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1 SAS 2016 SAS Network Meta-Analysis
2 SAS Network Meta-Analysis homogeneity consistency Ranking Network Meta-Analysis(homogeneity) (consistency) Ranking 1
3 Network Meta-Analysis Network Meta-Analysis P Ranking SAS 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 SAS 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 SAS 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, 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) 15
17 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 16
18 Network Meta-Analysis,Cov,,Cov 1,,5 1,,4 DerSimonian and Laird Cov 17 multi-arm τ /2 ID=5(acar vs. metf)
19 homogeneity consistency heterogeneity Within-designs Q statistic, inconsistency Between-designs Q statistic, / heterogeneity
20 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 19 Rucker G and Schwarzer G (2015)
21 Network Meta-Analysis proc iml ; y = {-0.37, -0.8, -1.9, -0.4, -1.2, -1} ; X = {1 0-1, 0 1 0, 1 0 0, 1 0 0, 1 0 0, 0 1 0} ; V = { , , , , , } ; theta_net = inv(t(x) * inv(v) * X) * t(x) * inv(v) *y ; v_theta_net = inv(t(x) * inv(v) * X) ; result1 = theta_net (theta_net-probit(0.975)#sqrt(vecdiag(v_theta_net))) (theta_net+probit(0.975)#sqrt(vecdiag(v_theta_net))) ; theta_dir = j(5, 1, 0) ; Va = j(5, 5, 0) ; Xa = X[{ },] ; theta_dir[1,1] = sum(inv(v[1,1]) * y[1]) # V[1,1] ; Va[1,1] = V[1,1] ; theta_dir[2,1] = sum(inv(v[2,2]) * y[2]) # V[2,2] ; Va[2,2] = V[2,2] ; theta_dir[3,1] = sum(inv(v[{3 4},{3,4}]) * y[{3 4}]) / sum(vecdiag(inv(v[{3 4},{3 4}]))) ; Va[3,3] = 1/sum(vecdiag(inv(V[{3 4},{3 4}]))) ; theta_dir[{4 5},1] = y[{5 6}] ; Va[{4 5},{4 5}] = V[{5 6},{5 6}] ; theta_net_a = inv(t(xa) * inv(va) * Xa) * t(xa) * inv(va) * theta_dir ; v_theta_net_a = inv(t(xa) * inv(va) * Xa) ; result2 = theta_net_a (theta_net_a-probit(0.975)#sqrt(vecdiag(v_theta_net_a))) (theta_net_a+probit(0.975)#sqrt(vecdiag(v_theta_net_a))) ; 20
22 Network Meta-Analysis Q_net = t(y - X * theta_net) * inv(v) * (y-x * theta_net) ; Q_inc = t(theta_dir - Xa * theta_net_a) * inv(va) * (theta_dir - Xa * theta_net_a) ; Q_het = Q_net - Q_inc ; CC = -1#i(3); CC[,1] = 1; E = CC * theta_net; z = j(1,3,0) ; do i=1 to 3 ; c = CC[i,] ; z[i] = sqrt(t(c * theta_net) * inv(c * v_theta_net * t(c)) * (c * theta_net)) ; if (E[i] < 0) then z[i] = -1*z[i] ; end ; p_metf = 1-(probnorm(z)) ; pscore_metf = p_metf[:] ; title "Treatment estimate (Fixed effect model)" ; print result1 result2, Q_net Q_het Q_inc pscore_metf ; quit ; result1 1-step 1 95%2 3 result2 2-step result1 Q_net Q_het Q_inc pscore_metf metf metformin P 21
23 inconsistency Detaching a single design inconsistency Krahn 2013 Detaching a single design, 1, 0, Cov 1 0 detach, 22
24 inconsistency Detaching a single design,,,,,,,,,,,, 0,,,,, 0 inconsistency, 0 inconsistency 23
25 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 24
26 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 25
