fc\u30bf\u306e\u7fa4\u9593\u6bd4\u8f03\u3092\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u60a3\u8005\u3055\u3093\u306e\u6b7b\u4ea1\u3092\u30a4\u30d9\u30f3\u30c8\u3068\u3057\u305f\u30c7\u30fc\u30bf\u3001\u75c5\u6c17\u304c\u518d\u767a\u3059\u308b\u3053\u3068\u3092\u30a4\u30d9\u30f3\u30c8\u3068\u3057\u305f\u30c7\u30fc\u30bf\u3001\u75c5\u6c17\u304c\u767a\u75c7\u3059\u308b\u3053\u3068\u3092\u30a4\u30d9\u30f3\u30c8\u3068\u3057\u305f\u30c7\u30fc\u30bf\u3001\u306a\u3069\u304c\u6271\u3048\u308b\u3002<\/p>\n\n\n\n

\u75c5\u6c17\u3070\u304b\u308a\u3067\u306f\u306a\u304f\u3001\u6642\u9593\u7d4c\u904e\u3068\u3068\u3082\u306b\u8d77\u304d\u3066\u304f\u308b\u4e8b\u67c4\u306a\u3089\u3001\u306a\u3093\u3067\u3082\u6271\u3048\u308b\u3002<\/p>\n\n\n\n

\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u524d\u306b\u3001\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306f\u3069\u3046\u3084\u308b\u304b\uff1f\u3092\u898b\u3066\u307f\u308b\u3002<\/p>\n\n\n\n

R \u306e survival \u30d1\u30c3\u30b1\u30fc\u30b8\u306e survdiff() \u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n

survival \u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u6e08\u307f\u306a\u306e\u3067\u3001library()\u3067\u547c\u3073\u51fa\u3059\u3060\u3051\u3067OK\u3002<\/p>\n\n\n\n

ovarian \u3068\u3044\u3046\u5375\u5de3\u304c\u3093\u306e\u6cbb\u7642\u5f8c\u751f\u5b58\u6642\u9593\u306e\u89e3\u6790\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n

futime \u304c\u751f\u5b58\u6642\u9593\u3001fustat \u304c\u6b7b\u4ea1\u767a\u751f\u306e\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n

rx \u304c\u6cbb\u7642\u7fa4\u306e\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n

