Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Plan of the Session Session V: Network Meta-Analysis James Carpenter1 , Ulrike Krahn2,3 , Gerta R¨ ucker4 , At the end of this session the aim is that you should understand Guido Schwarzer4 1 London School of Hygiene and Tropical Medicine & MRC Clinical Trials Unit, London, UK of Medical Biostatistics, Epidemiology and Informatics, Mainz, Germany 3 Institute of Medical Informatics, Biometry and Epidemiology, Duisburg-Essen, Germany 4 Institute for Medical Biometry and Statistics, Freiburg, Germany 2 Institute [email protected] 1 Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary the principal model and underlying assumptions; I how to assess heterogeneity/inconsistency; I how to assess the evidence flow. I carry out a network meta-analysis; I report and visualize results; I interpret the results taking diagnostic measures and graphics into account. Carpenter/Krahn/R¨ ucker/Schwarzer Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 2 Summary National Institute for Health and Care Excellence (NICE) Classical meta-analysis comparison between two treatments Network meta-analysis/ Multiple-treatments comparison/ Mixed-treatment comparison I I Overview Background: Evidence based healthcare decisions I the background for network meta-analysis; The objectives are that you are able to: IBC Short Course Florence, 6 July 2014 Overview I I ”has a preference for data from head-to-head RCTs [...]” I ”[...] evidence from mixed treatment analyses may be presented if it is considered to add information [...].” I ”If data from head-to-head RCTs are not available, indirect treatment comparison methods should be used [...].” comparison between a set of treatments (see NICE: Guide to the methods of technology appraisal, 2008 and NICE Decision Support Unit, Series of Technical Support Documents) Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 3 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 4 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Overview Illustrative example: Network meta-analysis in diabetes Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Adjusted indirect comparison HbA1c change in patients with type II diabetes and a baseline therapy of sulfonylurea (by Senn et al., 2013) Study migl ● 10 treatments benf ● plac plac acar ● ● MD= -1.150 26 RCTs: 25 two-armed, 1 three-armed Study 28 assessed pairwise comparisons SUal ● ● rosi versus plac vild rosi 15 different designs MD= -1.148 ● (defined by compared treatments, ● ● e.g. plac:acar, plac:acar:metf) ? sita metf rosi metf versus plac ● piog metf ind dir dir ˆ θrosi:metf =ˆ θrosi:plac −ˆ θmetf:plac dir ind dir Vrosi:metf = Vrosi:plac + Vmetf:plac 15 observed / 45 possible edges Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 5 Summary Carpenter/Krahn/R¨ ucker/Schwarzer Overview Combination of direct and indirect evidence Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 6 Summary Assumption Study I plac of transitivity I MD= -1.150 Study rosi versus plac I rosi MD= -1.148 ? I Study of consistency metf versus plac I metf MD= -0.073 I ˆ θdir ˆ dir V 1 V dir + + ˆ θind V ind 1 V ind , V nma = Carpenter/Krahn/R¨ ucker/Schwarzer extension of transitivity: direct and indirect estimates are in agreement can be tested statistically (see Salanti, 2012) metf versus rosi ˆ θnma = an indirect comparison validly estimates an unobserved head-to-head comparison cannot be tested statistically, but can be evaluated conceptually and contextually 1 1 V dir + 1 V ind Session V: Network Meta-Analysis Florence, 6 July 2014 7 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 8 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Overview Different models and estimation methods... Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Fixed effects model Bayesian approaches (using WinBUGS, see e.g. Dias et al. 2011, Lu & Ades 2004 or R package gemtc) Frequentist approaches I I using two-way linear mixed models with main effects for treatment and trial (Piepho et al. 2012, SAS) using multivariate meta-regression (White et al. 2012, R package mvmeta) two approaches using generalized least squares (Krahn et al. 2013, R¨ ucker 2012) leading to identical estimates (R¨ ucker 2014) implemented in R package netmeta : I I I each study with p treatments a) reducing dimensions p − 1 comparisons to a reference treatment with corresponding SEs Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Decomposition of Q with E() = 0 and Cov() =: V = diag(V1dir , . . . , Vkdir ) Example: 3 treatments, independent studies s = 1, · · · , 4, designs d = AB, AC, BC Y1.AB 1 1 Y2.AB , X = Y = Y3.AC 0 Y4.BC −1 b) reducing weights p(p−1) all 2 pairwise comparisons with adjusted SEs Session V: Network Meta-Analysis Model and Estimating Y = X θnma + Florence, 6 July 2014 Locating Inconsistency Flow of evidence 9 Summary Two-stage fixed effects model fitting Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction 0 ! θnma 0 nma , θ = AB , V = diag(V1.AB , ..., V4.BC ) nma 1 θAC 1 Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 10 Summary Two-stage fixed effects model 1. Aggregation per study design d by multivariate meta-analysis methods 1. Aggregation per study design d by multivariate meta-analysis methods ˆ θddir := Vddir X s∈Sd Vs−1 Ys , Vddir ˆ θddir := Vddir −1 X −1 dir ˆ Vs := Cov(θd ) = X s∈Sd s∈Sd Vs−1 Ys , Vddir −1 X −1 dir ˆ Vs := Cov(θd ) = s∈Sd 2. Model fitting dir 0 θˆdir = (θˆ1dir , . . . , θˆD ) = Xa θnma + a 2. Model fitting with E(a ) = 0 and Cov(a ) =: Va = diag(V1dir , . . . , VDdir ) dir 0 θˆdir = (θˆ1dir , . . . , θˆD ) = Xa θnma + a Example: dir ˆdir with one further study of design ABC with treatment effect estimates ˆ θAB ABC , θAC ABC , and dir covariance matrix VABC with E(a ) = 0 and Cov(a ) =: Va = diag(V1dir , . . . , VDdir ) Example: θ ˆdir ˆdir θAB 1 ˆdir = θAC , Xa = 0 ˆdir −1 θBC ! 0 θnma dir dir 1 , θnma = AB , Va = diag(VAB , ..., VBC ) nma θAC 1 ˆ θdir ˆdir θAB 1 ˆdir 0 θAC , X = −1 dir = ˆ θBC a ˆdir 1 θAB ABC ˆ 0 θdir AC ABC Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 11 Carpenter/Krahn/R¨ ucker/Schwarzer 0 ! 1 θnma dir dir 1 , θnma = AB nma , Va = diag(VAB , ..., VABC ) θAC 0 1 Session V: Network Meta-Analysis Florence, 6 July 2014 12 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary R package netmeta > > > > > > > > seTE treat1 treat2 0.1414 metf plac 0.0992 metf plac 0.3579 metf acar 0.1435 rosi plac 0.3758 0.4669 metf acar Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary R package netmeta: Object netmeta # 1. Install R package netmeta install.packages("netmeta") # 2. Load R package netmeta library(netmeta) # 3. Load data set Senn2013 data(Senn2013) # 4. Print data Set Senn2013 TE 1 -1.90 2 -0.82 3 -0.20 4 -1.34 ... 