{"id":314,"date":"2022-04-16T00:00:00","date_gmt":"2022-04-15T15:00:00","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/sample-size-determination-for-equivalence-test-in-r-and-ezr\/"},"modified":"2024-09-29T22:35:50","modified_gmt":"2024-09-29T13:35:50","slug":"sample-size-determination-for-equivalence-test-in-r-and-ezr","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/sample-size-determination-for-equivalence-test-in-r-and-ezr\/","title":{"rendered":"R \u3068 EZR \u3067\u540c\u7b49\u6027\u691c\u5b9a\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u7a4d\u6975\u7684\u306b\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u3066\u3044\u304f\u540c\u7b49\u6027\u306e\u691c\u5b9a\u3002<\/p>\n\n\n\n

\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3069\u306e\u3088\u3046\u306b\u3059\u308c\u3070\u3088\u3044\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u540c\u7b49\u6027\u691c\u5b9a\u306f\u3069\u306e\u3088\u3046\u306b\u3059\u308b\u306e\u304b\uff1f<\/h2>\n\n\n\n

\u540c\u7b49\u6027\u306e\u691c\u5b9a\u306f\u3001\u7c21\u5358\u306b\u8a00\u3048\u3070\u3001\u975e\u52a3\u6027\u691c\u5b9a\u306e\u7fa4\u3092\u5165\u308c\u66ff\u3048\u3066\u3001\u7247\u5074\u691c\u5b9a\u30922\u56de\u884c\u3046\u3053\u3068\u3067\u5b9f\u65bd\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

\u52a3\u3063\u3066\u3044\u306a\u3044\u304c\u3001\u512a\u308c\u3066\u3082\u3044\u306a\u3044\u3001\u3068\u3044\u3046\u306e\u304c\u540c\u7b49\u306e\u5b9a\u7fa9\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001\u3069\u306e\u304f\u3089\u3044\u306e\u5dee\u304c\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\uff08\u540c\u7b49\u3068\u8a00\u3048\u308b\u9650\u754c\uff09\u3067\u3042\u308b\u304b\u304c\u96e3\u3057\u3044\u3002<\/p>\n\n\n\n

\u975e\u52a3\u6027\u691c\u5b9a\u306e\u8a73\u7d30\u306f\u3053\u3061\u3089\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\t\u975e\u52a3\u6027\u30de\u30fc\u30b8\u30f3\u306e\u6c7a\u3081\u65b9\u3068 R \u3067\u975e\u52a3\u6027\u691c\u5b9a\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u3044\u307e\u307e\u3067\u306e\u65b9\u6cd5\u3068\u6bd4\u3079\u3066\u3001\u683c\u6bb5\u306b\u3044\u3044\u3068\u304b\u3001\u969b\u7acb\u3063\u3066\u3044\u3044\u3068\u304b\u3001\u3058\u3083\u306a\u304f\u3066\u3082\u3044\u3044\u5834\u5408\u304c\u3042\u308b\u3002 \u30c0\u30e1\u3058\u3083\u306a\u3051\u308c\u3070\u3044\u3044\u3002 \u52a3\u3063\u3066\u3044\u306a\u3051\u308c\u3070\u3044\u3044\u3002 \u52a3\u3063\u3066\u3044\u306a\u3051\u308c\u3070\u3044\u3044\u3068\u3044…<\/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

\u540c\u7b49\u6027\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3069\u306e\u3088\u3046\u306b\u3059\u308b\u306e\u304b\uff1f<\/h2>\n\n\n\n

\u5e73\u5747\u5024\u306e\u5834\u5408<\/h3>\n\n\n\n

\u5e73\u5747\u5024\u306e\u540c\u7b49\u6027\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3069\u306e\u3088\u3046\u306b\u3059\u308c\u3070\u3088\u3044\u304b\uff1f<\/p>\n\n\n\n

\u4e00\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

$$ n = 2 \\left( \\frac{Z_{\\alpha\/2} + Z_{\\beta\/2}}{\\Delta\/\\sigma} \\right)^2 $$<\/p>\n\n\n\n\n\n\n\n

\u0394\u306f\u3001\u81e8\u5e8a\u7684\u306b\u610f\u5473\u304c\u3042\u308b\u5dee\u3002<\/p>\n\n\n\n

\u03c3\u306f\u30012\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u3002<\/p>\n\n\n\n

\u03b1\u3001\u03b2 \u306f\u3001\u305d\u308c\u305e\u308c\u7b2c1\u7a2e\u3068\u7b2c2\u7a2e\u306e\u904e\u8aa4\u3002<\/p>\n\n\n\n

\u3044\u308f\u3086\u308b\u03b1\u30a8\u30e9\u30fc\u3068\u03b2\u30a8\u30e9\u30fc\u3002<\/p>\n\n\n\n

2\u7fa4\u306e\u6bcd\u96c6\u56e3\u306e\u5dee\u306f\u30bc\u30ed\u3068\u8003\u3048\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