library<\/span>(<\/span>survival)<\/span>\nsurvdiff<\/span>(<\/span>Surv<\/span>(<\/span>futime,<\/span> fustat)<\/span> ~<\/span> rx,<\/span>data=<\/span>ovarian)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306fp=0.3\u3067\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u3089\u306a\u304b\u3063\u305f\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
\u3082\u3046\u4e00\u3064\u306e\u4f8b\u306f\u3001MASS\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u4e2d\u306e\u3001gehan\u3068\u3044\u3046\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n
\u767d\u8840\u75c5\u306e\u60a3\u8005\u3055\u3093\u306e\u5bdb\u89e3\u304b\u3089\u518d\u71c3\u307e\u3067\u306e\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n
time\u304c\u518d\u71c3\u307e\u3067\u306e\u6642\u9593\u3001cens\u304c\u518d\u71c3\u3057\u305f\u304b\u3069\u3046\u304b\u3001treat\u304c6\uff0d\u30e1\u30eb\u30ab\u30d7\u30c8\u30d7\u30ea\u30f3\uff086-MP\uff09\u3067\u6cbb\u7642\u3057\u305f\u304b\u3001\u5bfe\u7167\u3060\u3063\u305f\u304b\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>MASS)<\/span>\nsurvdiff<\/span>(<\/span>Surv<\/span>(<\/span>time,<\/span> cens)<\/span> ~<\/span> treat,<\/span> data =<\/span> gehan)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b6-MP\u6cbb\u7642\u7fa4\u306e\u307b\u3046\u304c\u518d\u71c3\u304c\u5c11\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> library<\/span>(<\/span>MASS)<\/span>\n><\/span> survdiff<\/span>(<\/span>Surv<\/span>(<\/span>time,<\/span> cens)<\/span> ~<\/span> treat,<\/span> data =<\/span> gehan)<\/span>\nCall:<\/span>\nsurvdiff<\/span>(<\/span>formula =<\/span> Surv<\/span>(<\/span>time,<\/span> cens)<\/span> ~<\/span> treat,<\/span> data =<\/span> gehan)<\/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\ntreat=<\/span>6<\/span>-<\/span>MP    21<\/span>        9<\/span>     19.3<\/span>      5.46<\/span>      16.8<\/span>\ntreat=<\/span>control 21<\/span>       21<\/span>     10.7<\/span>      9.77<\/span>      16.8<\/span>\nChisq=<\/span> 16.8<\/span>  on 1<\/span> degrees of freedom,<\/span> p=<\/span> 4e-05<\/span>\n<\/code><\/pre>\n\n\n\n
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3069\u3046\u3084\u308b\u304b\uff1f<\/h2>\n\n\n\n
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3001\u5b9f\u306fCox\u306e\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u4f7f\u3046\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 \u3068 EZR \u3067\u751f\u5b58\u6642\u9593\u89e3\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u751f\u5b58\u6642\u9593\u89e3\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u65b9\u6cd5 Cox \u306e\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u3092\u4f7f\u3046\u524d\u63d0\u306e\u8a08\u7b97 \u751f\u5b58\u6642\u9593\u89e3\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 \u305d\u306e 1 R \u3067\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u66f8\u3044\u3066\u307f\u305f\u3002 S0\u304c\u30b3\u30f3…<\/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\n\n\n\n
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3082Cox\u3082\u751f\u5b58\u6642\u9593\u89e3\u6790\u3068\u8a00\u3044\u306a\u304c\u3089\u3001\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u308b\u9806\u756a\u3057\u304b\u4f7f\u3063\u3066\u3044\u306a\u3044\u3002<\/p>\n\n\n\n
\u3042\u3068\u306f\u30a4\u30d9\u30f3\u30c8\u304c\u8d77\u304d\u308b\u6bd4\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3069\u3061\u3089\u306b\u3082\u6d41\u7528\u3067\u304d\u308b\u3068\u3044\u3046\u3053\u3068\u3060\u3002<\/p>\n\n\n\n
sample.size.cox <-<\/span> function<\/span>(<\/span>S1,<\/span>S0,<\/span>alternative=<\/span>\"two.sided\"<\/span>,<\/span>power=<\/span>.8<\/span>,<\/span>\nsig.level=<\/span>.05<\/span>){<\/span>\nalternative <-<\/span> match.arg<\/span>(<\/span>alternative)<\/span>\ntside <-<\/span> switch<\/span>(<\/span>alternative,<\/span> one.sided=<\/span>1<\/span>,<\/span> two.sided=<\/span>2<\/span>)<\/span>\nbeta <-<\/span> log<\/span>(<\/span>log<\/span>(<\/span>S1)<\/span>\/<\/span>log<\/span>(<\/span>S0))<\/span>\nZa <-<\/span> qnorm<\/span>(<\/span>sig.level\/<\/span>tside,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nZb <-<\/span> qnorm<\/span>(<\/span>power)<\/span>\nd <-<\/span> ((<\/span>Za+<\/span>Zb)<\/span>*<\/span>(<\/span>1<\/span>+<\/span>exp<\/span>(<\/span>beta))<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>exp<\/span>(<\/span>beta)))<\/span>^<\/span>2<\/span>\nn <-<\/span> d\/<\/span>(((<\/span>1<\/span>-<\/span>S1)<\/span>+<\/span>(<\/span>1<\/span>-<\/span>S0))<\/span>\/<\/span>2<\/span>)<\/span>\nNOTE<\/span> <-<\/span> \"n