27 -1.20 28 -1.00 Overview > > > > > > + studlab DeFronzo1995 Lewin2007 Willms1999 Davidson2007 plac plac Fixed effects model (default) The netmeta function generates an object of class netmeta with corresponding functions print, summary, forest, netgraph, netheat, decomp.design, and netmeasures nma <- netmeta(TE, seTE, treat1, treat2, studlab, data=Senn2013, sm="MD", reference="plac") Warning messages: 1: In netmeta(TE, seTE, treat1, treat2, studlab, data = Senn2013, sm = "MD", : Treatments within a comparison have been re-sorted in increasing order. Willms1999 Willms1999 Session V: Network Meta-Analysis Model and Estimating # # # # Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 13 Summary Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence R package netmeta: Network graph R package netmeta: Estimating treatment effects > netgraph(nma, seq=c("plac", "benf", "migl", "acar", "sulf", + "metf", "rosi", "piog", "sita", "vild")) > print(nma,digits=2) 14 Summary Original data (with adjusted standard errors for multi-arm studies): migl ● benf plac acar ● ● SUal ● ● ● vild ● sita metf ● rosi Carpenter/Krahn/R¨ ucker/Schwarzer DeFronzo1995 Lewin2007 Willms1999 Davidson2007 ... Willms1999 Willms1999 ● treat1 treat2 TE seTE seTE.adj narms multiarm metf plac -1.90 0.14 0.14 2 metf plac -0.82 0.10 0.10 2 acar metf 0.20 0.36 0.39 3 * plac rosi 1.34 0.14 0.14 2 metf acar plac -1.20 0.38 plac -1.00 0.47 0.41 0.82 3 3 * * ● piog Session V: Network Meta-Analysis ... Florence, 6 July 2014 15 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 16 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary R package netmeta: Estimating treatment effects Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary R package netmeta: Estimating treatment effects Data utilised in network meta-analysis (fixed effect model): treat1 treat2 DeFronzo1995 metf plac Lewin2007 metf plac Willms1999 acar metf Davidson2007 plac rosi ... Willms1999 metf plac Willms1999 acar plac Number of treatment arms (by study): narms Alex1998 2 ... Willms1999 3 Wolffenbuttel1999 2 Yang2003 2 Zhu2003 2 ... > # ... 95%-CI [-1.23; -1.00] [-1.23; -1.00] [ 0.06; 0.51] [ 1.11; 1.30] -1.11 -0.83 [-1.23; -1.00] [-1.04; -0.61] Q leverage 30.89 0.18 8.79 0.36 0.05 0.09 0.93 0.11 0.04 0.04 0.02 0.02 each comparison's contribution to the heterogeneity statistic Q_total > # leverage: small leverage means that the precision of a contrast benefits largely from the indirect inference; a leverage of 1 means that there is no gain at all Carpenter/Krahn/R¨ ucker/Schwarzer Overview MD -1.11 -1.11 0.29 1.20 Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 17 Summary R package netmeta: Estimating treatment effects Q: Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 18 Summary R package netmeta: Estimating treatment effects Number of studies: k=26 Number of treatments: n=10 Number of pairwise comparisons: m=28 Without a specification of argument reference.group in function netmeta matrices of the TE estimates, lower and upper 95%-confidence limits for all possible contrasts are shown, e.g.: Fixed effect model Fixed effect model Treatment estimate (sm='MD', reference.group='plac'): MD 95%-CI acar -0.83 [-1.04; -0.61] benf -0.91 [-1.15; -0.66] metf -1.11 [-1.23; -1.00] migl -0.94 [-1.19; -0.70] piog -1.07 [-1.22; -0.92] plac 0.00 [ 0.00; 0.00] rosi -1.20 [-1.30; -1.11] sita -0.57 [-0.82; -0.32] sulf -0.44 [-0.62; -0.26] vild -0.70 [-0.95; -0.45] Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 Treatment estimate (sm='MD'): acar benf metf migl piog acar 0.00 0.08 0.29 0.12 0.24 benf -0.08 0.00 0.21 0.04 0.16 metf -0.29 -0.21 0.00 -0.17 -0.05 migl -0.12 -0.04 0.17 0.00 0.12 piog -0.24 -0.16 0.05 -0.12 0.00 plac 0.83 0.91 1.11 0.94 1.07 ... 