{"id":547,"date":"2018-07-08T14:29:42","date_gmt":"2018-07-08T05:29:42","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-integrate-odds-ratios-by-mantel-haenszel-method\/"},"modified":"2024-10-14T09:13:40","modified_gmt":"2024-10-14T00:13:40","slug":"how-to-integrate-odds-ratios-by-mantel-haenszel-method","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-integrate-odds-ratios-by-mantel-haenszel-method\/","title":{"rendered":"R \u3067\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u306e\u65b9\u6cd5\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\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\uff08Mantel-Haenszel\uff09\u306e\u65b9\u6cd5\u3067\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u306e\u89e3\u8aac\u3002<\/p>\n\n\n\n

\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u6cd5\u306f\u3001\uff12\uff58\uff12\u306e\u5206\u5272\u8868\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u3067\u3001\u5c64\u5225\u89e3\u6790\u306e\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306b\u5fdc\u7528\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n\n\n\n\n

\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u6cd5\u306e\u6e96\u5099<\/h2>\n\n\n\n

\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\u5206\u6790\u306e\u6e96\u5099\u3002<\/p>\n\n\n\n
\u4e0b\u56f3\u3068\u540c\u3058\u3088\u3046\u306b\u5909\u6570\u540d\u3092\u4f5c\u6210\u3002<\/p>\n\n\n\n
\u30aa\u30c3\u30ba\u6bd4\u306f\u3001$ \\frac{ad}{bc} $ \u3067\u8a08\u7b97\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n\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\nn1 <-<\/span> dat$<\/span>n1\nn0 <-<\/span> dat$<\/span>n0\nm1 <-<\/span> ai +<\/span> ci\nm0 <-<\/span> bi +<\/span> di\n<\/code><\/pre>\n\n\n\n
\u5404\u7814\u7a76\u306e\u30aa\u30c3\u30ba\u6bd4\u3001\u6a19\u6e96\u8aa4\u5dee\u3001\u5bfe\u6570\u30aa\u30c3\u30ba\u6bd4\u300195%\u4fe1\u983c\u533a\u9593\u4e0b\u9650\u30fb\u4e0a\u9650\u3001\u5404\u7814\u7a76\u306e\u91cd\u307f\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
or <-<\/span> ai*<\/span>di\/<\/span>bi\/<\/span>ci\nse <-<\/span> sqrt<\/span>(<\/span>tn\/<\/span>bi\/<\/span>ci)<\/span>\nlgor <-<\/span> log<\/span>(<\/span>or)<\/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>\nw <-<\/span> 1<\/span>\/<\/span>se\/<\/span>se\n<\/code><\/pre>\n\n\n\n
\u5404\u7814\u7a76\u306e\u30aa\u30c3\u30ba\u6bd4\u300195%\u4fe1\u983c\u533a\u9593\u3092\u4e26\u3079\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