27 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 26
28 Network Meta-Analysis Network Meta-Analysis P Ranking SAS Bayesian Network Meta-Analysis 27
29 iml iml Network Meta-Analysis ranking 500 Q 2 3 R netmeta SAS 28
30 Network Meta-Analysis SAS 1. R + C: temp 2. %MYNETMETA R Backup Slides R install.packages("netmeta", dep=t) %MYNETMETA Network Meta-Analysis SAS R output.pdf %MYNETMETA 29
31 Network Meta-Analysis SAS %macro MYNETMETA(dataset =, sm = MD, level = 0.95, reference =, seq =, small = good, path = C:/temp) ; dataset 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 reference reference=plac seq small good bad path output.pdf 30
32 Network Meta-Analysis data Senn2013_char ; length STUDLAB $100. ; input TE SETE TREAT1 $ TREAT2 $ STUDLAB $ ; cards ; metf plac DeFronzo metf plac Lewin metf acar Willms rosi plac Davidson rosi plac Wolffenbuttel piog plac Kipnes rosi plac Kerenyi piog metf Hanefeld piog rosi Derosa rosi plac Baksi rosi plac Rosenstock rosi plac Zhu rosi metf Yang rosi sulf Vongthavaravat acar sulf Oyama acar plac Costa sita plac Hermansen vild plac Garber metf sulf Alex migl plac Johnston migl plac Johnston1998a rosi metf Kim migl plac Johnston1998b metf plac Gonzalez-Ortiz benf plac Stucci benf plac Moulin metf plac Willms acar plac Willms1999 ; run ;
33 Network Meta-Analysis %MYNETMETA(dataset = Senn2013_char, sm = MD, level = 0.95) ; dataset Senn2013_char sm MD Mean Difference level 95% output.pdf TE_FIXED TE_FIXED_LCL TE_FIXED_UCL TE_RANDOM TE_RANDOM_LCL TE_RANDOM_UCL Q1_STATISTICS Q homogeneity / consistency Q1_WITHINDESIGNS Design-specific decomposition of within-designs Q statistic Q1_BETWEENDESIGNS Between-designs Q statistic after detaching of single designs Q1_XXX 3 Q2_STATISTICS Q2_WITHINDESIGNS Q2_BETWEENDESIGNS RANK_FIXED RANK_RANDOM Network Ranking 32
34 Network Meta-Analysis %MYNETMETA(dataset = Senn2013_char, sm = MD, level = 0.95, reference = plac, seq = %str('plac','acar','benf','metf', 'migl','piog','rosi','sita', 'sulf', 'vild')) ; reference reference=plac seq 33
35 Network Meta-Analysis PDF 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 1 Forest Plot 3 34 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
36 Network Meta-Analysis PDF 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 2 Forest Plot 4 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 35 Random Effect Model multi-arm Willms1999
37 Network Meta-Analysis TE_FIXED Q1_STATISTICS Q homogeneity / consistency Q1_WITHINDESIGNS Within-designs Q statistic RANK_FIXED Network P Q1_BETWEENDESIGNS Between-designs Q statistic after detaching of single designs 36
38 Network Meta-Analysis TE_RANDOM Q2_STATISTICS Q homogeneity / consistency Q2_WITHINDESIGNS Within-designs Q statistic RANK_RANDOM Network P Q2_BETWEENDESIGNS Between-designs Q statistic after detaching of single designs 37
39 Arm-based Contrast-based STUDY Group1 TE1 sete1 Group2 TE2 sete2 Group3 TE3 sete TE sete treat1 treat2 studlab contrast-based format arm-based format 38 Dias et. al. (2013) Parkinson