R\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n

sample.size.equivalence.mean <-<\/span> function<\/span>\n(<\/span>sig.level=<\/span>.05<\/span>,<\/span> power=<\/span>.8<\/span>,<\/span>Delta=<\/span>0<\/span>,<\/span> Delta1,<\/span> sd=<\/span>1<\/span>,<\/span> alternative=<\/span>\"two.sided\"<\/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>\n# sample size calculation<\/span>\nd <-<\/span> (<\/span>Delta +<\/span> Delta1)<\/span>\/<\/span>sd\nZa <-<\/span> qnorm<\/span>(<\/span>sig.level\/<\/span>tside,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nZb <-<\/span> qnorm<\/span>(<\/span>1<\/span>-<\/span>(<\/span>1<\/span>-<\/span>power)<\/span>\/<\/span>2<\/span>)<\/span>\nn <-<\/span> 2<\/span>*<\/span>((<\/span>Za+<\/span>Zb)<\/span>\/<\/span>d)<\/span>^<\/span>2<\/span>\n# output<\/span>\nNOTE<\/span> <-<\/span> \"n is number in *each* group\"<\/span>\nMETHOD <-<\/span> \"Equivalence Test Sample Size (Mean)\"<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n =<\/span> n,<\/span> \"Sample Diff\"<\/span> =<\/span> Delta,<\/span>\n\"Clin.Sig.Diff\"<\/span>=<\/span>Delta1,<\/span> SD =<\/span> sd,<\/span> sig.level =<\/span> sig.level,<\/span>\npower =<\/span> power,<\/span> alternative =<\/span> alternative,<\/span> note =<\/span> NOTE<\/span>,<\/span>\nmethod =<\/span> METHOD),<\/span> class =<\/span> \"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\uff12\u3064\u4f8b\u984c\u3092\u5b9f\u884c\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u6a19\u6e96\u504f\u5dee 1 \u306b\u5bfe\u3057\u3066\u3001\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\u304c0.5\u306e\u6642\u3068\u30010.1\u306e\u6642\u3092\u8a08\u7b97\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
0.5\u306f\u73fe\u5b9f\u7684\u3060\u304c\u30010.1\u306f\u975e\u73fe\u5b9f\u7684\u306a\u6570\u5b57\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> sample.size.equivalence.mean<\/span>(<\/span>power=<\/span>0.8<\/span>,<\/span> Delta1=<\/span>0.5<\/span>)<\/span>\nEquivalence Test Sample Size <\/span>(<\/span>Mean)<\/span>\nn =<\/span> 84.05938<\/span>\nSample Diff =<\/span> 0<\/span>\nClin.Sig.Diff =<\/span> 0.5<\/span>\nSD =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n><\/span> sample.size.equivalence.mean<\/span>(<\/span>power=<\/span>0.8<\/span>,<\/span> Delta1=<\/span>0.1<\/span>)<\/span>\nEquivalence Test Sample Size <\/span>(<\/span>Mean)<\/span>\nn =<\/span> 2101.485<\/span>\nSample Diff =<\/span> 0<\/span>\nClin.Sig.Diff =<\/span> 0.1<\/span>\nSD =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n<\/code><\/pre>\n\n\n\n
EZR\u3067\u8a08\u7b97\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u30dd\u30a4\u30f3\u30c8\u306f\u03b2\u30a8\u30e9\u30fc\u3092\u534a\u5206\u306b\u3059\u308b\u3068\u3053\u308d\u3002<\/p>\n\n\n\n
\u691c\u51fa\u529b80\uff05\u306e\u5834\u5408\u3001\u03b2\u30a8\u30e9\u30fc\u306f20\uff05\u3002<\/p>\n\n\n\n
\u305d\u306e\u534a\u5206\u306e10\uff05\u3092100\uff05\u304b\u3089\u5f15\u3044\u3066\u300190\uff05\u3002<\/p>\n\n\n\n
\u3053\u306e90\uff05\u306e\u5c0f\u6570\u30010.9\u3092\u691c\u51fa\u529b\u306b\u5165\u529b\u3059\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u7d50\u679c\u306f\u4e0a\u8a18\u3068\u540c\u3058\u306b\u306a\u308b\u3002\u5fc5\u8981\u75c7\u4f8b\u6570\u306f\u5207\u308a\u4e0a\u3052\u308b\u306e\u3067\u3001R function\u3067\u306e\u7d50\u679c\u3068\u540c\u3058\u3060\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u975e\u73fe\u5b9f\u7684\u306a\u8a2d\u5b9a\u3082\u3001\u540c\u3058\u6570\u5b57\u306b\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u6bd4\u7387\u306e\u5834\u5408<\/h3>\n\n\n\n
\u6bd4\u7387\uff08\u5272\u5408\uff09\u306e\u5834\u5408\u306f\u3001\u304b\u306a\u308a\u8907\u96d1\u306a\u306e\u3067\u5f0f\u306f\u5272\u611b\u3002<\/p>\n\n\n\n
\u8a73\u3057\u304f\u77e5\u308a\u305f\u3044\u4eba\u306f\u53c2\u8003\u66f8\u7c4d\u3092\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
\"\u65b0\u7248<\/a><\/figure>\n\n\n\n
<\/div>\n\n\n\n
\n
\u65b0\u7248 \u7121\u4f5c\u70ba\u5316\u6bd4\u8f03\u8a66\u9a13 \u2015\u30c7\u30b6\u30a4\u30f3\u3068\u7d71\u8a08\u89e3\u6790\u2015 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba5)<\/a><\/p>\n