><\/span> round<\/span>(<\/span>cbind<\/span>(<\/span>ORi=<\/span>or,<\/span> LLi=<\/span>low,<\/span> ULi=<\/span>upp),<\/span>4<\/span>)<\/span>\n        ORi    LLi    ULi\n[<\/span>1<\/span>,]<\/span> 1.0286<\/span> 0.1920<\/span> 5.5103<\/span>\n[<\/span>2<\/span>,]<\/span> 0.4766<\/span> 0.2211<\/span> 1.0274<\/span>\n[<\/span>3<\/span>,]<\/span> 0.5824<\/span> 0.2274<\/span> 1.4912<\/span>\n[<\/span>4<\/span>,]<\/span> 0.7818<\/span> 0.6064<\/span> 1.0079<\/span>\n[<\/span>5<\/span>,]<\/span> 1.0719<\/span> 0.6125<\/span> 1.8760<\/span>\n[<\/span>6<\/span>,]<\/span> 0.5576<\/span> 0.1789<\/span> 1.7377<\/span>\n[<\/span>7<\/span>,]<\/span> 0.5991<\/span> 0.4726<\/span> 0.7594<\/span>\n[<\/span>8<\/span>,]<\/span> 0.9244<\/span> 0.6241<\/span> 1.3692<\/span>\n[<\/span>9<\/span>,]<\/span> 0.6543<\/span> 0.4051<\/span> 1.0568<\/span>\n[<\/span>10<\/span>,]<\/span> 0.7155<\/span> 0.5799<\/span> 0.8826<\/span>\n[<\/span>11<\/span>,]<\/span> 0.8078<\/span> 0.5610<\/span> 1.1633<\/span>\n[<\/span>12<\/span>,]<\/span> 0.9618<\/span> 0.6162<\/span> 1.5015<\/span>\n[<\/span>13<\/span>,]<\/span> 0.5525<\/span> 0.2730<\/span> 1.1184<\/span>\n[<\/span>14<\/span>,]<\/span> 1.3252<\/span> 0.8614<\/span> 2.0387<\/span>\n[<\/span>15<\/span>,]<\/span> 0.7252<\/span> 0.4236<\/span> 1.2416<\/span>\n[<\/span>16<\/span>,]<\/span> 1.0558<\/span> 0.7349<\/span> 1.5169<\/span>\n[<\/span>17<\/span>,]<\/span> 0.4893<\/span> 0.2986<\/span> 0.8020<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u3092\u63a8\u5b9a\u3057\u3001\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306e95%\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
#----- Mantel-Haenszel Odds Ratio -----<\/span>\nmhor <-<\/span> sum<\/span>(<\/span>ai*<\/span>di\/<\/span>tn)<\/span>\/<\/span>sum<\/span>(<\/span>bi*<\/span>ci\/<\/span>tn)<\/span>\n#----- Variance of Mantel-Haenszel Odds Ratio -----<\/span>\nP <-<\/span> (<\/span>ai+<\/span>di)<\/span>\/<\/span>tn\nQ <-<\/span> (<\/span>bi+<\/span>ci)<\/span>\/<\/span>tn\nR <-<\/span> ai*<\/span>di\/<\/span>tn\nS <-<\/span> bi*<\/span>ci\/<\/span>tn\nmhv <-<\/span> (<\/span>sum<\/span>(<\/span>P*<\/span>R)<\/span>\/<\/span>sum<\/span>(<\/span>R)<\/span>^<\/span>2<\/span> +<\/span> sum<\/span>(<\/span>P*<\/span>S+<\/span>Q*<\/span>R)<\/span>\/<\/span>sum<\/span>(<\/span>R)<\/span>\/<\/span>sum<\/span>(<\/span>S)<\/span> +<\/span> sum<\/span>(<\/span>Q*<\/span>S)<\/span>\/<\/span>sum<\/span>(<\/span>S)<\/span>^<\/span>2<\/span>)<\/span>\/<\/span>2<\/span>\n#----- 95% confidence interval -----<\/span>\nmhorl <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>mhor)<\/span>-<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>mhv))<\/span>\nmhoru <-<\/span> exp<\/span>(<\/span>log<\/span>(<\/span>mhor)<\/span>+<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>mhv))<\/span>\nlist<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORmh=<\/span>mhor,<\/span> LL=<\/span>mhorl,<\/span> UL=<\/span>mhoru),<\/span>4<\/span>))<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306895%\u4fe1\u983c\u533a\u9593\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
