{"id":545,"date":"2018-07-13T08:27:15","date_gmt":"2018-07-12T23:27:15","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-integrate-odds-ratios-by-reml\/"},"modified":"2024-10-14T08:58:55","modified_gmt":"2024-10-13T23:58:55","slug":"how-to-integrate-odds-ratios-by-reml","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-integrate-odds-ratios-by-reml\/","title":{"rendered":"R \u3067\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf REML \u3067\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9"},"content":{"rendered":"\n

\u30aa\u30c3\u30ba\u6bd4\u3092\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf REML \u3067\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u306e\u89e3\u8aac\u3002<\/p>\n\n\n\n

R \u3067\u5b9f\u884c\u3059\u308b\u3002<\/p>\n\n\n\n\n\n\n\n

\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\u3067\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u610f\u5473<\/h2>\n\n\n\n

\u30aa\u30c3\u30ba\u6bd4\u306e\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3092\u3059\u308b\u3068\u304d\u306b\u3001\u5bfe\u6570\u3092\u53d6\u308b\u306e\u306f\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u4f3c\u3057\u305f\u5206\u5e03\u306b\u3057\u305f\u3044\u304b\u3089\u3060\u3002<\/p>\n\n\n\n

\u6f38\u8fd1\u7684\u6b63\u898f\u8fd1\u4f3c\u3068\u547c\u3076\u3002<\/p>\n\n\n\n

\u6f38\u8fd1\u7684\u6b63\u898f\u8fd1\u4f3c\u306e\u6761\u4ef6\u3067\u306f\u3001\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf Restricted Maximum Likelihood (REML) estimator \u304c\u7406\u8ad6\u7684\u306b\u81ea\u7136\u3067\u6027\u8cea\u304c\u3044\u3044\u3002<\/p>\n\n\n\n

\u3088\u308a\u67d4\u8edf\u306a\u5909\u91cf\u30e2\u30c7\u30eb\u3002<\/p>\n\n\n\n

\u30aa\u30c3\u30ba\u6bd4\u306e\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3092\u3059\u308b\u306b\u306f\u3053\u306e\u65b9\u6cd5\u304c\u6700\u3082\u9069\u5207\u3002<\/p>\n\n\n\n

\u53cd\u5fa9\u8a08\u7b97\u304c\u542b\u307e\u308c\u3066\u3044\u3066\u3001\u8907\u96d1\u306a\u305f\u3081\u306b\u3001\u7c21\u4fbf\u306a\u65b9\u6cd5 DerSimonian-Laird \u306e\u65b9\u6cd5\u304c\u3068\u3089\u308c\u3066\u3044\u305f\u3002<\/p>\n\n\n\n

DerSimonian-Laird \u306e\u65b9\u6cd5\u306f\u3001\u4ee5\u4e0b\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 DerSimonian-Laird \u6cd5\u3067\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9<\/a>\n\t\t\t\t\t\t\u5404\u7814\u7a76\u3067\u7121\u8996\u3067\u304d\u306a\u3044\u7570\u8cea\u6027\u304c\u3042\u308b\u5834\u5408\u3067\u3082\u3001\u9069\u5207\u306b\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3067\u304d\u308b\u65b9\u6cd5\u306e\u89e3\u8aac\u3002 \u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u30c7\u30fc\u30bf\u6e96\u5099 \u4f7f\u7528\u3059\u308b\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002 a <- c(3,7,5,102,…<\/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

\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u304c\u7c21\u5358\u306b\u4f7f\u3048\u308b\u4eca\u3084\u3001\u53cd\u5fa9\u8a08\u7b97\u306f\u96e3\u3057\u304f\u306a\u304f\u306a\u3063\u305f\u3002<\/p>\n\n\n\n

\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\u306e\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u3092\u6c42\u3081\u308b\u306b\u306f\uff1f<\/h2>\n\n\n\n