is total number of subjects in *both* of groups\"<\/span>\nMETHOD <-<\/span> \"Sample Size Calculation of Cox Propotional Hazard Model\"<\/span>\nstructure<\/span>(<\/span>\nlist<\/span>(<\/span>\"Total number of death\"<\/span> =<\/span> d,<\/span>\n\"Total number of subjects\"<\/span> =<\/span> n,<\/span>\n\"Surv. rate of trt. arm\"<\/span> =<\/span> S1,<\/span>\n\"Surv. rate of ctl. arm\"<\/span> =<\/span> S0,<\/span>\n\"Hazard ratio\"<\/span> =<\/span> exp<\/span>(<\/span>beta),<\/span>\nsig.level =<\/span> sig.level,<\/span>\npower =<\/span> power,<\/span>\nalternative =<\/span> alternative,<\/span>\nnote =<\/span> NOTE<\/span>,<\/span>\nmethod =<\/span> METHOD),<\/span>\nclass =<\/span> \"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u5148\u307b\u3069\u306eovarian\u306e\u7d50\u679c\u3092\u3082\u3068\u306b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u3059\u308b\u3068\u3001\u4e21\u7fa4\u5408\u308f\u305b\u3066151\u4f8b\u306e\u6b7b\u4ea1\u3001326\u4f8b\u306e\u60a3\u8005\u3055\u3093\u304c\u5fc5\u8981\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
\u5404\u7fa413\u4f8b\u306e\u8a66\u9a13\u3067\u306f\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u306a\u3089\u306a\u304f\u3066\u5f53\u7136\u3060\u3002<\/p>\n\n\n\n
><\/span> sample.size.cox<\/span>(<\/span>S1=<\/span>8<\/span>\/<\/span>13<\/span>,<\/span> S0=<\/span>6<\/span>\/<\/span>13<\/span>)<\/span>\nSample Size Calculation of Cox Propotional Hazard Model\nTotal number of death =<\/span> 150.2536<\/span>\nTotal number of subjects =<\/span> 325.5495<\/span>\nSurv. rate of trt. arm =<\/span> 0.6153846<\/span>\nSurv. rate of ctl. arm =<\/span> 0.4615385<\/span>\nHazard ratio =<\/span> 0.6279283<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is total number of subjects in<\/span> *<\/span>both*<\/span> of groups\n<\/code><\/pre>\n\n\n\n
gehan\u30c7\u30fc\u30bf\u306f\u3001\u5168\u90e8\u30678\u4f8b\u306e\u518d\u71c3\u75c7\u4f8b\u304c\u3042\u308c\u3070\u3088\u304f\u3001\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u4e8c\u7fa4\u5168\u4f53\u306711\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
><\/span> sample.size.cox<\/span>(<\/span>S1=<\/span>(<\/span>21<\/span>-<\/span>9<\/span>)<\/span>\/<\/span>21<\/span>,<\/span> S0=<\/span>(<\/span>21<\/span>-<\/span>21<\/span>)<\/span>\/<\/span>21<\/span>)<\/span>\nSample Size Calculation of Cox Propotional Hazard Model\nTotal number of death =<\/span> 7.84888<\/span>\nTotal number of subjects =<\/span> 10.98843<\/span>\nSurv. rate of trt. arm =<\/span> 0.5714286<\/span>\nSurv. rate of ctl. arm =<\/span> 0<\/span>\nHazard ratio =<\/span> 0<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is total number of subjects in<\/span> *<\/span>both*<\/span> of groups\n<\/code><\/pre>\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\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u30a8\u30af\u30bb\u30eb\u3067<\/h2>\n\n\n\n
Cox\u306e\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u7528\u3060\u304c\u3001\u4e0a\u8a18\u306e\u901a\u308a\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306b\u4f7f\u3048\u308b\u3002<\/p>\n\n\n\n
\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
\u30b3\u30c3\u30af\u30b9\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3010\u30a8\u30af\u30bb\u30eb\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3011Cox proportional hazard model sample size calculator | TKER SHOP<\/a><\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
R \u3067\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u3092\u884c\u3046\u306b\u306f\u3001survival\u30d1\u30c3\u30b1\u30fc\u30b8\u306esurvdiff()\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
\u305d\u306e\u3068\u304d\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u3092\u8868\u3059\u30c7\u30fc\u30bf\u3068\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u307e\u3067\u306e\u6642\u9593\u3001\u7fa4\u5206\u3051\u306e\u5909\u6570\u304c\u5fc5\u8981\u3060\u3002<\/p>\n\n\n\n
\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3001Cox\u306e\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3068\u540c\u4e00\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u4f7f\u3063\u3066\u884c\u3048\u308b\u3002<\/p>\n\n\n\n
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\u53c2\u8003\u66f8\u7c4d<\/h2>\n\n\n\n
\"\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba<\/a><\/figure>\n\n\n\n
<\/div>\n\n\n\n
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