19 Carpenter/Krahn/R¨ ucker/Schwarzer plac... -0.83 -0.91 -1.11 -0.94 -1.07 0.00 Session V: Network Meta-Analysis Florence, 6 July 2014 20 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Generalization to a random effects model Y = X θnma + b + with Cov(Y ) =: Vτ = V + Vhet (τ) Example: studies of design AB, AC, BC, and ABC 0 Var(YAC ) 0 0 0 0 0 1 0 0 0 0 0 1 1/2 Introduction 0 0 0 0 0 0 Var(YAB ABC ) Cov(YAB ABC , YAC ABC ) + Cov(YAB ABC , YAC ABC ) Var(YAC ABC ) Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Florence, 6 July 2014 Flow of evidence > # In order to explicitely conduct a random effects model > nma_re <- netmeta(TE, seTE, treat1, treat2, studlab, + data=Senn2013, sm="MD", reference="plac", + comb.random=TRUE) Warning messages: 1: In netmeta(TE, seTE, treat1, treat2, studlab, data = Senn2013, sm = "MD", : Treatments within a comparison have been re-sorted in increasing order. Note: Even though object nma has been generated without argument comb.random all necessary information on the random effects network meta-analysis is also part of object nma. 0 0 0 1/2 1 Carpenter/Krahn/R¨ ucker/Schwarzer Overview 0 0 Var(YBC ) 0 0 Introduction R package netmeta: Estimating treatment effects Estimation of τ2 e.g. by a generalized DerSimonian-Laird method with the assumptions: I τ2 is the same for all designs/comparisons I random effects of multi-arm studies have correlation 1/2 Var(Y AB ) 0 0 Vτ = 0 0 1 0 0 1 2 0 τ 0 0 0 0 0 Overview 21 Summary R package netmeta: Estimating treatment effects Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 22 Summary R package netmeta: Forest plot > forest(nma,xlab="HbA1c mean difference", xlim=c(-1.5,1.5)) Treatment Fixed Effect Model acar benf metf migl piog plac rosi sita sulf vild > # with object nma or nma_re we obtain Quantifying heterogeneity/inconsistency: tau^2 = 0.1087; I^2 = 81.4% Test of heterogeneity/inconsistency: Q d.f. p.value 96.99 18 < 0.0001 −1.5 −1 −0.5 0 0.5 1 MD 95%−CI −0.83 −0.91 −1.11 −0.94 −1.07 0.00 −1.20 −0.57 −0.44 −0.70 [−1.04; −0.61] [−1.15; −0.66] [−1.23; −1.00] [−1.19; −0.70] [−1.22; −0.92] [−1.30; −1.11] [−0.82; −0.32] [−0.62; −0.26] [−0.95; −0.45] 1.5 HbA1c mean difference Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 23 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 24 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary R package netmeta: Forest plot Decomposition of Cochran’s Q in network meta-analysis > forest(nma_re,xlab="HbA1c mean difference") Heterogeneity of the whole network XX (Ys − Xs θˆnma )0 Vs−1 (Ys − Xs θˆnma ) Q nma := Treatment Random Effects Model acar benf metf migl piog plac rosi sita sulf vild −1.5 −1 −0.5 0 0.5 1 MD 95%−CI −0.84 −0.73 −1.13 −0.95 −1.13 0.00 −1.23 −0.57 −0.42 −0.70 [−1.32; −0.36] [−1.29; −0.17] [−1.43; −0.82] [−1.40; −0.50] [−1.56; −0.70] d s∈Sd P (χ2 distributed with s (as − 1) − (n − 1) degrees of freedom n: number of treatments, as : number of arms in study s) [−1.48; −0.98] [−1.26; 0.12] [−0.89; 0.06] [−1.39; −0.01] Q nma = Q within + Q inc 1.5 HbA1c mean difference Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 25 Summary I Q within : Heterogeneity within pairwise comparisons OR within designs I Q inc : Inconsistency/Heterogeneity between pairwise comparisons OR between designs Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence Decomposition of Q nma in pairwise comparisons Decomposition of Q nma in pairwise comparisons > #Heterogeneity of the whole network > round(nma$Q, 1) > > > > > 97 > #Heterogeneity within pairwise comparisons > round(nma$Q.heterogeneity, 1) > #Heterogeneity between pairwise comparisons > round(nma$Q.inconsistency, 1) 22.5 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 27 Summary #Decomposition of the heterogeneity within pairwise comparisons Qd <- nma$Q.decomp Qd$Q <- round(Qd$Q, 1) Qd$pval.Q <- round(Qd$pval.Q, 3) Qd[Qd$df!