\u4f7f\u7528\u3059\u308b\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n

a <-<\/span> c<\/span>(<\/span>3<\/span>,<\/span>7<\/span>,<\/span>5<\/span>,<\/span>102<\/span>,<\/span>28<\/span>,<\/span>4<\/span>,<\/span>98<\/span>,<\/span>60<\/span>,<\/span>25<\/span>,<\/span>138<\/span>,<\/span>64<\/span>,<\/span>45<\/span>,<\/span>9<\/span>,<\/span>57<\/span>,<\/span>25<\/span>,<\/span>65<\/span>,<\/span>17<\/span>)<\/span>\nn1 <-<\/span> c<\/span>(<\/span>38<\/span>,<\/span>114<\/span>,<\/span>69<\/span>,<\/span>1533<\/span>,<\/span>355<\/span>,<\/span>59<\/span>,<\/span>945<\/span>,<\/span>632<\/span>,<\/span>278<\/span>,<\/span>1916<\/span>,<\/span>873<\/span>,<\/span>263<\/span>,<\/span>291<\/span>,<\/span>858<\/span>,<\/span>154<\/span>,<\/span>1195<\/span>,<\/span>298<\/span>)<\/span>\nc <-<\/span> c<\/span>(<\/span>3<\/span>,<\/span>14<\/span>,<\/span>11<\/span>,<\/span>127<\/span>,<\/span>27<\/span>,<\/span>6<\/span>,<\/span>152<\/span>,<\/span>48<\/span>,<\/span>37<\/span>,<\/span>188<\/span>,<\/span>52<\/span>,<\/span>47<\/span>,<\/span>16<\/span>,<\/span>45<\/span>,<\/span>31<\/span>,<\/span>62<\/span>,<\/span>34<\/span>)<\/span>\nn0 <-<\/span> c<\/span>(<\/span>39<\/span>,<\/span>116<\/span>,<\/span>93<\/span>,<\/span>1520<\/span>,<\/span>365<\/span>,<\/span>52<\/span>,<\/span>939<\/span>,<\/span>471<\/span>,<\/span>282<\/span>,<\/span>1921<\/span>,<\/span>583<\/span>,<\/span>266<\/span>,<\/span>293<\/span>,<\/span>883<\/span>,<\/span>147<\/span>,<\/span>1200<\/span>,<\/span>309<\/span>)<\/span>\ndat <-<\/span> data.frame<\/span>(<\/span>a,<\/span>n1,<\/span>c,<\/span>n0)<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u305a\u500b\u3005\u306e\u7814\u7a76\u306e\u30aa\u30c3\u30ba\u6bd4\u3068\u6a19\u6e96\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
ai <-<\/span> dat$<\/span>a\nbi <-<\/span> dat$<\/span>n1 -<\/span> dat$<\/span>a\nci <-<\/span> dat$<\/span>c\ndi <-<\/span> dat$<\/span>n0 -<\/span> dat$<\/span>c\ntn <-<\/span> dat$<\/span>n1 +<\/span> dat$<\/span>n0\nlgor <-<\/span> log<\/span>(<\/span>ai*<\/span>di\/<\/span>bi\/<\/span>ci)<\/span>\nse <-<\/span> sqrt<\/span>(<\/span>1<\/span>\/<\/span>ai+<\/span>1<\/span>\/<\/span>bi+<\/span>1<\/span>\/<\/span>ci+<\/span>1<\/span>\/<\/span>di)<\/span>\nlow <-<\/span> exp<\/span>(<\/span>lgor-<\/span>1.96<\/span>*<\/span>se)<\/span>\nupp <-<\/span> exp<\/span>(<\/span>lgor+<\/span>1.96<\/span>*<\/span>se)<\/span>\nround<\/span>(<\/span>cbind<\/span>(<\/span>ORi=<\/span>exp<\/span>(<\/span>lgor),<\/span> LLi=<\/span>low,<\/span> ULi=<\/span>upp),<\/span>4<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u56fa\u5b9a\u52b9\u679c\u30e2\u30c7\u30eb\u306e\u6f38\u8fd1\u5206\u6563\u6cd5\u3067\u7d71\u5408\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u5747\u8cea\u6027\u306e\u691c\u5b9aQ1\u3068\u6709\u610f\u6027\u306e\u691c\u5b9aQ2\u3092\u884c\u3046\u3002<\/p>\n\n\n\n
