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1 R Network Meta-Analysis
2 R Network Meta-Analysis homogeneity consistency Ranking Network Meta-Analysis(homogeneity) (consistency) Ranking 1
3 Network Meta-Analysis Network Meta-Analysis P Ranking R Bayesian Network Meta-Analysis 2
4 Network Meta-Analysis Meta-Analysis 2 Network Meta-Analysis Multiple Treatments Comparison Mixed Treatments Comparison 3 3
5 Network Meta-Analysis Network Meta-Analysis Meta-Analysis Network Meta-Analysis I. II. homogeneity consistency III. IV I II R 4
6 Network Meta-Analysis Network Meta-Analysis Network Meta-Analysis 3 multi-arm study Network A vs. B A vs. C B vs. C + A vs. D A B C D 5
7 Network Meta-Analysis Incomplete Block Design Sequence Incomplete Block Design IBD Period A B Patient 11,...,1n 1 2 B A Patient 21,...,2n 2 3 C B Patient 31,...,3n 3 4 B C Patient 41,...,4n 4 Network Meta-Analysis NMA 1: A vs. B Study 11,...,1n 1 IBD A B B C A C B A C GLM MIXED A 2: B vs. C Study 21,...,2n 2 B C 6
8 Network Meta-Analysis Incomplete Block Design Network Meta-Analysis NMA Incomplete Block Design IBD Senn et al IBD Sequence Sequence NMA IBD 1 NMA IBD NMA transitivity consistency 7
9 Network Meta-Analysis Network Meta-Analysis homogeneity consistency Ranking Bayesian Network Meta-Analysis B Treatment Mean Diff. 95% CI A D A B C D [-1.94; -1.57] [-0.61; -0.19] [-1.15; -0.74] C
10 Network Meta-Analysis homogeneity heterogeneity transitivity similarity Network Meta-Analysis Network Meta-Analysis effect modifier consistency Network Meta-Analysis consistency inconsistency 9 Caldwell (2014) Krahn (2013)
11 Network Meta-Analysis Network Meta-Analysis P Ranking R Bayesian Network Meta-Analysis 10
12 Senn2013 Senn et al. (2013) Senn et al. (2013) multi-arm study 1 10 acarbose benfluorex metformin miglitol pioglitazone rosiglitazone sitagliptin sulfonylurea alone vildagliptin placebo HbA1c % Senn2013 studlab treat1 1 treat2 2 TE HbA1c % TREAT1 TREAT2 sete TE 11
13 Senn2013 metf 1 benf migl 1 1 acar piog vild plac 2 1 sulf 6 rosi 1 sita multi-arm Willms
14 Senn2013 TE sete treat1 treat2 studlab metf sulf Alex rosi plac Baksi acar plac Costa rosi plac Davidson metf plac DeFronzo piog rosi Derosa vild plac Garber metf plac Gonzalez-Ortiz piog metf Hanefeld sita plac Hermansen migl plac Johnston migl plac Johnston1998a migl plac Johnston1998b rosi plac Kerenyi rosi metf Kim piog plac Kipnes metf plac Lewin benf plac Moulin acar sulf Oyama rosi plac Rosenstock benf plac Stucci rosi sulf Vongthavaravat acar metf Willms metf plac Willms acar plac Willms rosi plac Wolffenbuttel rosi metf Yang rosi plac Zhu
15 Senn2013 ID TE sete treat1 treat2 studlab s d metf sulf Alex acar plac Costa metf plac DeFronzo metf plac Gonzalez-Ortiz acar metf Willms metf plac Willms acar plac Willms acar metf sulf Senn metf vs. plac 3 multi-arm 1 3 ID=5 plac 14