=0,] 2 4 6 7 9 12 74.5 26 treat1 treat2 Q df pval.Q acar plac 0.1 1 0.811 benf plac 4.4 1 0.036 metf plac 42.2 3 0.000 metf rosi 0.2 1 0.665 migl plac 6.4 2 0.040 plac rosi 21.3 5 0.001 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 28 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Decomposition of Q nma in design components Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Decomposition of Q nma in design components Design-specific decomposition of within-designs Q statistic Design Q df p.value acar:sulf 0.00 0 -metf:piog 0.00 0 -metf:rosi 0.19 1 0.6655 metf:sulf 0.00 0 -piog:rosi 0.00 0 -plac:acar 0.00 0 -plac:benf 4.38 1 0.0363 plac:metf 42.16 2 < 0.0001 plac:migl 6.45 2 0.0398 plac:piog 0.00 0 -plac:rosi 21.27 5 0.0007 plac:sita 0.00 0 -plac:vild 0.00 0 -rosi:sulf 0.00 0 -plac:acar:metf 0.00 0 -- > decomp.design(nma) Q statistics to assess homogeneity / consistency Q df p.value Whole network 96.99 18 < 0.0001 Within designs 74.46 11 < 0.0001 Between designs 22.53 7 0.0021 ... Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 29 Summary > netheat(nma) Introduction Model and Estimating Q inc := Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 30 Summary X Qdinc with d Qdinc := (θˆddir − Xd θˆnma )0 Vd−1 (θˆddir − Xd θˆnma ) 8 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 Overview Session V: Network Meta-Analysis Generalized Cochran’s Q for design inconsistency 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 Locating inconsistency: The net heat plot Carpenter/Krahn/R¨ ucker/Schwarzer P (χ2 distributed with d (ad − 1) − (n − 1) degrees of freedom n: number of treatments, ad : number of arms in design d) 6 4 Network meta-analysis example in diabetes: 2 Q inc =0.04 + 0.00 + 0.20 + · · · = 22.53 0 with df = 16 − 9 = 7 (p value: 0.002) -2 (see Krahn et al., 2013) Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 31 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 32 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Detaching of single designs Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Detaching of single designs in the diabetes example 1. Model fitting that allows for a deviating effect in one design d 2. Recalculation of the Q statistic I inc = Q(d) P d0 Qdinc 0 (d) migl 3. Investigation of the change in inconsistency for each summand I Q inc d0 − benf acar plac 0 Qdinc 0 (d) ∀ d = 1, . . . , D SUal vild Visualization ∀d = 1, . . . , D in the nma heat plot: metf rosi Summary Decomposition of Q Locating Inconsistency Flow of evidence 34 Summary migl plac benf acar plac:metf * Net heat plot in the diabetes example benf acar Model and Estimating plac:acar * migl Introduction rosi:SUal Detaching of single designs in the diabetes example Overview Florence, 6 July 2014 piog:rosi Flow of evidence Session V: Network Meta-Analysis metf:SUal Locating Inconsistency Carpenter/Krahn/R¨ ucker/Schwarzer metf:rosi Decomposition of Q 33 metf:piog Model and Estimating Florence, 6 July 2014 acar:SUal Introduction Session V: Network Meta-Analysis = 0.04 + 0.00 + 0.20 + · · · = 22.53 with dfQ inc = 16 − 9 = 7 (p value: 0.002) plac:rosi Overview piog Q inc Carpenter/Krahn/R¨ ucker/Schwarzer sita plac:piog inc Qdinc 0 < Qd 0 (d) increase after detaching/ inconsistent evidence decrease after detaching/ supporting evidence plac:metf > Qdinc 0 (d) plac:acar Qdinc 0 plac:acar plac 8 plac:metf plac:piog SUal vild SUal vild 6 plac:rosi acar:SUal 