40 Arm-based Contrast-based %MYCONVERT(dataset =, studlab =, treat =, event =, n =, mean =, sd =, TE =, sete =, time =, sm =, path = C:/temp) ; dataset studlab treat event n mean sd TE sete TE time sm path 39
41 Arm-based Contrast-based %MYCONVERT(dataset = Parkinson, studlab = STUDY, treat = %str(group1, Group2, Group3), TE = %str(te1, TE2, TE3), sete = %str(sete1, sete2, sete3)) ; dataset studlab treat 1 2 TE sete %MYCONVERT Parkinson Parkinson_contrast 40 treat n mean sd
42 Arm-based Contrast-based 2 %MYCONVERT(dataset = MYDATA, treat = %str(treat1, treat2, treat3), event = %str(event1, event2, event3), n = %str(n1, n2, n3), sm=rr) ; %MYNETMETA(dataset = MYDATA_contrast, sm=rr) ; 2 OR SAS %str() %MYCONVERT(dataset = MYDATA, treat = %str(treat1, treat2, treat3), event = %str(event1, event2, event3), n = %str(n1, n2, n3), sm=%str(or)) ; %MYNETMETA(dataset = MYDATA_contrast, sm=%str(or)) ; 2 treat event n 41 sm=rd
43 Arm-based Contrast-based %MYCONVERT(dataset = MYDATA, studlab=id, treat = %str(treat1, treat2, treat3), time = %str(years1, years2, years3), event = %str(d1, d2, d3), sm=ird) ; %MYNETMETA(dataset = MYDATA_contrast, sm=ird) ; %MYCONVERT(dataset = MYDATA, studlab=id, treat = %str(treat1, treat2, treat3), time = %str(years1, years2, years3), event = %str(d1, d2, d3), sm=irr) ; %MYNETMETA(dataset = MYDATA_contrast, sm=irr) ; treat time event 42
44 Network Meta-Analysis Network Meta-Analysis P Ranking SAS Bayesian Network Meta-Analysis 43
45 Bayesian Network Meta-Analysis SAS Bayesian Network Meta-Analysis 2014 Bayesian Network Meta-Analysis Network Meta-Analysis ~ 0, ,,9 : acarbose placebo : vildagliptin placebo : 0 placebo 2-arm study: ~,, 1,, 10 ; : 3-arm study: ~, /2 /2 44
46 Bayesian Network Meta-Analysis Senn mcmc studlab TE1 TE2 TE3 sete1 sete2 sete3 treat1_1 treat1_2 treat1_3 treat2_1 treat2_2 treat2_3 v1 v2 v
47 Bayesian Network Meta-Analysis ods graphics on ; proc mcmc data=senn nbi=5000 nmc= thin=10 seed=777 missing=ac diagnostics=all plots=all monitor=(theta) ; 46 array te[2] te1 te2 ; array theta[9] ; array s[2,2] ; array mu[2] mu1 mu2 ; parms theta: 0 ; prior theta: ~ normal(0,var=10000) ; if studlab=3 then do ; do i=1 to 9 ; if treat1_1=i then mu1_1=theta[i] ; if treat2_1=i then mu2_1=theta[i] ; if treat1_2=i then mu1_2=theta[i] ; if treat2_2=i then mu2_2=theta[i] ; end ; if treat1_1=10 then mu1_1=0 ; if treat2_1=10 then mu2_1=0 ; if treat1_2=10 then mu1_2=0 ; if treat2_2=10 then mu2_2=0 ; mu[1]=mu1_1-mu2_1 ; mu[2]=mu1_2-mu2_2 ; s[1,1]=v1 ; s[2,2]=v2 ; s[1,2]=(v1+v2-v3)/2 ; s[2,1]=s[1,2] ; ll=lpdfmvn(te,mu,s) ; end ;
48 Bayesian Network Meta-Analysis else do ; do i=1 to 9 ; if treat1_1=i then mu1_1=theta[i] ; if treat2_1=i then mu2_1=theta[i] ; end ; if treat1_1=10 then mu1_1=0 ; if treat2_1=10 then mu2_1=0 ; mu[1]=mu1_1-mu2_1 ; ll=lpdfnorm(te[1],mu[1],sqrt(v1)) ; end ; model general(ll) ; run ; ods graphics off ; θ 1 θ 2 θ 3 θ 9 47