k <-<\/span> length<\/span>(<\/span>ai)<\/span>\n# --------------- fixed effects ---------------<\/span>\nw <-<\/span> 1<\/span>\/<\/span>se\/<\/span>se\nsw <-<\/span> sum<\/span>(<\/span>w)<\/span>\nvaror <-<\/span> exp<\/span>(<\/span>sum<\/span>(<\/span>lgor*<\/span>w)<\/span>\/<\/span>sw)<\/span>\nvarorl <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>varor)<\/span>-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>sw))<\/span>\nvaroru <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>varor)<\/span>+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>sw))<\/span>\nq1 <-<\/span> sum<\/span>(<\/span>w*<\/span>(<\/span>lgor-<\/span>log<\/span>(<\/span>varor))<\/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> log<\/span>(<\/span>varor)<\/span>^<\/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
\u5909\u91cf\u52b9\u679c\u30e2\u30c7\u30ebDerSimonian-Laird\u306e\u65b9\u6cd5\u3067\u3082\u7d71\u5408\u3057\u3066\u307f\u308b\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>\nvarord <-<\/span> exp<\/span>(<\/span>sum<\/span>(<\/span>lgor*<\/span>wx)<\/span>\/<\/span>swx)<\/span>\nvarordl <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>varord)<\/span>-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swx))<\/span>\nvarordu <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>varord)<\/span>+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swx))<\/span>\nqx2 <-<\/span> log<\/span>(<\/span>varord)<\/span>^<\/span>2<\/span>*<\/span>swx\ndfx2 <-<\/span> 1<\/span>\npvalx2 <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>qx2,<\/span> dfx2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cfREML estimator\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
DerSimonian-Laird\u306e\u65b9\u6cd5\u3067\u8a08\u7b97\u3055\u308c\u305f $ \\hat{\\tau}^2 $ \u3092\u521d\u671f\u5024\u306b\u3059\u308b\u3002<\/p>\n\n\n\n
# ----------- REML method -----------<\/span>\nintau <-<\/span> tau2\ntau <-<\/span> intau\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>\normb <-<\/span> exp<\/span>(<\/span>sum<\/span>(<\/span>lgor*<\/span>wb)<\/span>\/<\/span>sum<\/span>(<\/span>wb))<\/span>\nqf <-<\/span> k\/<\/span>(<\/span>k-<\/span>1<\/span>)<\/span>*<\/span>(<\/span>lgor-<\/span>log<\/span>(<\/span>ormb))<\/span>^<\/span>2<\/span>-<\/span>se*<\/span>se\ndkx <-<\/span> (<\/span>-<\/span>1<\/span>*<\/span>sum<\/span>(<\/span>lgor*<\/span>wb*<\/span>wb)<\/span>+<\/span>log<\/span>(<\/span>ormb)<\/span>*<\/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>lgor-<\/span>log<\/span>(<\/span>ormb))<\/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<\/code><\/pre>\n\n\n\n
$ \\hat{\\tau}^2 $ \u304c4\u56de\u76ee\u306e\u53cd\u5fa9\u8a08\u7b97\u3067\u53ce\u675f\u3057\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
><\/span> newt\n[<\/span>1<\/span>]<\/span> 0.02115981<\/span> 0.02206697<\/span> 0.02209898<\/span> 0.02209902<\/span> 0.02209902<\/span> 0.02209902<\/span> 0.02209902<\/span>\n[<\/span>8<\/span>]<\/span> 0.02209902<\/span> 0.02209902<\/span> 0.02209902<\/span>\n<\/code><\/pre>\n\n\n\n
\u53cd\u5fa9\u8a08\u7b97\u3067\u63a8\u5b9a\u3055\u308c\u305f $ \\hat{\\tau}^2 $ \u3092\u7528\u3044\u3066\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