4 metf:piog metf sita metf metf:rosi sita 2 metf:SUal rosi piog rosi piog piog:rosi rosi:SUal 0 plac:acar * plac:metf * -2 Q inc = 0.04 + 0.00 + 0.20 + · · · = 22.53 with dfQ inc = 16 − 9 = 7 (p value: 0.002) inc Q(metf:SUal) = 0.48 + 0.00 + 0.23 + · · · = 7.52 Q inc = 0.04 + 0.00 + 0.20 + · · · = 22.53 with dfQ inc = 16 − 9 = 7 (p value: 0.002) inc Q(metf:SUal) = 0.48 + 0.00 + 0.23 + · · · = 7.52 diff Q.,metf:SUal = (−0.45, 0.00, −0.03, . . . )0 diff Q.,metf:SUal = (−0.45, 0.00, −0.03, . . . )0 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 34 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 34 Locating Inconsistency Flow of evidence Summary plac:metf * plac:acar * rosi:SUal piog:rosi metf:SUal metf:rosi plac:acar plac:metf * plac:acar * piog:rosi metf:rosi plac:metf plac:rosi metf:piog metf:piog 6 plac:rosi vild acar:SUal metf:rosi piog Summary 8 plac:piog SUal 4 4 metf:piog 2 piog:rosi rosi Flow of evidence plac:metf metf:piog plac:metf sita Locating Inconsistency plac:acar plac 6 plac:rosi metf benf acar plac:piog vild Decomposition of Q acar:SUal migl 8 rosi:SUal SUal Model and Estimating Net heat plot in the diabetes example metf:SUal plac Introduction acar:SUal acar plac:piog benf rosi:SUal migl metf:SUal Net heat plot in the diabetes example Overview plac:rosi Decomposition of Q plac:piog Model and Estimating plac:metf Introduction plac:acar Overview metf plac:acar * metf:rosi sita 2 metf:SUal plac:metf * 0 rosi piog piog:rosi plac:acar rosi:SUal acar:SUal 0 plac:acar * -2 * three-armed study Q inc = 0.04 + 0.00 + 0.20 + · · · = 22.53 with dfQ inc = 16 − 9 = 7 (p value: 0.002) inc Q(metf:SUal) = 0.48 + 0.00 + 0.23 + · · · = 7.52 plac:metf * -2 * three-armed study diff Q.,metf:SUal = (−0.45, 0.00, −0.03, . . . )0 Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 34 Summary acar Introduction Model and Estimating plac:piog vild piog H := Xa (Xa0 Va−1 Xa )−1 Xa0 Va−1 . metf:rosi 2 piog:rosi rosi Summary Xa θˆnma =H θˆdir 4 plac:metf sita Flow of evidence 6 metf:piog plac:rosi metf Locating Inconsistency 35 θˆdir = Xa θnma + a 8 rosi:SUal SUal Decomposition of Q Florence, 6 July 2014 acar:SUal plac:acar plac:metf * plac:acar * piog:rosi metf:rosi plac:metf plac:rosi metf:SUal plac Overview Session V: Network Meta-Analysis Contributions of direct estimates metf:piog plac:piog benf rosi:SUal migl metf:SUal Net heat plot in the diabetes example Carpenter/Krahn/R¨ ucker/Schwarzer plac:acar * plac:metf * 0 plac:acar acar:SUal * three-armed study Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis -2 Florence, 6 July 2014 36 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 37 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Contributions of direct estimates Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency SUal vild metf sita rosi piog metf:SUal rosi:SUal plac:piog metf:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar * plac:metf * plac:acar acar:SUal 56 28 -5 9 17 -24 8 4 3 -4 13 16 42 41 4 -10 -43 22 -10 -6 2 acar 4 5 0 plac 3 5 -4 22 68 2 -21 5 -10 1 -1 -2 -1 1 83 10 6 benf 0 16 17 -6 3 36 49 24 35 -6 -15 -1 2 3 -6 4 metf:SUal rosi:SUal plac:piog metf:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar * plac:metf * plac:acar acar:SUal migl 0 2 2 -11 7 14 -18 23 56 -11 -5 -2 4 5 4 SUal 14 -13 -10 19 60 -46 18 10 2 -3 -3 -2 vild metf sita 9 -9 -32 -48 59 -25 12 20 1 -2 -1 0 rosi 18 15 4 -5 18 17 -2 -1 9 -6 57 -34 -11 7 14 -18 23 56 -11 -5 -2 4 5 piog 4 18 15 4 -5 18 17 -2 -1 9 -6 57 -34 27 20 4 -4 21 15 -1 0 -7 6 -40 53 Network Estimate plac Network Estimate