{"id":458,"date":"2019-01-01T16:26:43","date_gmt":"2019-01-01T07:26:43","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/meta-analysis-of-mean-differences-in-r\/"},"modified":"2024-10-12T17:32:05","modified_gmt":"2024-10-12T08:32:05","slug":"meta-analysis-of-mean-differences-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/meta-analysis-of-mean-differences-in-r\/","title":{"rendered":"R \u3067\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u89e3\u6790\u3092\u884c\u3046\u65b9\u6cd5"},"content":{"rendered":"\n

\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u3092\u89e3\u8aac\u3002<\/p>\n\n\n\n\n\n\n\n

\u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u89e3\u8aac\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf<\/h2>\n\n\n\n

\u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u3092\u89e3\u8aac\u3059\u308b\u305f\u3081\u306e\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n

m\u304c\u5e73\u5747\u3001s\u304c\u6a19\u6e96\u504f\u5dee\u3001n\u304c\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3002<\/p>\n\n\n\n

n1 <-<\/span> c<\/span>(<\/span>155<\/span>,<\/span>31<\/span>,<\/span>75<\/span>,<\/span>18<\/span>,<\/span>8<\/span>,<\/span>57<\/span>,<\/span>34<\/span>,<\/span>110<\/span>,<\/span>60<\/span>)<\/span>\nm1 <-<\/span> c<\/span>(<\/span>55.0<\/span>,<\/span>27.0<\/span>,<\/span>64.0<\/span>,<\/span>66.0<\/span>,<\/span>14.0<\/span>,<\/span>19.0<\/span>,<\/span>52.0<\/span>,<\/span>21.0<\/span>,<\/span>30.0<\/span>)<\/span>\ns1 <-<\/span> c<\/span>(<\/span>47.0<\/span>,<\/span>7.0<\/span>,<\/span>17.0<\/span>,<\/span>20.0<\/span>,<\/span>8.0<\/span>,<\/span>7.0<\/span>,<\/span>45.0<\/span>,<\/span>16.0<\/span>,<\/span>27.0<\/span>)<\/span>\nn0 <-<\/span> c<\/span>(<\/span>156<\/span>,<\/span>32<\/span>,<\/span>71<\/span>,<\/span>18<\/span>,<\/span>13<\/span>,<\/span>52<\/span>,<\/span>33<\/span>,<\/span>183<\/span>,<\/span>52<\/span>)<\/span>\nm0 <-<\/span> c<\/span>(<\/span>75.0<\/span>,<\/span>29.0<\/span>,<\/span>119.0<\/span>,<\/span>137.0<\/span>,<\/span>18.0<\/span>,<\/span>18.0<\/span>,<\/span>41.0<\/span>,<\/span>31.0<\/span>,<\/span>23.0<\/span>)<\/span>\ns0 <-<\/span> c<\/span>(<\/span>64.0<\/span>,<\/span>4.0<\/span>,<\/span>29.0<\/span>,<\/span>48.0<\/span>,<\/span>11.0<\/span>,<\/span>4.0<\/span>,<\/span>34.0<\/span>,<\/span>27.0<\/span>,<\/span>20.0<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e26\u3079\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u305d\u308c\u305e\u308c\u306e\u8a66\u9a13\u306e\u5e73\u5747\u5024\u306e\u5dee\u306895%\u4fe1\u983c\u533a\u9593<\/h2>\n\n\n\n
\u5404\u8a66\u9a13\u306e\u5e73\u5747\u5024\u306e\u5dee\u3092\u8a08\u7b97\u3057\u300195\uff05\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