wg <-<\/span> 1<\/span>\/<\/span>(<\/span>tau+<\/span>se*<\/span>se)<\/span>\nswg <-<\/span> sum<\/span>(<\/span>wg)<\/span>\norRM <-<\/span> exp<\/span>(<\/span>sum<\/span>(<\/span>lgor*<\/span>wg)<\/span>\/<\/span>swg)<\/span>\norRMl <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>orRM)<\/span>-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swg))<\/span>\norRMu <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>orRM)<\/span>+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>swg))<\/span>\nqx2RM <-<\/span> log<\/span>(<\/span>orRM)<\/span>^<\/span>2<\/span>*<\/span>swg\npvalx2RM <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>qx2RM,<\/span> dfx2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d71\u5408\u3057\u305f\u7d50\u679c3\u3064\u3092\u6bd4\u8f03\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
#----- Fixed Effect Variance-based -----<\/span>\nlist<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORv=<\/span>varor,<\/span> LL=<\/span>varorl,<\/span> UL=<\/span>varoru,<\/span> Q1=<\/span>q1,<\/span> df1=<\/span>df1,<\/span>\nP1=<\/span>pval1,<\/span> Q2=<\/span>q2,<\/span> df2=<\/span>df2,<\/span> P2=<\/span>pval2),<\/span>4<\/span>))<\/span>\n#----- Random Effect DerSimonian-Laird -----<\/span>\nlist<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORdl=<\/span>varord,<\/span> LL=<\/span>varordl,<\/span> UL=<\/span>varordu,<\/span> Q2dl=<\/span>qx2,<\/span>\ndf2dl=<\/span>dfx2,<\/span> P2dl=<\/span>pvalx2,<\/span> tau2=<\/span>tau2),<\/span>4<\/span>))<\/span>\n#----- Restricted Maximum Likelihood -----<\/span>\nlist<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORrm=<\/span>orRM,<\/span> LL=<\/span>orRMl,<\/span> UL=<\/span>orRMu,<\/span> Q2rm=<\/span>qx2RM,<\/span>\ndf2rm=<\/span>dfx2,<\/span> P2rm=<\/span>pvalx2RM,<\/span> tau2=<\/span>tau),<\/span> 4<\/span>))<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306e\u63a8\u5b9a\u5024\u306f\u3069\u308c\u3082\u4f3c\u901a\u3063\u3066\u3044\u308b\u304c\u3001\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\u306f95%\u4fe1\u983c\u533a\u9593\u304c\u82e5\u5e72\u5e83\u304f\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
><\/span> #----- Fixed Effect Variance-based -----<\/span>\n><\/span> list<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORv=<\/span>varor,<\/span> LL=<\/span>varorl,<\/span> UL=<\/span>varoru,<\/span> Q1=<\/span>q1,<\/span> df1=<\/span>df1,<\/span>\n+<\/span> P1=<\/span>pval1,<\/span> Q2=<\/span>q2,<\/span> df2=<\/span>df2,<\/span> P2=<\/span>pval2),<\/span>4<\/span>))<\/span>\n1<\/span>\n   ORv      LL      UL      Q1     df1      P1      Q2     df2      P2\n0.7831<\/span>  0.7067<\/span>  0.8677<\/span> 21.4798<\/span> 16.0000<\/span>  0.1608<\/span> 21.8063<\/span>  1.0000<\/span>  0.0000<\/span>\n><\/span>\n><\/span> #----- Random Effect DerSimonian-Laird -----<\/span>\n><\/span> list<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORdl=<\/span>varord,<\/span> LL=<\/span>varordl,<\/span> UL=<\/span>varordu,<\/span> Q2dl=<\/span>qx2,<\/span>\n+<\/span> df2dl=<\/span>dfx2,<\/span> P2dl=<\/span>pvalx2,<\/span> tau2=<\/span>tau2),<\/span>4<\/span>))<\/span>\n1<\/span>\n  ORdl      LL      UL    Q2dl   df2dl    P2dl    tau2\n0.7908<\/span>  