49 Bayesian Network Meta-Analysis Bayesian Network Meta-Analysis 48
50 Bayesian Network Meta-Analysis ~ 0, ,,9 : acarbose placebo : vildagliptin placebo : 0 placebo ~ igamma 1, arm study: ~,, 1,,10 ; : 3-arm study: ~, /2 1 1/2 /2 1/2 1 49
51 Bayesian Network Meta-Analysis ods graphics on ; proc mcmc data=senn nbi=10000 nmc= thin=50 seed=777 missing=ac diagnostics=all plots=all stats(percent=( ))=all monitor=(theta var_h sd) ; array te[2] te1 te2 ; array theta[9] ; array s[2,2] ; array g[2,2] ; array mu[2] mu1 mu2 ; array delta[2] delta1 delta2 ; parms theta: 0 ; parms var_h 1; prior theta: ~ normal(0,var=10000) ; prior var_h ~ igamma(1,scale= ) ; if studlab=3 then do ; do i=1 to 9 ; if treat1_1=i then mu1_1=theta[i] ; if treat2_1=i then mu2_1=theta[i] ; if treat1_2=i then mu1_2=theta[i] ; if treat2_2=i then mu2_2=theta[i] ; end ; if treat1_1=10 then mu1_1=0 ; if treat2_1=10 then mu2_1=0 ; if treat1_2=10 then mu1_2=0 ; if treat2_2=10 then mu2_2=0 ; 50
52 Bayesian Network Meta-Analysis mu[1]=mu1_1-mu2_1 ; mu[2]=mu1_2-mu2_2 ; s[1,1]=v1 ; s[2,2]=v2 ; s[1,2]=(v1+v2-v3)/2 ; s[2,1]=s[1,2] ; g[1,1]=var_h ; g[2,2]=g[1,1] ; g[1,2]=var_h/2 ; g[2,1]=g[1,2] ; random delta ~ mvn(mu,g) subject=_obs_ ; ll=lpdfmvn(te,delta,s) ; end ; else do ; do i=1 to 9 ; if treat1_1=i then mu1_1=theta[i] ; if treat2_1=i then mu2_1=theta[i] ; end ; if treat1_1=10 then mu1_1=0 ; if treat2_1=10 then mu2_1=0 ; mu[1]=mu1_1-mu2_1 ; vt=sqrt(v1) ; random delta3 ~ normal(mu[1],v=var_h) subject=_obs_ ; ll=lpdfnorm(te[1],delta3,vt) ; end ; model general(ll) ; sd=sqrt(var_h) ; run ; ods graphics off ; 51
53 Bayesian Network Meta-Analysis Bayesian Network Meta-Analysis 52
54 Network Meta-Analysis Network Meta-Analysis P Ranking SAS Bayesian Network Meta-Analysis 53
55 Network Meta-Analysis Network Meta-Analysis SAS homogeneity consistency Ranking Bayesian Network Meta-Analysis 54
56 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. 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:
57 Rucker G, Schwarzer G, Krahn U and Konig J (2014) Netmeta: network meta-analysis with R. R package (version 0.8-0). License GPL-2+ License GPL-2+ 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), ,, (2014). SAS 56
58 2016/7/20
59 Backup Files 2016/7/20
60 Q homogeneity consistency
61 Windows R CRAN R R exe 60
62 Windows R OK (N) > 61
63 Windows R 1. Message translations 2. PC SAS 64-bit 64-bit Files 32-bit Files 32-bit Files (N) > 62
64 Windows R SDI 63
65 Windows R (N) > 64
66 Windows R R or 65
67 Windows R R R install.packages("netmeta", dep=t) Japan (Tokyo) OK R 66
68 Windows R C temp R R.exe C: Program Files R R bin i386 %MYNETMETA %macro MYNETMETA(dataset =, sm = MD, level = 0.95, reference =, seq =, small = good, path = C:/temp) ; options noxwait xsync ; %let Rexepath='C: Program Files R R bin i386 R.exe' ; 67
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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