# ---- difference in means -----<\/span>\nad <-<\/span> m1-<\/span>m0\ns <-<\/span> ((<\/span>n1-<\/span>1<\/span>)<\/span>*<\/span>s1^<\/span>2<\/span>+<\/span>(<\/span>n0-<\/span>1<\/span>)<\/span>*<\/span>s0^<\/span>2<\/span>)<\/span>\/<\/span>(<\/span>n1-<\/span>1<\/span>+<\/span>n0-<\/span>1<\/span>)<\/span>\nse <-<\/span> sqrt<\/span>((<\/span>1<\/span>\/<\/span>n1+<\/span>1<\/span>\/<\/span>n0)<\/span>*<\/span>s)<\/span>\ntn <-<\/span> n1+<\/span>n0\nlow <-<\/span> ad-<\/span>1.96<\/span>*<\/span>se\nupp <-<\/span> ad+<\/span>1.96<\/span>*<\/span>se\n<\/code><\/pre>\n\n\n\n
\u5e73\u5747\u5024\u306e\u5dee\u306895\uff05\u4fe1\u983c\u533a\u9593\u306e\u4e00\u89a7\u3092\u51fa\u529b\u3057\u3066\u307f\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/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>
\u305d\u308c\u305e\u308c\u306e\u8a66\u9a13\u306e\u5e73\u5747\u5024\u306e\u5dee\u306895%\u4fe1\u983c\u533a\u9593\u306e\u30b0\u30e9\u30d5\u5316<\/h2>\n\n\n\n
\u5404\u8a66\u9a13\u306e\u5e73\u5747\u5024\u306e\u5dee\u306895\uff05\u4fe1\u983c\u533a\u9593\u3092\u30b0\u30e9\u30d5\u306b\u66f8\u3044\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
# ----- individual graph -----<\/span>\nk <-<\/span> length<\/span>(<\/span>n1)<\/span>\nid <-<\/span> k:<\/span>1<\/span>\nplot<\/span>(<\/span>ad,<\/span> id,<\/span> ylim=<\/span>c<\/span>(<\/span>-<\/span>4<\/span>,<\/span>10<\/span>),<\/span> pch=<\/span>\" \"<\/span>,<\/span>\nxlim=<\/span>c<\/span>(<\/span>-<\/span>100<\/span>,<\/span>100<\/span>),<\/span> yaxt=<\/span>\"n\"<\/span>,<\/span>\nylab=<\/span>\"Citation\"<\/span>,<\/span> xlab=<\/span>\"Difference in means\"<\/span>)<\/span>\ntitle<\/span>(<\/span>main=<\/span>\" Mean difference model \"<\/span>)<\/span>\nsymbols<\/span>(<\/span>ad,<\/span> id,<\/span> squares=<\/span>sqrt<\/span>(<\/span>tn),<\/span> add=<\/span>T<\/span>,<\/span> inches=<\/span>0.25<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>0<\/span>)<\/span>\nfor<\/span> (<\/span>i in<\/span> 1<\/span>:<\/span>k){<\/span>\nj <-<\/span> k-<\/span>i+<\/span>1<\/span>\nx <-<\/span> c<\/span>(<\/span>low[<\/span>i],<\/span> upp[<\/span>i])<\/span>\ny <-<\/span> c<\/span>(<\/span>j,<\/span> j)<\/span>\nlines<\/span>(<\/span>x,<\/span> y,<\/span> type=<\/span>\"l\"<\/span>)<\/span>\ntext<\/span>(<\/span>50<\/span>,<\/span> i,<\/span> j)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\uff11\u3000\u56fa\u5b9a\u52b9\u679c\u306e\u8a08\u7b97<\/h2>\n\n\n\n
\u56fa\u5b9a\u52b9\u679c\u3068\u306f\u3001\u7814\u7a76\u306e\u7d50\u679c\u304c\u4f3c\u3066\u3044\u308b\u3068\u601d\u3048\u308b\u3068\u304d\u306b\u4f7f\u3048\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\u306b\u306f\u3001\u307e\u305a\u56fa\u5b9a\u52b9\u679c\u3067\u7d71\u5408\u3059\u308b\u3002<\/p>\n\n\n\n
# ----- fixed effects -----<\/span>\nw <-<\/span> 1<\/span>\/<\/span>se\/<\/span>se\nsw <-<\/span> sum<\/span>(<\/span>w)<\/span>\nadm <-<\/span> sum<\/span>(<\/span>ad*<\/span>w)<\/span>\/<\/span>sw\nadl <-<\/span> adm-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>sw)<\/span>\nadu <-<\/span> adm+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>sw)<\/span>\nq1 <-<\/span> sum<\/span>(<\/span>w*<\/span>(<\/span>ad-<\/span>adm)<\/span>^<\/span>2<\/span>)<\/span>\ndf1 <-<\/span> k-<\/span>1<\/span>\npval1 <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>q1,<\/span> df1)<\/span>\nq2 <-<\/span> adm^<\/span>2<\/span>*<\/span>sw\ndf2 <-<\/span> 1<\/span>\npval2 <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>q2,<\/span> df2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d71\u5408\u5e73\u5747\u5024\u5dee\u300195\uff05\u4fe1\u983c\u533a\u9593\u4e0b\u9650\u3001\u4e0a\u9650\u3092\u4e26\u3079\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u5747\u8cea\u6027\u306e\u691c\u5b9a\u3001\u6709\u610f\u6027\u306e\u691c\u5b9a\u306e\u5404p\u5024\u3092\u4e26\u3079\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u3042\u308b\u304c\u3001\u5747\u8cea\u6027\u306e\u691c\u5b9a\u306b\u95a2\u3057\u3066\u3082\u6709\u610f\u3001\u3064\u307e\u308a\u7570\u8cea\u6027\u3042\u308a\u306a\u306e\u3067\u3001\u5909\u91cf\u52b9\u679c\u3067\u7d71\u5408\u3059\u308b\u307b\u3046\u304c\u3088\u3055\u305d\u3046\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\uff12\u3000\u5909\u91cf\u52b9\u679c\u306e\u8a08\u7b97\uff08DerSimonian-Laird\u306e\u65b9\u6cd5\uff09<\/h2>\n\n\n\n
\u5909\u91cf\u52b9\u679c\u3068\u306f\u3001\u7814\u7a76\u540c\u58eb\u306b\u7121\u8996\u3067\u304d\u306a\u3044\u9055\u3044\uff08\u7570\u8cea\u6027\uff09\u304c\u3042\u308b\u3068\u304d\u306b\u4f7f\u3046\u65b9\u6cd5\u3002<\/p>\n\n\n\n
# ----- random effects -----<\/span>\ntau2 <-<\/span> (<\/span>q1-<\/span>(<\/span>k-<\/span>1<\/span>))<\/span>\/<\/span>(<\/span>sw-<\/span>sum<\/span>(<\/span>w*<\/span>w)<\/span>\/<\/span>sw)<\/span>\ntau2 <-<\/span> max<\/span>(<\/span>0<\/span>,<\/span> tau2)<\/span>\nwx <-<\/span> 1<\/span>\/<\/span>(<\/span>tau2+<\/span>se*<\/span>se)<\/span>\nswx <-<\/span> sum<\/span>(<\/span>wx)<\/span>\nadmx <-<\/span> sum<\/span>(<\/span>ad*<\/span>wx)<\/span>\/<\/span>swx\nadxl <-<\/span> admx-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swx)<\/span>\nadxu <-<\/span> admx+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swx)<\/span>\nqx2 <-<\/span> admx^<\/span>2<\/span>*<\/span>swx\npvalx2 <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>qx2,<\/span> df2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u5909\u91cf\u52b9\u679c\u306b\u3088\u308b\u7d71\u5408\u70b9\u63a8\u5b9a\u5024\u300195\uff05\u4fe1\u983c\u533a\u9593\u3092\u8868\u793a\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u6709\u610f\u6027\u306e\u691c\u5b9a\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\u306e\u30b0\u30e9\u30d5\u306b\u7d71\u5408\u5e73\u5747\u5024\u306895%\u4fe1\u983c\u533a\u9593\u3092\u66f8\u304d\u5165\u308c\u308b<\/h2>\n\n\n\n
\u5148\u307b\u3069\u306e\u30b0\u30e9\u30d5\u306b\u7d71\u5408\u5e73\u5747\u5024\u306895%\u4fe1\u983c\u533a\u9593\u3092\u66f8\u304d\u5165\u308c\u308b\u3002<\/p>\n\n\n\n