16 Network Meta-Analysis 1 2 metf acar sulf plac metf % [-1.10, -0.43] % [-0.60, -0.14] % [-1.88, -1.40] acar 0.76 % [ 0.42, 1.10] 0.39 % [-0.02, 0.80] % [-1.14, -0.62] sulf 0.37 % [ 0.14, 0.60] % [-0.80, 0.02] % [-1.61, -0.94] plac 1.64 % [ 1.40, 1.88] 0.88 % [ 0.62, 1.14] 1.27 % [ 0.94, 1.61] Treatment metf acar sulf plac Mean Diff % -0.88% -1.27% 95% CI [-1.88, -1.40] [-1.14, -0.62] [-1.61, -0.94] [95%, 95% ]
17 Network Meta-Analysis, Cov, diag,,,,, plac 1,,5 1,,4 metf acar sulf V 1 V 4 V 5 Y 1 Y 4 Y 5 Willms metf acar plac M A P ID=6 SETE Var(M-P) = Var(M) + Var(P) - 2Cov(M,P) ID=5 ID=7 Cov(M-P, A-P) = Cov(M,A) Cov(M,P) Cov(P,A) +Var(P) 16
18 Network Meta-Analysis 1-step Network Estimate: 1.64, 0.88, step metf acar sulf, Cov Direct Estimate:,,,, Cov, diag,,, Network Estimate: 1.64, 0.88, 1.27 X 1 X 3 X 4 17
19 Network Meta-Analysis,Cov,,Cov 1,,5 1,,4 DerSimonian and Laird Cov 18 multi-arm τ /2 ID=5(acar vs. metf)
20 homogeneity consistency heterogeneity Within-designs Q statistic, inconsistency Between-designs Q statistic, / heterogeneity
21 P Ranking Cov( ) Ranking metf metformin P 1. metf p,,,, 2. P : 1, metf metformin P Ranking P P Bayesian Network Meta-Analysis SUCRA Surface Under the Cumulative RAnking 20 Rucker G and Schwarzer G (2015)
22 Network Meta-Analysis > # 1-step > y <- matrix(c(-0.37, -0.8, -1.9, -0.4, -1.2, -1), ncol=1) > X <- matrix(c(1, 0, -1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0), ncol=3, by=t) > V <- matrix(c( , 0, 0, 0, 0, 0, + 0, , 0, 0, 0, 0, + 0, 0, , 0, 0, 0, + 0, 0, 0, , 0, 0, + 0, 0, 0, 0, , , + 0, 0, 0, 0, , ), ncol=6, by=t) > ( theta <- solve(t(x) %*% solve(v) %*% X) %*% t(x) %*% solve(v) %*% y ) [,1] [1,] [2,] [3,] > ( Cov <- solve(t(x) %*% solve(v) %*% X) ) [,1] [,2] [,3] [1,] [2,] [3,] > ( theta_ci <- cbind(theta-qnorm(0.975)*sqrt(diag(cov)), + theta+qnorm(0.975)*sqrt(diag(cov))) ) [,1] [,2] [1,] [2,] [3,]
23 Network Meta-Analysis > # 2-step > theta_dir <- matrix(rep(0, 5), ncol=1) > Xa <- X[c(1, 2, 3, 5, 6),] > Va <- matrix(rep(0,25), ncol=5) > theta_dir[1,1] <- sum(solve(v[1,1]) %*% y[1]) * V[1,1]; Va[1,1] <- V[1,1] > theta_dir[2,1] <- sum(solve(v[2,2]) %*% y[2]) * V[2,2]; Va[2,2] <- V[2,2] > theta_dir[3,1] <- sum(solve(v[3:4,3:4]) %*% y[3:4]) / sum(diag(solve(v[3:4,3:4]))) > Va[3,3] <- 1/sum(diag(solve(V[3:4,3:4]))) > theta_dir[4:5,1] <- y[5:6]; Va[4:5,4:5] <- V[5:6,5:6] > ( theta_a <- solve(t(xa) %*% solve(va) %*% Xa) %*% t(xa) %*% solve(va) %*% theta_dir ) [,1] [1,] [2,] [3,] > ( Cov_a <- solve(t(xa) %*% solve(va) %*% Xa) ) [,1] [,2] [,3] [1,] [2,] [3,] > ( theta_ci_a <- cbind(theta-qnorm(0.975)*sqrt(diag(cov_a)), + theta+qnorm(0.975)*sqrt(diag(cov_a))) ) [,1] [,2] [1,] [2,] [3,]