acar Direct Estimate metf:SUal rosi:SUal plac:piog metf:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar * plac:metf * plac:acar acar:SUal benf metf:SUal rosi:SUal plac:piog metf:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar * plac:metf * plac:acar acar:SUal * three-armed study Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Summary Contributions of direct estimates Direct Estimate migl Flow of evidence * three-armed study Florence, 6 July 2014 Locating Inconsistency Flow of evidence 38 Summary Contributions of direct estimates Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 39 Summary Net heat plot in the diabetes example plac SUal vild metf sita rosi piog Network Estimate acar metf:SUal rosi:SUal plac:piog metf:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar * plac:metf * plac:acar acar:SUal acar acar:SUal plac:acar plac:metf * plac:acar * piog:rosi metf:rosi plac:metf plac:rosi metf:SUal plac 8 rosi:SUal plac:piog SUal vild 6 metf:piog plac:rosi 4 plac:metf metf sita metf:rosi 2 piog:rosi rosi piog plac:acar * plac:metf * 0 plac:acar acar:SUal * three-armed study Carpenter/Krahn/R¨ ucker/Schwarzer metf:piog benf plac:piog migl rosi:SUal benf metf:SUal migl metf:SUal rosi:SUal plac:piog metf:piog plac:rosi plac:metf metf:rosi piog:rosi plac:acar * plac:metf * plac:acar acar:SUal Direct Estimate Session V: Network Meta-Analysis * three-armed study Florence, 6 July 2014 40 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis -2 Florence, 6 July 2014 41 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary acar Decomposition of Q dir wtu := 8 rosi:SUal 4 plac:metf piog 3. Minimal parallelism (large is nice) 2 plac:acar * plac:metf * πtu = 0 plac:acar acar:SUal Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency ˜ with (where hi,j is one element of H. In the case of multi-arm studies, H design specific net flows is used instead; see K¨onig et al., 2013) Florence, 6 July 2014 Flow of evidence 42 Summary Examples Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Florence, 6 July 2014 Locating Inconsistency Flow of evidence 43 Summary Characterizing measures in the diabetes example 3 3 2 2 3 > m <- netmeasures(nma) > # Direct evidence proportion > m$proportion[order(m$proportion)] Direct evidence proportion 2/3 Mean path length 2/3 × 1 + 1/3 × 2 = 4/3 Minimal parallelism 1/2 × 2 + 1/2 × 1 = 3/2 1 1 1 1 maxd htu,d -2 * three-armed study Introduction htu,d d piog:rosi Overview X metf:rosi sita rosi Summary nma ) var(θˆtu = htu,tu dir ) var(θˆtu ηtu = plac:rosi metf Flow of evidence 6 metf:piog vild Locating Inconsistency 2. Mean path length (short is nice) plac:piog SUal Model and Estimating In the case of only two-arm studies: 1. Direct evidence proportion acar:SUal plac:acar plac:metf * plac:acar * piog:rosi metf:rosi plac:metf plac:rosi metf:SUal plac Introduction Characterizing the flow of evidence metf:piog plac:piog benf rosi:SUal migl metf:SUal Net heat plot in the diabetes example Overview ... sulf:vild acar:metf metf:rosi piog:rosi plac:piog rosi:sulf ... 