# ----- graph -----<\/span>\nx <-<\/span> c<\/span>(<\/span>adl,<\/span> adu)<\/span>\ny <-<\/span> c<\/span>(<\/span>-<\/span>1<\/span>,<\/span> -<\/span>1<\/span>)<\/span>\nlines<\/span>(<\/span>x,<\/span> y,<\/span> type=<\/span>\"b\"<\/span>)<\/span>\nx <-<\/span> c<\/span>(<\/span>adxl,<\/span> adxu)<\/span>\ny <-<\/span> c<\/span>(<\/span>-<\/span>2<\/span>,<\/span> -<\/span>2<\/span>)<\/span>\nlines<\/span>(<\/span>x,<\/span> y,<\/span> type=<\/span>\"b\"<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>c<\/span>(<\/span>adm,<\/span> admx),<\/span> lty=<\/span>2<\/span>)<\/span>\ntext<\/span>(<\/span>60<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"Combined: fixed\"<\/span>)<\/span>\ntext<\/span>(<\/span>60<\/span>,<\/span> -<\/span>2<\/span>,<\/span> \"Combined: random\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\u306e\u7d50\u679c\u3092\u51fa\u529b\u3059\u308b<\/h2>\n\n\n\n
\u3053\u3053\u307e\u3067\u3001\u9014\u4e2d\u9014\u4e2d\u3067\u7d50\u679c\u3092\u51fa\u529b\u3057\u3066\u304d\u305f\u304c\u3001\u4ee5\u4e0b\u306b\u307e\u3068\u3081\u3066\u51fa\u529b\u3059\u308b\u3002<\/p>\n\n\n\n
adFE, LL, UL\u306f\u3001\u56fa\u5b9a\u52b9\u679c\u306e\u7d71\u5408\u5e73\u5747\u5024\u306895%\u4fe1\u983c\u533a\u9593\u3001Q1, df1, p1\u306f\u5747\u8cea\u6027\u306e\u691c\u5b9a\uff08\u691c\u5b9a\u7d71\u8a08\u91cf\u3001\u81ea\u7531\u5ea6\u3001P\u5024\uff09\u3001Q2, df2, p2\u306f\u6709\u610f\u6027\u306e\u691c\u5b9a\uff08\u691c\u5b9a\u7d71\u8a08\u91cf\u3001\u81ea\u7531\u5ea6\u3001P\u5024\uff09\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
adDL, LL, UL\u306f\u5909\u91cf\u52b9\u679c\u306e\u7d71\u5408\u5e73\u5747\u5024\u306895%\u4fe1\u983c\u533a\u9593\u3001Q2DL, df2, p2DL \u306f\u5909\u91cf\u52b9\u679c\u306e\u6709\u610f\u6027\u306e\u691c\u5b9a\u3001tau2\u306f $ \\tau^2 $ \u306e\u63a8\u5b9a\u5024\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\u3092\u3088\u308a\u67d4\u8edf\u306a\u5909\u91cf\u30e2\u30c7\u30eb\u2015\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\uff08REML\uff09\u3067\u884c\u3046<\/h2>\n\n\n\n
\u5909\u91cf\u30e2\u30c7\u30eb\u306eDerSimonian-Laird\u306e\u65b9\u6cd5\u306f\u7c21\u4fbf\u306a\u65b9\u6cd5\u3060\u304c\u3001\u3088\u308a\u67d4\u8edf\u3067\u7406\u8ad6\u7684\u306b\u81ea\u7136\u306a\u65b9\u6cd5\u304c\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\uff08REML, restricted maximum likelihood estimator\uff09\u3060\u3002<\/p>\n\n\n\n
\u73fe\u4ee3\u306fPC\u3092\u4f7f\u3063\u3066\u53cd\u5fa9\u8a08\u7b97\u304c\u7c21\u5358\u306b\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u306e\u3067\u3001REML\u306e\u9069\u7528\u304c\u671b\u307e\u3057\u3044\u3002<\/p>\n\n\n\n
Newton-Raphson\u6cd5\u3092\u7528\u3044\u3066\u7e70\u308a\u8fd4\u3057\u53ce\u675f\u8a08\u7b97\u3067 $ \\tau^2 $ \u306e\u63a8\u5b9a\u5024\u3092\u6c42\u3081\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