><\/span> list<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>ORmh=<\/span>mhor,<\/span> LL=<\/span>mhorl,<\/span> UL=<\/span>mhoru),<\/span>4<\/span>))<\/span>\n1<\/span>\n  ORmh     LL     UL\n0.7816<\/span> 0.7058<\/span> 0.8655<\/span>\n<\/code><\/pre>\n\n\n\n
\u5747\u8cea\u6027\u306e\u691c\u5b9a\uff08\u91cd\u307f\u306f\u6f38\u8fd1\u5206\u6563\u6cd5\u3068\u540c\u3058\u8a08\u7b97\u65b9\u6cd5\uff09\u3001\u6709\u610f\u6027\u306e\u691c\u5b9a\uff08Peto\u306e\u65b9\u6cd5\u3068\u540c\u3058\uff09\u3092\u884c\u3046\u3002<\/p>\n\n\n\n
k <-<\/span> length<\/span>(<\/span>ai)<\/span>\nw1 <-<\/span> 1<\/span>\/<\/span>(<\/span>1<\/span>\/<\/span>ai+<\/span>1<\/span>\/<\/span>bi+<\/span>1<\/span>\/<\/span>ci+<\/span>1<\/span>\/<\/span>di)<\/span>\nq1 <-<\/span> sum<\/span>(<\/span>w1*<\/span>(<\/span>lgor-<\/span>log<\/span>(<\/span>mhor))<\/span>^<\/span>2<\/span>)<\/span>\ndf1 <-<\/span> k-<\/span>1<\/span>\npval1 <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>q1,<\/span> df1)<\/span>\no <-<\/span> ai\ne <-<\/span> (<\/span>ai+<\/span>bi)<\/span>*<\/span>(<\/span>ai+<\/span>ci)<\/span>\/<\/span>tn\nv <-<\/span> ((<\/span>ai+<\/span>bi)<\/span>*<\/span>(<\/span>ci+<\/span>di)<\/span>\/<\/span>tn)<\/span>*<\/span>((<\/span>ai+<\/span>ci)<\/span>*<\/span>(<\/span>bi+<\/span>di)<\/span>\/<\/span>tn)<\/span>\/<\/span>(<\/span>tn-<\/span>1<\/span>)<\/span>\nq2 <-<\/span> (<\/span>abs<\/span>(<\/span>sum<\/span>(<\/span>o-<\/span>e))<\/span>-<\/span>0.5<\/span>)<\/span>^<\/span>2<\/span>\/<\/span>sum<\/span>(<\/span>v)<\/span>\ndf2 <-<\/span> 1<\/span>\npval2 <-<\/span> 1<\/span>-<\/span>pchisq<\/span>(<\/span>q2,<\/span> df2)<\/span>\nlist<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>Q1=<\/span>q1,<\/span> df1=<\/span>df1,<\/span>P1=<\/span>pval1,<\/span> Q2=<\/span>q2,<\/span> df2=<\/span>df2,<\/span> P2=<\/span>pval2),<\/span>4<\/span>))<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
><\/span> list<\/span>(<\/span>round<\/span>(<\/span>c<\/span>(<\/span>Q1=<\/span>q1,<\/span> df1=<\/span>df1,<\/span>P1=<\/span>pval1,<\/span> Q2=<\/span>q2,<\/span> df2=<\/span>df2,<\/span> P2=<\/span>pval2),<\/span>4<\/span>))<\/span>\n1<\/span>\n     Q1     df1      P1      Q2     df2      P2\n21.4811<\/span> 16.0000<\/span>  0.1607<\/span> 22.2667<\/span>  1.0000<\/span>  0.0000<\/span>\n<\/code><\/pre>\n\n\n\n
\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u3067\u306e\u5747\u8cea\u6027\u306e\u691c\u5b9a\u306f\u3001\u6f38\u8fd1\u5206\u6563\u6cd5\u306e\u91cd\u307f\u3092\u4f7f\u3063\u305f\u4e0a\u8ff0\u306e\u65b9\u6cd5\u3088\u308a\u3082Breslow-Day\u691c\u5b9a\u306e\u307b\u3046\u304c\u9069\u5207\u3002<\/p>\n\n\n\n