0.0000 0.1025 0.1750 0.1995 0.3578 0.4106 plac:rosi plac:benf plac:migl plac:sita plac:vild 0.8317 1.0000 1.0000 1.0000 1.0000 migl ● benf ● plac acar ● ● 1 1 3 3 1 ½ ½ 2 SUal Direct evidence proportion 0 Mean path length 4 Minimal parallelism 2 ● ● ● ● sita metf ● rosi Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 44 Carpenter/Krahn/R¨ ucker/Schwarzer vild ● piog Session V: Network Meta-Analysis Florence, 6 July 2014 45 Overview Introduction Model and Estimating Decomposition of Q Locating Inconsistency Flow of evidence Summary Characterizing measures in the diabetes example Overview I > # Minimal parallelism > m$minpar[order(m$minpar)] I ● benf Summary ● ● R package netmeta provides some methods: effect estimating, decomposition of a generalized Q statistic, net heat plot, measures for characterizing the evidence flow vild ● sita metf ● rosi ● piog Session V: Network Meta-Analysis Decomposition of Q I ● ● Locating Inconsistency Florence, 6 July 2014 Flow of evidence 46 Summary Assumption of consistency Issues known from classical meta-analysis when evaluating the validity of results (e.g. heterogeneity, limited power for assessing heterogeneity, selection bias, extent to which results rest on a few studies) plac ● Model and Estimating Flow of evidence I ● acar SUal Introduction Locating Inconsistency Estimating the effects of all pairwise treatment comparisons in a trial network Indirect evidence is taken into account I migl Overview Decomposition of Q Network meta-analysis plac:benf ... sita:sulf sulf:vild 1.0000 3.1383 3.1383 Carpenter/Krahn/R¨ ucker/Schwarzer Model and Estimating Summary > # Mean path length > m$meanpath[order(m$meanpath)] plac:benf ... plac:sulf rosi:sulf 1.0000 2.2156 2.3054 Introduction Carpenter/Krahn/R¨ ucker/Schwarzer Overview Introduction Session V: Network Meta-Analysis Model and Estimating Decomposition of Q Locating Inconsistency Florence, 6 July 2014 Flow of evidence 47 Summary I R¨ ucker G, Schwarzer G, Krahn U, K¨ onig J (2014). netmeta: Network References I Dias S, Welton NJ, Sutton AJ, Ades AE (2011). NICE DSU Technical Support Document 2: A Generalised Linear Modelling Framework for Pairwise and Network Meta-Analysis of Randomised Controlled Trials. http://www.nicedsu.org.uk. meta-analysis with R. http://www.CRAN.R-project.org/package=netmeta. R package, version 0.5-0. I Salanti G (2012). Indirect and mixed-treatment comparison, network, or multiple-treatments meta-analysis: many names, many benefits, many concerns for the next generation evidence synthesis tool. Research Synthesis Methods 2012. I Krahn U, Binder H, K¨ onig J (2013). A graphical tool for locating inconsistency in network meta-analyses. BMC Med Res Methodol. I Senn S, Gavini F, Magrez D, Scheen A (2013). Issues in performing a network I K¨ onig J, Krahn U, Binder H (2013). Visualizing the flow of evidence in network meta-analysis. Stat Methods Med Res. meta-analysis and characterizing mixed treatment comparisons. Stat Med. I White IR, Barrett JK, Jackson D, Higgins JPT (2012). Consistency and I Lu G, Ades AE (2004). Combination of direct and indirect evidence in mixed inconsistency in network metaanalysis: model estimation using multivariate meta-regression. Res Syn Meth. treatment comparisons. Stat Med. I NICE (2008). Evidence synthesis. Guide to the Methods of Technology Appraisal. http://www.nicedsu.org.uk/Evidence-Synthesis-TSDseries%282391675%29.htm. I NICE DSU Technical Support Documents (2011). http://www.nicedsu.org.uk. I Piepho HP, Williams ER, Madden LV (2012). The use of two-way linear mixed models in multitreatment meta-analysis. Biometrics. I R¨ ucker G (2012). Network meta-analysis, electrical networks and graph theory. Res SynMeth. I R¨ ucker G, Schwarzer G (2012). Reduce dimension or reduce weights? Comparing two approaches to multi-arm studies in network meta-analysis. Stat Med. Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 47 Carpenter/Krahn/R¨ ucker/Schwarzer Session V: Network Meta-Analysis Florence, 6 July 2014 47
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