# ----- REML method -----<\/span>\nintau <-<\/span> tau2\ntau <-<\/span> intau\n#<\/span>\nnrep <-<\/span> 10<\/span>\nnewt <-<\/span> 1<\/span>:<\/span>nrep\nfor<\/span> (<\/span>i in<\/span> 1<\/span>:<\/span>nrep){<\/span>\nwb <-<\/span> 1<\/span>\/<\/span>(<\/span>tau+<\/span>se*<\/span>se)<\/span>\nadmb <-<\/span> sum<\/span>(<\/span>ad*<\/span>wb)<\/span>\/<\/span>sum<\/span>(<\/span>wb)<\/span>\nqf <-<\/span> k\/<\/span>(<\/span>k-<\/span>1<\/span>)<\/span>*<\/span>(<\/span>ad-<\/span>admb)<\/span>^<\/span>2<\/span>-<\/span>se*<\/span>se\ndkx <-<\/span> (<\/span>-<\/span>1<\/span>*<\/span>sum<\/span>(<\/span>ad*<\/span>wb*<\/span>wb)<\/span>+<\/span>admb*<\/span>sum<\/span>(<\/span>wb*<\/span>wb))<\/span>\/<\/span>sum<\/span>(<\/span>wb)<\/span>\nqf2 <-<\/span> -<\/span>2<\/span>*<\/span>k\/<\/span>(<\/span>k-<\/span>1<\/span>)<\/span>*<\/span>(<\/span>ad-<\/span>admb)<\/span>*<\/span>dkx\nh <-<\/span> sum<\/span>(<\/span>wb*<\/span>wb*<\/span>(<\/span>qf-<\/span>tau))<\/span>\ndh <-<\/span> sum<\/span>(<\/span>-<\/span>2<\/span>*<\/span>wb*<\/span>wb*<\/span>wb*<\/span>(<\/span>qf-<\/span>tau)<\/span>+<\/span>wb*<\/span>wb*<\/span>(<\/span>qf2-<\/span>1<\/span>))<\/span>\nnewt[<\/span>i]<\/span> <-<\/span> tau -<\/span> h\/<\/span>dh\nrel <-<\/span> abs<\/span>((<\/span>newt[<\/span>i]<\/span>-<\/span>tau)<\/span>\/<\/span>tau)<\/span>\ntau <-<\/span> newt[<\/span>i]<\/span>\n}<\/span>\n# ----- \u7d71\u5408\u5024\u306e\u8a08\u7b97 \u6709\u610f\u6027\u306e\u691c\u5b9a -----<\/span>\nwg <-<\/span> 1<\/span>\/<\/span>(<\/span>tau+<\/span>se*<\/span>se)<\/span>\nswg <-<\/span> sum<\/span>(<\/span>wg)<\/span>\nadRM <-<\/span> sum<\/span>(<\/span>ad*<\/span>wg)<\/span>\/<\/span>swg\nadRMl <-<\/span> adRM-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swg)<\/span>\nadRMu <-<\/span> adRM+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swg)<\/span>\nqx2RM <-<\/span> adRM^<\/span>2<\/span>*<\/span>swg\npvalx2RM <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>qx2RM,<\/span> df2)<\/span>\ntau2 <-<\/span> tau\n# ----- \u7d71\u5408\u5024\u3092\u30b0\u30e9\u30d5\u306b\u66f8\u304d\u5165\u308c\u308b -----<\/span>\nx <-<\/span> c<\/span>(<\/span>adRMl,<\/span> adRMu)<\/span>\ny <-<\/span> c<\/span>(<\/span>-<\/span>3<\/span>,<\/span> -<\/span>3<\/span>)<\/span>\nlines<\/span>(<\/span>x,<\/span> y,<\/span> type=<\/span>\"b\"<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>adRM,<\/span> lty=<\/span>2<\/span>)<\/span>\ntext<\/span>(<\/span>60<\/span>,<\/span> -<\/span>3<\/span>,<\/span> \"Combined: REML\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
REML\u306e\u7d50\u679c\u3092\u30b0\u30e9\u30d5\u306b\u8db3\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306f\u3001\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
DerSimonian-Laird\u306e\u65b9\u6cd5\u3088\u308a\u3082\u3055\u3089\u306b95%\u4fe1\u983c\u533a\u9593\u304c\u5e83\u304c\u3063\u3066\u3044\u3066\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u306a\u304f\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u30e1\u30bf\u89e3\u6790\u3092 metafor \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3063\u3066\u884c\u3046\u65b9\u6cd5<\/h2>\n\n\n\n
R\u306emetafor \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3046\u3068\u7c21\u5358\u306b\u30e1\u30bf\u89e3\u6790\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u305f\u3042\u3068\u3001library() \u3067\u547c\u3073\u51fa\u3057\u3066\u304a\u304f\u3002<\/p>\n\n\n\n