24 Network Meta-Analysis > # Qnet, Qhet, Qinc > ( Q_net <- t(y - X %*% theta) %*% solve(v) %*% (y-x %*% theta) ) [,1] [1,] > ( Q_inc <- t(theta_dir - Xa %*% theta_a) %*% solve(va) %*% (theta_dir - Xa %*% theta_a) ) [,1] [1,] > ( Q_het <- Q_net - Q_inc ) [,1] [1,] > # P score for metf > CC <- -1*diag(3); CC[,1] = 1; E <- CC %*% theta; z <- rep(0,3) > for (i in 1:3) { + c <- CC[i,,drop=F] + z[i] <- sqrt(t(c %*% theta) %*% solve(c %*% Cov %*% t(c)) %*% (c %*% theta)) + if (E[i] < 0) z[i] <- -1*z[i] + } > p_metf <- 1-(pnorm(z)) > ( pscore_metf <- mean(p_metf) ) [1]
25 inconsistency Detaching a single design inconsistency Krahn 2013 Detaching a single design, 1, 0, Cov 1 0 detach, 24
26 inconsistency Detaching a single design,,,,,,,,,,,, 0,,,,, 0 inconsistency, 0 inconsistency 25
27 inconsistency network estimate plac:metf_ plac:acar:metf plac:acar plac:metf plac:acar_ plac:acar:metf plac:metf_ plac:acar:metf direct estimate plac:acar plac:metf plac:acar_ plac:acar:metf (inconsistency) direct estimate network estimate Network estimate 26
28 inconsistency plac:metf_ plac:acar:metf Detach plac:acar plac:metf plac:acar_ plac:acar:metf Detach plac:metf_ plac:acar:metf plac:acar plac:metf plac:acar_ plac:acar:metf = inconsistent evidence = supportive evidence 27
29 inconsistency Detach plac:metf_ plac:acar:metf plac:acar plac:metf plac:acar_ plac:acar:metf plac:metf_ plac:acar:metf Detach plac:acar plac:metf plac:acar_ plac:acar:metf multi-arm metf vs. plac inconsistency metf vs. plac network estimate direct estimate metf vs. plac 3 2-arm 2 metf vs. plac 3 inconsistency 28
30 Network Meta-Analysis Network Meta-Analysis P Ranking R Bayesian Network Meta-Analysis 29
31 Network Meta-Analysis netmeta() netmeta(te, sete, treat1, treat2, studlab, data=senn2013, sm, level=0.95, level.comb=0.95, comb.fixed=true, comb.random=true, reference="", seq=null, title="",...) data TE sete treat1 treat2 studlab sm TE RD Risk Difference RR Risk Ratio OR Odds Ratio MD Mean Difference SMD Standardized Mean Difference IRR Incidence Rate Ratio IRD Incidence Rate Difference level level.comb pooled estimate comb.fixed comb.random reference reference="plac" seq title 30
32 Network Meta-Analysis # install.packages("netmeta", dep=t) library(netmeta) data(senn2013) options(width=1000) x <- netmeta(te, sete, treat1, treat2, studlab, data=senn2013, sm="md", comb.fixed=true, comb.random=true) d1 <- decomp.design(x) # Q d2 <- netmeta:::decomp.tau(x, tau=x$tau) # Q r2 <- netrank(x, small="good") # P forest(x, pooled='fixed') # Forest Plot() forest(x, pooled='random') # Forest Plot() netgraph(x, thickness='se.fixed'); title('fixed Effect Model') # () netgraph(x, thickness='se.random'); title('random Effect Model') # () netheat(x, random=f); mtext('fixed Effect Model', 1, 1, cex=1.8) # Heatmap ( ) netheat(x,random=t,tau=x$tau); mtext('random Effect Model',1,1,cex=1.8) #( ) x$te.random <- x$te.fixed; x$pval.random <- x$pval.fixed r1 <- netrank(x, small="good") # P ( small="good" or "bad" 31