0.6949<\/span>  0.8998<\/span> 12.6794<\/span>  1.0000<\/span>  0.0004<\/span>  0.0169<\/span>\n><\/span>\n><\/span> #----- Restricted Maximum Likelihood -----<\/span>\n><\/span> list<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORrm=<\/span>orRM,<\/span> LL=<\/span>orRMl,<\/span> UL=<\/span>orRMu,<\/span> Q2rm=<\/span>qx2RM,<\/span>\n+<\/span> df2rm=<\/span>dfx2,<\/span> P2rm=<\/span>pvalx2RM,<\/span> tau2=<\/span>tau),<\/span> 4<\/span>))<\/span>\n1<\/span>\n  ORrm      LL      UL    Q2rm   df2rm    P2rm    tau2\n0.7910<\/span>  0.6906<\/span>  0.9060<\/span> 11.4700<\/span>  1.0000<\/span>  0.0007<\/span>  0.0221<\/span>\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>
\u500b\u3005\u306e\u7814\u7a76\u3068\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306e\u30d5\u30a9\u30ec\u30b9\u30c8\u30d7\u30ed\u30c3\u30c8\u3092\u63cf\u304f<\/h2>\n\n\n\n
\u500b\u3005\u306e\u7814\u7a76\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u3001\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306895%\u4fe1\u983c\u533a\u9593\u3092\u63cf\u304f\u3002<\/p>\n\n\n\n
\u6f38\u8fd1\u5206\u6563\u6cd5\u3001DerSimonian-Laird\u306e\u65b9\u6cd5\u3001\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\u306e3\u3064\u3002<\/p>\n\n\n\n
# ------------- individual graph ----------------<\/span>\nid <-<\/span> k:<\/span>1<\/span>\nplot<\/span>(<\/span>exp<\/span>(<\/span>lgor),<\/span> id,<\/span> ylim=<\/span>c<\/span>(<\/span>-<\/span>4<\/span>,<\/span>20<\/span>),<\/span>\nlog=<\/span>\"x\"<\/span>,<\/span> xlim=<\/span>c<\/span>(<\/span>0.1<\/span>,<\/span>10<\/span>),<\/span> yaxt=<\/span>\"n\"<\/span>,<\/span> pch=<\/span>\"\"<\/span>,<\/span>\nylab=<\/span>\"Citation\"<\/span>,<\/span> xlab=<\/span>\"Odds ratio\"<\/span>)<\/span>\ntitle<\/span>(<\/span>main=<\/span>\" Variance-based method \"<\/span>)<\/span>\nsymbols<\/span>(<\/span>exp<\/span>(<\/span>lgor),<\/span> id,<\/span> squares=<\/span>sqrt<\/span>(<\/span>tn),<\/span>\nadd=<\/span>TRUE<\/span>,<\/span> inches=<\/span>0.25<\/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>0.1<\/span>,<\/span> i,<\/span> j)<\/span>\n}<\/span>\n# -------------- Combined graph --------------<\/span>\nvarorx <-<\/span> c<\/span>(<\/span>varorl,<\/span> varoru)<\/span>\nvarory <-<\/span> c<\/span>(<\/span>-<\/span>1<\/span>,<\/span> -<\/span>1<\/span>)<\/span>\nlines<\/span>(<\/span>varorx,<\/span> varory,<\/span> type=<\/span>\"o\"<\/span>,<\/span> lty=<\/span>1<\/span>,<\/span> lwd=<\/span>2<\/span>)<\/span>\nvarordx <-<\/span> c<\/span>(<\/span>varordl,<\/span> varordu)<\/span>\nvarordy <-<\/span> c<\/span>(<\/span>-<\/span>2<\/span>,<\/span> -<\/span>2<\/span>)<\/span>\nlines<\/span>(<\/span>varordx,<\/span> varordy,<\/span> type=<\/span>\"o\"<\/span>,<\/span> lty=<\/span>1<\/span>,<\/span> lwd=<\/span>2<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>c<\/span>(<\/span>varor,<\/span> varord),<\/span> lty=<\/span>2<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>1<\/span>)<\/span>\ntext<\/span>(<\/span>0.2<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"Combined:fixed\"<\/span>)<\/span>\ntext<\/span>(<\/span>0.2<\/span>,<\/span> -<\/span>2<\/span>,<\/span> \"Combined:random\"<\/span>)<\/span>\norRMx <-<\/span> c<\/span>(<\/span>orRMl,<\/span> orRMu)<\/span>\norRMy <-<\/span> c<\/span>(<\/span>-<\/span>3<\/span>,<\/span> -<\/span>3<\/span>)<\/span>\nlines<\/span>(<\/span>orRMx,<\/span> orRMy,<\/span> type=<\/span>\"o\"<\/span>,<\/span> lty=<\/span>1<\/span>,<\/span> lwd=<\/span>2<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>c<\/span>(<\/span>varor,<\/span> varord,<\/span> orRM),<\/span> lty=<\/span>2<\/span>)<\/span>\ntext<\/span>(<\/span>0.2<\/span>,<\/span> -<\/span>3<\/span>,<\/span> \"Combined:REML\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3046\u3068\u3069\u3046\u306a\u308b\u304b\uff1f<\/h2>\n\n\n\n
metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3063\u3066REML\u3092\u3084\u3063\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
escalc()\u3067\u63a8\u5b9a\u5024 esitimate\u3068\u5206\u6563 variance\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
measure\u306f\u6307\u6a19\u3068\u3059\u308b\u6570\u5024\u3002\u4eca\u56de\u306f\u30aa\u30c3\u30ba\u6bd4\u3002<\/p>\n\n\n\n
yi\u306f\u63a8\u5b9a\u5024\u3001vi\u306f\u5206\u6563\u3002<\/p>\n\n\n\n
rma.uni()\u3067\u3001method=”REML”\u3067\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\u306e\u8a08\u7b97\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>metafor)<\/span>\ndat.escalc <-<\/span> escalc<\/span>(<\/span>measure=<\/span>\"OR\"<\/span>,<\/span> ai=<\/span>a,<\/span> n1i=<\/span>n1,<\/span> ci=<\/span>c,<\/span> n2i=<\/span>n0,<\/span> data=<\/span>dat)<\/span>\nres.reml <-<\/span> rma.uni<\/span>(<\/span>yi,<\/span> vi,<\/span> method=<\/span>\"REML\"<\/span>,<\/span> data=<\/span>dat.escalc,<\/span> control=<\/span>list<\/span>(<\/span>verbose=<\/span>T<\/span>,<\/span> tau2.init=<\/span>tau2))<\/span>\nsummary<\/span>(<\/span>res.reml)<\/span>\nround<\/span>(<\/span>exp<\/span>(<\/span>c<\/span>(<\/span>ORrm=<\/span>res.reml$<\/span>b,<\/span> LLrm=<\/span>res.reml$<\/span>ci.lb,<\/span> ULrm=<\/span>res.reml$<\/span>ci.ub)),<\/span>4<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u63a8\u5b9a\u7d50\u679c\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
><\/span> res.reml <-<\/span> rma.uni<\/span>(<\/span>yi,<\/span> vi,<\/span> method=<\/span>\"REML\"<\/span>,<\/span> data=<\/span>dat.escalc,<\/span> control=<\/span>list<\/span>(<\/span>verbose=<\/span>T<\/span>,<\/span> tau2.init=<\/span>tau2))<\/span>\nIteration 0<\/span>     tau^<\/span>2<\/span> =<\/span> 0.0169<\/span>\nIteration 1<\/span>     tau^<\/span>2<\/span> =<\/span> 0.0235<\/span>\nIteration 2<\/span>     tau^<\/span>2<\/span> =<\/span> 0.0237<\/span>\nIteration 3<\/span>     tau^<\/span>2<\/span> =<\/span> 0.0237<\/span>\nFisher scoring algorithm converged after 3<\/span> iterations.