DescTools\u30d1\u30c3\u30b1\u30fc\u30b8\u306e BreslowDayTest() \u3067\u5b9f\u65bd\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\uff12\uff58\uff12\u306e\u5206\u5272\u8868\u306e\u6e96\u5099\u304c\u624b\u9593\u304c\u304b\u304b\u308b\u3002<\/p>\n\n\n\n
array()\u3067\u6e96\u5099\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
all <-<\/span> c<\/span>(<\/span>0<\/span>,<\/span>0<\/span>,<\/span>0<\/span>,<\/span>0<\/span>)<\/span>\nfor<\/span> (<\/span>i in<\/span> 1<\/span>:<\/span>17<\/span>){<\/span>\nnew <-<\/span> c<\/span>(<\/span>ai[<\/span>i],<\/span> ci[<\/span>i],<\/span> bi[<\/span>i],<\/span> di[<\/span>i])<\/span>\nall <-<\/span> c<\/span>(<\/span>all,<\/span> new)<\/span>\n}<\/span>\nout <-<\/span> all[<\/span>5<\/span>:<\/span>72<\/span>]<\/span>\nout.bd <-<\/span> array<\/span>(<\/span>out,<\/span>\ndim=<\/span>c<\/span>(<\/span>2<\/span>,<\/span>2<\/span>,<\/span>17<\/span>),<\/span>\ndimnames=<\/span>list<\/span>(<\/span>exposure=<\/span>c<\/span>(<\/span>\"Beta brokade\"<\/span>,<\/span> \"Control\"<\/span>),<\/span>\nevent=<\/span>   c<\/span>(<\/span>\"Yes\"<\/span>,<\/span>\"No\"<\/span>),<\/span>\nsite=<\/span>    c<\/span>(<\/span>paste<\/span>(<\/span>\"site\"<\/span>,<\/span> 1<\/span>:<\/span>17<\/span>,<\/span> sep=<\/span>\"\"<\/span>))<\/span>\n)<\/span>\n)<\/span>\nlibrary<\/span>(<\/span>DescTools)<\/span>\nBreslowDayTest<\/span>(<\/span>out.bd)<\/span>\nBreslowDayTest<\/span>(<\/span>out.bd,<\/span> correct=<\/span>T<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
Breslow-Day\u691c\u5b9a\u306e\u7d50\u679c\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
\u9023\u7d9a\u6027\u88dc\u6b63\u306e\u6709\u7121\u3067\u306f\u7d50\u679c\u5909\u308f\u3089\u305a\u3002<\/p>\n\n\n\n
><\/span> BreslowDayTest<\/span>(<\/span>out.bd)<\/span>\nBreslow-<\/span>Day test on Homogeneity of Odds Ratios\ndata:<\/span>  out.bd\nX-<\/span>squared =<\/span> 21.714<\/span>,<\/span> df =<\/span> 16<\/span>,<\/span> p-<\/span>value =<\/span> 0.1527<\/span>\n><\/span> BreslowDayTest<\/span>(<\/span>out.bd,<\/span> correct=<\/span>T<\/span>)<\/span>\nBreslow-<\/span>Day Test on Homogeneity of Odds Ratios <\/span>(<\/span>with Tarone correction)<\/span>\ndata:<\/span>  out.bd\nX-<\/span>squared =<\/span> 21.714<\/span>,<\/span> df =<\/span> 16<\/span>,<\/span> p-<\/span>value =<\/span> 0.1527<\/span>\n<\/code><\/pre>\n\n\n\n
\u30aa\u30c3\u30ba\u6bd4\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u30b0\u30e9\u30d5\u8868\u793a<\/h2>\n\n\n\n