33 Network Meta-Analysis x$te.fixed x$lower.fixed x$upper.fixed x$te.random x$lower.random x$upper.random d1$q.decomp Q homogeneity / consistency d1$q.het.design Design-specific decomposition of within-designs Q statistic d1$q.inc.detach Between-designs Q statistic after detaching of single designs d1$xxx 3 d2$q.decomp d2$q.het.design d2$q.inc.detach Q r1$pscore r2$pscore Network Ranking / 32
34 Network Meta-Analysis x <- netmeta(te, sete, treat1, treat2, studlab, data=senn2013, sm="md", comb.fixed=true, comb.random=true, reference="plac", seq=c('plac', 'acar', 'benf', 'metf', 'migl', 'piog','rosi', 'sita', 'sulf', 'vild')) # reference reference="plac" seq 33
35 Network Meta-Analysis > x$te.fixed # acar benf metf migl piog plac rosi sita sulf vild acar benf metf migl piog plac rosi sita sulf vild > x$lower.fixed # acar benf metf migl piog plac rosi sita sulf vild acar benf metf migl piog plac rosi sita sulf vild > r2$pscore # P acar benf metf migl piog plac rosi sita sulf vild
36 Network Meta-Analysis metf:sulf rosi:sulf metf:piog plac:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar_plac:acar:metf plac:metf_plac:acar:metf acar:sulf plac:acar Forest Plot 35 metf:sulf rosi:sulf metf:piog plac:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar_plac:acar:metf plac:metf_plac:acar:metf acar:sulf plac:acar Fixed Effect Model inconsistency multi-arm Willms1999
37 Network Meta-Analysis acar:sulf plac:acar_plac:acar:metf plac:metf plac:acar metf:rosi piog:rosi plac:metf_plac:acar:metf plac:rosi metf:piog plac:piog metf:sulf rosi:sulf Forest Plot acar:sulf plac:acar_plac:acar:metf plac:metf plac:acar metf:rosi piog:rosi plac:metf_plac:acar:metf plac:rosi metf:piog plac:piog metf:sulf rosi:sulf inconsistency 36 Random Effect Model multi-arm Willms1999
38 Arm-based Contrast-based Study Treatment1 y1 sd1 n1 Treatment2 y2 sd2 n2 Treatment3 y3 sd3 n NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA TE sete treat1 treat2 studlab contrast-based format arm-based format 37 Dias et. al. (2013) Parkinson
39 Arm-based Contrast-based pairwise(treat, event, n, time, mean, sd, TE, sete, data, studlab,...) treat 1 2 event n time mean sd TE sete data studlab 38 treat n mean sd
40 Arm-based Contrast-based Parkinson > data(parkinson) > p <- pairwise(list(treatment1, Treatment2, Treatment3), + n=list(n1, n2, n3), + mean=list(y1, y2, y3), + sd=list(sd1, sd2, sd3), + data=parkinson, studlab=study) > p TE sete studlab treat1 treat2 n1 mean1 sd1 n2 mean2 sd
41 Arm-based Contrast-based 2 data(smokingcessation) p1 <- pairwise(list(treat1, treat2, treat3), event=list(event1, event2, event3), n=list(n1, n2, n3), data=smokingcessation, sm="rr") 2 p2 <- pairwise(list(treat1, treat2, treat3), event=list(event1, event2, event3), n=list(n1, n2, n3), data=smokingcessation, sm="or") 2 treat event n 40 sm="rd"