install.packages<\/span>(<\/span>\"metafor\"<\/span>)<\/span> #1\u56de\u306e\u307f<\/span>\nlibrary<\/span>(<\/span>metafor)<\/span> #\u4f7f\u3046\u3068\u304d\u306b<\/span>\n<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u884c\u3046\u3002<\/p>\n\n\n\n
\u30dd\u30a4\u30f3\u30c8\u306f\u3001escalc()\u95a2\u6570\u3068rma.uni()\u95a2\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
# \u30c7\u30fc\u30bf\u518d\u63b2<\/span>\nn1 <-<\/span> c<\/span>(<\/span>155<\/span>,<\/span>31<\/span>,<\/span>75<\/span>,<\/span>18<\/span>,<\/span>8<\/span>,<\/span>57<\/span>,<\/span>34<\/span>,<\/span>110<\/span>,<\/span>60<\/span>)<\/span>\nm1 <-<\/span> c<\/span>(<\/span>55.0<\/span>,<\/span>27.0<\/span>,<\/span>64.0<\/span>,<\/span>66.0<\/span>,<\/span>14.0<\/span>,<\/span>19.0<\/span>,<\/span>52.0<\/span>,<\/span>21.0<\/span>,<\/span>30.0<\/span>)<\/span>\ns1 <-<\/span> c<\/span>(<\/span>47.0<\/span>,<\/span>7.0<\/span>,<\/span>17.0<\/span>,<\/span>20.0<\/span>,<\/span>8.0<\/span>,<\/span>7.0<\/span>,<\/span>45.0<\/span>,<\/span>16.0<\/span>,<\/span>27.0<\/span>)<\/span>\nn0 <-<\/span> c<\/span>(<\/span>156<\/span>,<\/span>32<\/span>,<\/span>71<\/span>,<\/span>18<\/span>,<\/span>13<\/span>,<\/span>52<\/span>,<\/span>33<\/span>,<\/span>183<\/span>,<\/span>52<\/span>)<\/span>\nm0 <-<\/span> c<\/span>(<\/span>75.0<\/span>,<\/span>29.0<\/span>,<\/span>119.0<\/span>,<\/span>137.0<\/span>,<\/span>18.0<\/span>,<\/span>18.0<\/span>,<\/span>41.0<\/span>,<\/span>31.0<\/span>,<\/span>23.0<\/span>)<\/span>\ns0 <-<\/span> c<\/span>(<\/span>64.0<\/span>,<\/span>4.0<\/span>,<\/span>29.0<\/span>,<\/span>48.0<\/span>,<\/span>11.0<\/span>,<\/span>4.0<\/span>,<\/span>34.0<\/span>,<\/span>27.0<\/span>,<\/span>20.0<\/span>)<\/span>\n# \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306b\u5909\u63db<\/span>\ndat <-<\/span> data.frame<\/span>(<\/span>m1,<\/span> s1,<\/span> n1,<\/span> m0,<\/span> s0,<\/span> n0)<\/span>\n# \u63a8\u5b9a\u5024\u3068\u5206\u6563\u306e\u8a08\u7b97<\/span>\ndat.escalc <-<\/span> escalc<\/span>(<\/span>measure=<\/span>\"MD\"<\/span>,<\/span> vtype=<\/span>\"HO\"<\/span>,<\/span>\nm1i=<\/span>m1,<\/span> sd1i=<\/span>s1,<\/span> n1i=<\/span>n1,<\/span>\nm2i=<\/span>m0,<\/span> sd2i=<\/span>s0,<\/span> n2i=<\/span>n0,<\/span>\ndata=<\/span>dat)<\/span>\n# \u7d71\u5408\u5024\u306e\u8a08\u7b97<\/span>\nres.reml <-<\/span> rma.uni<\/span>(<\/span>yi,<\/span> vi,<\/span> method=<\/span>\"REML\"<\/span>,<\/span>\ndata=<\/span>dat.escalc)<\/span>\nsummary<\/span>(<\/span>res.reml)<\/span>\n<\/code><\/pre>\n\n\n\n
escalc()\u95a2\u6570\u3067\u3001measure=”MD”\u3068\u3057\u3066\u3044\u308b\u3068\u3053\u308d\u304c\u5e73\u5747\u5024\u306e\u5dee (mean difference) \u306e\u7d71\u5408\u306b\u5411\u3051\u305f\u8a08\u7b97\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
vtype=”HO” \u306f\u3001\u5206\u6563\u5747\u4e00\u6027 homoscedasticity \u3092\u60f3\u5b9a\u3059\u308b\u305f\u3081\u306e\u6307\u5b9a\u3060\u3002<\/p>\n\n\n\n