\n><\/span>\n><\/span> summary<\/span>(<\/span>res.reml)<\/span>\nRandom-<\/span>Effects Model <\/span>(<\/span>k =<\/span> 17<\/span>;<\/span> tau^<\/span>2<\/span> estimator:<\/span> REML)<\/span>\nlogLik  deviance       AIC       BIC      AICc\n-<\/span>4.3260<\/span>    8.6519<\/span>   12.6519<\/span>   14.1971<\/span>   13.5750<\/span>\ntau^<\/span>2 <\/span>(<\/span>estimated amount of total heterogeneity):<\/span> 0.0237 <\/span>(<\/span>SE =<\/span> 0.0257<\/span>)<\/span>\ntau <\/span>(<\/span>square root of estimated tau^<\/span>2<\/span> value):<\/span>      0.1540<\/span>\nI^<\/span>2 <\/span>(<\/span>total heterogeneity \/<\/span> total variability):<\/span>   32.51<\/span>%\nH^<\/span>2 <\/span>(<\/span>total variability \/<\/span> sampling variability):<\/span>  1.48<\/span>\nTest for<\/span> Heterogeneity:<\/span>\nQ<\/span>(<\/span>df =<\/span> 16<\/span>)<\/span> =<\/span> 21.4798<\/span>,<\/span> p-<\/span>val =<\/span> 0.1608<\/span>\nModel Results:<\/span>\nestimate      se     zval    pval    ci.lb    ci.ub\n-<\/span>0.2345<\/span>  0.0702<\/span>  -<\/span>3.3404<\/span>  0.0008<\/span>  -<\/span>0.3720<\/span>  -<\/span>0.0969<\/span>  ***<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n><\/span>\n><\/span> round<\/span>(<\/span>exp<\/span>(<\/span>c<\/span>(<\/span>ORrm=<\/span>res.reml$<\/span>b,<\/span> LLrm=<\/span>res.reml$<\/span>ci.lb,<\/span> ULrm=<\/span>res.reml$<\/span>ci.ub)),<\/span>4<\/span>)<\/span>\nORrm   LLrm   ULrm\n0.7910<\/span> 0.6893<\/span> 0.9077<\/span>\n<\/code><\/pre>\n\n\n\n
\u53c2\u8003\u66f8\u7c4d \u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u306e\u7d50\u679c\u3068\u4fe1\u983c\u533a\u9593\u306e\u4e0a\u9650\u4e0b\u9650\u304c\u82e5\u5e72\u7570\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
$ \\hat{\\tau}^2 $ \u306e\u521d\u671f\u5024\u3092\u5408\u308f\u305b\u3066\u307f\u305f\u304c\u3001\u89e3\u6c7a\u3057\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n
\u307b\u3093\u306e\u5c11\u3057\u306e\u9055\u3044\u306a\u306e\u3067\u3001\u554f\u984c\u306b\u3059\u308b\u3053\u3068\u306f\u306a\u3044\u3068\u8003\u3048\u308b\u3002<\/p>\n\n\n\n
metafor \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u7528\u3057\u305f\u7d50\u679c\u3092\u4f7f\u3048\u3070\u3088\u3044\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001\u30d5\u30a9\u30ec\u30b9\u30c8\u30d7\u30ed\u30c3\u30c8\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
forest<\/span>(<\/span>res.reml)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u3088\u308a\u67d4\u8edf\u306a\u5909\u91cf\u30e2\u30c7\u30eb\u3001\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf\uff08REML\uff09\u3092 R \u3067\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u305f\u3002<\/p>\n\n\n\n
metafor \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3059\u308b\u306e\u304c\u826f\u3044\u3002<\/p>\n\n\n\n
\u53c2\u8003\u306b\u306a\u308c\u3070\u3002<\/p>\n\n\n\n
\u53c2\u8003\u66f8\u7c4d<\/h2>\n\n\n\n
\u4e39\u5f8c\u4fca\u90ce\u8457\u3000\u30e1\u30bf\u30fb\u30a2\u30ca\u30ea\u30b7\u30b9\u5165\u9580\u3000\u671d\u5009\u66f8\u5e97
5.1 \u3088\u308a\u67d4\u8edf\u306a\u5909\u91cf\u30e2\u30c7\u30eb\u2015\u5236\u9650\u4ed8\u304d\u6700\u5c24\u63a8\u5b9a\u91cf
5.3.1 \u03b2\u30d6\u30ed\u30c3\u30ab\u30fc\u306e\u81e8\u5e8a\u8a66\u9a13\u2015\u30aa\u30c3\u30ba\u6bd4
\u4ed8\u9332B.10 varorRM.s: varor.s + REML for odds ratio<\/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