42 Arm-based Contrast-based data(dietaryfat) p3 <- pairwise(list(treat1, treat2, treat3), list(d1, d2, d3), time=list(years1, years2, years3), studlab=id, data=dietaryfat, sm="ird") p4 <- pairwise(list(treat1, treat2, treat3), list(d1, d2, d3), time=list(years1, years2, years3), studlab=id, data=dietaryfat, sm="irr") treat time event 41
43 Network Meta-Analysis Network Meta-Analysis P Ranking R Bayesian Network Meta-Analysis 42
44 Bayesian Network Meta-Analysis Bayesian Network Meta-Analysis gemtc Network Meta-Analysis gemtc 1. JAGS JAGS exe 2. R LANGUAGE=en 3. install.packages(c("rjags","gemtc"), dep=t) gemtc > install.packages(c("rjags","gemtc"), dep=t) # > Sys.setlocale(locale="C") # locale US [1] "C" > # Sys.setlocale(locale="Japanese_Japan.932") # locale > plot.new() # History Recording ON > library(gemtc) WinBUGS 43
45 Bayesian Network Meta-Analysis > data <- read.table(textconnection(' + study treatment diff std.err + Alex1998 metf Alex1998 sulf NA NA... + Zhu2003 rosi Zhu2003 plac NA NA'), head=t) # Senn2013 > network <- mtc.network(data.re=data) > plot(network) > summary(network) $Description [1] "MTC dataset: Network" $`Studies per treatment` acar benf metf migl piog plac rosi sita sulf vild $`Number of n-arm studies` 2-arm 3-arm 25 1 $`Studies per treatment comparison` t1 t2 nr 1 acar metf 1 2 acar plac 2 3 acar sulf rosi sulf 1 44
46 Bayesian Network Meta-Analysis > # > model.fe <- mtc.model(network, linearmodel='fixed', likelihood='normal',link='identity') > result.fe <- mtc.run(model.fe, n.adapt=1000, n.iter=5000) > plot(result.fe) > gelman.diag(result.fe) # > summary(result.fe) Results on the Mean Difference scale Iterations = 1:5000 Thinning interval = 1 Number of chains = 4 Sample size per chain = Empirical mean and standard deviation for each variable, plus standard error of the mean: Mean SD Naive SE Time-series SE d.acar.metf d.acar.plac d.acar.sulf d.plac.benf d.plac.migl d.plac.piog d.plac.rosi d.plac.sita d.plac.vild
47 Bayesian Network Meta-Analysis > # > model.fe <- mtc.model(network, linearmodel='fixed', likelihood='normal',link='identity') > result.fe <- mtc.run(model.fe, n.adapt=1000, n.iter=5000) > plot(result.fe) > gelman.diag(result.fe) # > summary(result.fe) 2. Quantiles for each variable: 2.5% 25% 50% 75% 97.5% d.acar.metf d.acar.plac d.acar.sulf d.plac.benf d.plac.migl d.plac.piog d.plac.rosi d.plac.sita d.plac.vild Model fit (residual deviance): Dbar pd DIC data points, ratio 3.926, I^2 = 75% > forest(relative.effect(result.fe, t1="plac")) > ranks <- rank.probability(result.fe, preferreddirection=-1) > plot(ranks) 46
![Bayesian Network Meta-Analysis > ranks Rank probability; preferred direction = -1 [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] acar 0.0002 0.00410 0.01615 0.11545 0.26335 0.38985 0.17680 0.](/docs-images/90/103224731/images/48-6.jpg "03395 0.00015 0.00000 benf 0.0129 0.03970 0.06615 0.24900 0.32565 0.21250 0.08000 0.01315 0.00095 0.00000 metf 0.0875 0.57185 0.27800 0.05690 0.00560 0.00015 0.00000 0.00000 0.00000 0.00000 migl 0.")