\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\u3001\u5206\u6563\u5747\u4e00\u6027\u3092\u60f3\u5b9a\u3057\u306a\u3044\u65b9\u6cd5 vtype=”LS” \u3092\u7528\u3044\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u901a\u5e38\u3067\u306f\u3001\u6307\u5b9a\u305b\u305a\u3001\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u307e\u307e\u3067\u3088\u3044\u3002<\/p>\n\n\n\n
\u4eca\u56de\u306e\u8a18\u4e8b\u3067\u306f\u3001\u6a19\u6e96\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u304c\u5206\u6563\u5747\u4e00\u6027\u3092\u4eee\u5b9a\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u305d\u308c\u306b\u5408\u308f\u305b\u308b\u305f\u3081\u306b\u6307\u5b9a\u3057\u305f\u3002<\/p>\n\n\n\n
\u5404\u8a66\u9a13\u306b\u304a\u3051\u308b\uff12\u7fa4\u306e\u6a19\u6e96\u504f\u5dee\u3092\u5e73\u5747\u5024\u306e\u5dee\u306e\u6a19\u6e96\u504f\u5dee\u53ca\u3073\u6a19\u6e96\u8aa4\u5dee\u306b\u5909\u63db\u3059\u308b\u969b\u306b\u3001\u5206\u6563\u5747\u4e00\u6027\u3092\u60f3\u5b9a\u3057\u305f\u8a08\u7b97\u306b\u4ed5\u65b9\u3092\u3057\u3066\u3044\u308b\u3068\u3053\u308d\u306b\u7531\u6765\u3059\u308b\u3002<\/p>\n\n\n\n
\u7d71\u5408\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3060\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u4e0a\u8a18\u306eREML\u6cd5\u3067\u306e\u7d50\u679c\u3068\u82e5\u5e72\u7570\u306a\u308b\u3082\u306e\u306e\u3001\u307b\u307c\u540c\u69d8\u306e\u70b9\u63a8\u5b9a\u5024\u300195\uff05\u4fe1\u983c\u533a\u9593\u3001p\u5024\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u8a66\u9a13\u306e\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u304c\u5e73\u5747\u5024\u306e\u5dee\u306e\u691c\u5b9a\u3067\u3042\u308b\u8a66\u9a13\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u3092\u4e0b\u8a18\u5f15\u7528\u66f8\u7c4d\u306b\u6cbf\u3063\u3066\u5b9f\u65bd\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
\u56f3\u3092\u898b\u308b\u3068\u660e\u3089\u304b\u306b\u8a66\u9a13\u540c\u58eb\u304c\u5927\u304d\u304f\u7570\u306a\u3063\u3066\u3044\u3066\u3001\u7121\u8996\u3067\u304d\u306a\u3044\u5dee\u304c\u3042\u308b\u3068\u7406\u89e3\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u8a66\u9a13\u540c\u58eb\u306b\u7121\u8996\u3067\u304d\u306a\u3044\u5dee\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30eb\uff08REML\uff09\u3092\u4f7f\u3046\u3053\u3068\u304c\u671b\u307e\u3057\u3044\u3002<\/p>\n\n\n\n
\u5f15\u7528\u66f8\u7c4d<\/h2>\n\n\n\n
\u4e39\u5f8c\u654f\u90ce\u8457\u3000\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580<\/p>\n\n\n\n
3.2\u3000\u5e73\u5747\u5024\u3068\u6a19\u6e96\u504f\u5dee<\/p>\n\n\n\n
\"\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u2015\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5<\/a><\/figure>\n\n\n\n
<\/div>\n\n\n\n
\n
\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u2015\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u7d71\u5408\u3092\u3081\u3056\u3059\u7d71\u8a08\u624b\u6cd5 (\u533b\u5b66\u7d71\u8a08\u5b66\u30b7\u30ea\u30fc\u30ba)<\/a><\/p>\n