\u500b\u3005\u306e\u7814\u7a76\u306e\u30aa\u30c3\u30ba\u6bd495%\u4fe1\u983c\u533a\u9593\u306e\u30b0\u30e9\u30d5\u306b\u3001\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u306e\u65b9\u6cd5\u3067\u63a8\u5b9a\u3057\u305f\u3001\u7d71\u5408\u30aa\u30c3\u30ba\u6bd4\u306895%\u4fe1\u983c\u533a\u9593\u3092\u4e57\u305b\u3066\u56f3\u793a\u3059\u308b\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>2<\/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>\" Mantel-Haenszel 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>\nmhorx <-<\/span> c<\/span>(<\/span>mhorl,<\/span> mhoru)<\/span>\nmhory <-<\/span> c<\/span>(<\/span>-<\/span>1<\/span>,<\/span> -<\/span>1<\/span>)<\/span>\nlines<\/span>(<\/span>mhorx,<\/span> mhory,<\/span> type=<\/span>\"o\"<\/span>,<\/span> lty=<\/span>1<\/span>,<\/span> lwd=<\/span>2<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>c<\/span>(<\/span>mhor),<\/span> lty=<\/span>2<\/span>)<\/span>\nabline<\/span>(<\/span>v=<\/span>1<\/span>)<\/span>\ntext<\/span>(<\/span>0.3<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"Combined\"<\/span>)<\/span>\n<\/code><\/pre>\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>
\u30aa\u30c3\u30ba\u6bd4\u306e\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u3092metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u884c\u3046<\/h2>\n\n\n\n
metafor\u30d1\u30c3\u30b1\u30fc\u30b8\u306erma.mh()\u3092\u4f7f\u3063\u305f\u65b9\u6cd5\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>metafor)<\/span>\nrma.mh.res <-<\/span> rma.mh<\/span>(<\/span>ai=<\/span>a,<\/span> bi=<\/span>n1-<\/span>a,<\/span> ci=<\/span>c,<\/span> di=<\/span>n0-<\/span>c,<\/span> data=<\/span>dat)<\/span>\nrma.mh.res\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001estimate, ci.lb, ci.ub\u3002
\u5747\u8cea\u6027\u306e\u691c\u5b9a\u306f\u3001Test for Heterogeneity\u3002
\u6709\u610f\u6027\u306e\u691c\u5b9a\u306f\u3001Cochran-Mantel-Haenszel Test\u3002
Breslow-Day\u691c\u5b9a\u306f\u3001Tarone’s Test for Heterogeneity\u3002<\/p>\n\n\n\n
\u305d\u308c\u305e\u308c\u30c1\u30a7\u30c3\u30af\u3002<\/p>\n\n\n\n
><\/span> rma.mh.res\nFixed-<\/span>Effects Model <\/span>(<\/span>k =<\/span> 17<\/span>)<\/span>\nTest for<\/span> Heterogeneity:<\/span>\nQ<\/span>(<\/span>df =<\/span> 16<\/span>)<\/span> =<\/span> 21.4811<\/span>,<\/span> p-<\/span>val =<\/span> 0.1607<\/span>\nModel Results <\/span>(<\/span>log scale):<\/span>\nestimate      se     zval    pval    ci.lb    ci.ub\n-<\/span>0.2464<\/span>  0.0520<\/span>  -<\/span>4.7370<\/span>  <<\/span>.0001<\/span>  -<\/span>0.3484<\/span>  -<\/span>0.1445<\/span>\nModel Results <\/span>(<\/span>OR scale):<\/span>\nestimate   ci.lb   ci.ub\n0.7816<\/span>  0.7058<\/span>  0.8655<\/span>\nCochran-<\/span>Mantel-<\/span>Haenszel Test:<\/span>    CMH =<\/span> 22.2667<\/span>,<\/span> df =<\/span> 1<\/span>,<\/span>  p-<\/span>val <<\/span> 0.0001<\/span>\nTarone's Test for Heterogeneity: X^2 = 21.7143, df = 16, p-val = 0.1527<\/span>\n<\/code><\/pre>\n\n\n\n
\u30d5\u30a9\u30ec\u30b9\u30c8\u30d7\u30ed\u30c3\u30c8\u3092\u63cf\u304f\u306e\u3082\u7c21\u5358\u3002<\/p>\n\n\n\n