48 Bayesian Network Meta-Analysis > ranks Rank probability; preferred direction = -1 [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] acar benf metf migl piog plac rosi sita sulf vild
49 Bayesian Network Meta-Analysis Bayesian Network Meta-Analysis 48
50 Bayesian Network Meta-Analysis > # > model.re <- mtc.model(network, linearmodel='random', likelihood='normal',link='identity') > result.re <- mtc.run(model.re, n.adapt=1000, n.iter=5000) > plot(result.re) > gelman.diag(result.re) > summary(result.re) > forest(relative.effect(result.re, t1="plac")) > # DIC > result.fe$deviance$dic [1] > result.re$deviance$dic [1] > # Node-splitting Inconsistency > result.ns <- mtc.nodesplit(network, linearmodel='random', n.adapt=500, n.iter=2000) > plot(result.ns) > summary.ns <- summary(result.ns) > plot(summary.ns) > summary.ns 49
51 Bayesian Network Meta-Analysis Bayesian Network Meta-Analysis 50
52 Network Meta-Analysis Network Meta-Analysis P Ranking R Bayesian Network Meta-Analysis 51
53 Network Meta-Analysis Network Meta-Analysis R homogeneity consistency Ranking Bayesian Network Meta-Analysis 52
54 Caldwell DM (2014) An overview of conducting systematic reviews with network meta-analysis. Systematic Reviews, 3:109. Dias S, Sutton AJ, Ades AE and Welton NJ (2013) Evidence synthesis for decision making 2: A generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Medical Decision Making, 33, Higgins JPT, Jackson D, Barrett JK, Lu G, et. al. (2012) Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Research Synthesis Methods, 3(2), pages Hutton B, Salanti G, Caldwell DM, Chaimani A, et. al. (2015) The PRISMA extension statement for reporting of systematic reviews incorporating network meta-analyses of health care interventions: checklist and explanations. Annals of Internal Medicine, 162(11): Krahn U, Binder H and Konig J (2013) A graphical tool for locating inconsistency in network meta analyses. BMC Medical Research Methodology, 13:35. 53
55 Mills EJ, Thorlund K and Ioannidis JP (2013) Demystifying trial networks and network meta-analysis. BMJ. May14; 346:f2914. DerSimonian R and Laird N (1986) Meta-analysis in clinical trials. Controlled Clinical Trials 7: Rucker G, Schwarzer G, Krahn U and Konig J (2014) Netmeta: network meta-analysis with R. R package (version 0.8-0). Rucker G and Schwarzer G (2015) Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Medical Research Methodology, 15:58. Senn S, Gavini F, Magrez D, and Scheen A (2013) Issues in performing a network meta-analysis. Statistical Methods in Medical Research, 22 (2), Gert van Valkenhoef, and Joel Kuiper (2015) Gemtc: Network Meta-Analysis Using Bayesian Methods (Version 0.7-1). 54
56 2016/8/3
57 Backup Slides 2016/8/3
58 Q homogeneity consistency
59 Windows R CRAN R R exe 58
60 Windows R OK (N) > 59
61 Windows R 1. Message translations 2. PC 64-bit 64-bit Files 32-bit Files 32-bit Files (N) > 60
62 Windows R SDI 61
63 Windows R (N) > 62
64 Windows R R or 63
65 Windows R R R install.packages("netmeta", dep=t) Japan (Tokyo) OK R 64
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SAS 2016 SAS Network Meta-Analysis SAS Network Meta-Analysis homogeneity consistency Ranking Network Meta-Analysis(homogeneity) (consistency) Ranking 1 Network Meta-Analysis Network Meta-Analysis P Ranking
Network Meta-Analysis
SAS ユーザー総会 2016 SAS での Network Meta-Analysis の実施例 ~ 頻度論に基づくアプローチ ~ 武田薬品工業株式会社日本開発センター生物統計室舟尾暢男 黒田晋吾 要旨 SAS による Network Meta-Analysis の実施方法として 均質性 (homogeneity) や一致性 (consistency) の評価 各薬剤の Ranking の算出方法を含めて紹介する
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Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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kubostat7f p statistaical models appeared in the class 7 (f) kubo@eeshokudaiacjp https://googl/z9cjy 7 : 7 : The development of linear models Hierarchical Baesian Model Be more flexible Generalized Linear