forest<\/span>(<\/span>rma.mh.res)<\/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
\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u306e\u65b9\u6cd5\u3067\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u305f\u3002<\/p>\n\n\n\n
\u3059\u3079\u3066\u306e\u8a66\u9a13\u3067\u3001\uff12\uff58\uff12\u306e\u5206\u5272\u8868\u304c\u5f97\u3089\u308c\u3066\u3001\u5747\u8cea\u6027\u306e\u691c\u5b9a\u3067\u3001\u4e0d\u5747\u8cea\u306e\u7d50\u8ad6\u304c\u3067\u306a\u3051\u308c\u3070\u3001\u30de\u30f3\u30c6\u30eb\u30fb\u30d8\u30f3\u30c4\u30a7\u30eb\u306e\u65b9\u6cd5\u304c\u304a\u3059\u3059\u3081\u3002<\/p>\n\n\n\n
\u305f\u3060\u3057\u3001\u4ea4\u7d61\u8981\u56e0\u3092\u8abf\u6574\u3057\u306a\u304f\u3066\u3044\u3044\u3001\u30e9\u30f3\u30c0\u30e0\u5272\u4ed8\u306e\u8a66\u9a13\u306b\u9650\u308b\u3002<\/p>\n\n\n\n
\u4ea4\u7d61\u8981\u56e0\u306e\u8abf\u6574\u304c\u5fc5\u8981\u306a\u89b3\u5bdf\u7814\u7a76\u3067\u306f\u3001\u8abf\u6574\u6e08\u307f\u30aa\u30c3\u30ba\u6bd4\u306895%\u4fe1\u983c\u533a\u9593\u304b\u3089\u6a19\u6e96\u8aa4\u5dee\u3092\u6c42\u3081\u3066\u3001\u6f38\u8fd1\u5206\u6563\u6cd5\u3067\u7d71\u5408\u3059\u308b\u306e\u304c\u3044\u3044\u3002<\/p>\n\n\n\n
\u95a2\u9023\u8a18\u4e8b<\/h2>\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 Peto \u306e\u65b9\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\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u7814\u7a76\u3067\u7b97\u51fa\u3055\u308c\u305f\u6570\u5024\u3092\u3001\u9069\u5207\u306b\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u3002 \u4e00\u3064\u4e00\u3064\u306e\u7814\u7a76\u3067\u306f\u3001\u691c\u51fa\u529b\u304c\u4e0d\u8db3\u3057\u3066\u3044\u305f\u3082\u306e\u304c\u3001\u7d71\u5408\u3059\u308b\u3053\u3068\u3067\u691c\u51fa\u529b\u3092\u5897\u3057\u3001\u7d71\u8a08\u5b66\u7684…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n
\t\t\t
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\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\u6f38\u8fd1\u5206\u6563\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\u30e1\u30bf\u30a2\u30ca\u30ea\u30b7\u30b9\u306e\u305f\u3081\u306b\u30aa\u30c3\u30ba\u6bd4\u3092\u7d71\u5408\u3057\u305f\u3044\u5834\u5408\u3067\u3001\u305d\u308c\u305e\u308c\u306e\u7814\u7a76\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u30aa\u30c3\u30ba\u6bd4\u306e\u5bfe\u6570\u304c\u6f38\u8fd1\u7684\u306b\u6b63\u898f\u8fd1\u4f3c\u3067\u304d\u308b\u3002 \u500b\u3005\u306e\u7814\u7a76\u306e\u30b5\u30f3\u30d7\u30eb\u30b5…<\/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
\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
3.1 \uff12\u00d7\uff12\u5206\u5272\u8868\u30003.1.3 Mantel-Haenszel\u306e\u65b9\u6cd5\u2015\u30aa\u30c3\u30ba\u6bd4
\u4ed8\u9332B.5\u3000\u30a2\u30eb\u30b4\u30ea\u30ba\u30e03.3 mhor.s<\/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