Plan of the Session. Session I: Basic Methods of Meta-Analysis Short Introduction to R. Why Conduct a Meta-Analysis? What is a Meta-Analysis?

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1 Session I: Basic Methods of Meta-Analysis Short Introduction to R James Carpenter 1, Ulrike Krahn 2,3, Gerta Rücker 4, Guido Schwarzer 4 1 London School of Hygiene and Tropical Medicine & MRC Clinical Trials Unit, London, UK 2 Institute 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 sc@imbi.uni-freiburg.de IBC Short Course Florence, 6 July 2014 Plan of the Session At the end of this session the aim is that you should understand the basic principles of meta-analysis; how R works. The objectives are that you are able to: use the help system and read data into R; conduct a meta-analysis with binary outcomes; summarize the main result of a meta-analysis to a medical audience. 1 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July What is a Meta-Analysis? Why Conduct a Meta-Analysis? See Egger and Smith (1997), BMJ Definitions: Term Meta : Implies occuring later, more comprehensive, new but related discipline which critically deals with original discipline Term Meta-Analysis : Statistically combining and analysing data from separate studies Term Systematic Review : Any type of review utilising strategies to avoid bias Meta-analysis: May or may not be part of a systematic review Medical Subject Heading (MeSH) in Medline Egger and Smith (1997), BMJ More objective appraisal of evidence which may lead to resolution of uncertainty and disagreement Reduce probability of false negative results and thus prevent undue delays in introduction of effective treatments into practice Heterogeneity between study results may be explored (and sometimes explained) Allows testing of a priori hypotheses regarding treatment effects in subgroups of patients Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

2 What is R? General purpose statistical package ( Based on statistical programming language S ( S-PLUS) Almost 20 years old, actively developed and maintained Available for Windows, Linux, Unix, Mac OS Released under the GNU General Public License (GPL) version 2 (or any later version) Licence costs: 0e / 0$ R can be used in regulated clinical trial environments ( More than 5000 add-on packages available on CRAN ( Short introductions / reviews of add-on packages in The R Journal ( successor of R News Mailing lists: (R-help) R Used as an overgrown calculator > [1] 4 > [1] 3 > exp(1) [1] > x = 2. > x + x [1] 4.5 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July R Working with vectors > 1: [1] > c(1:4, 6:) [1] > y = c(1,4,9,16) > sqrt(y) [1] > sqrt(y)[4] [1] 4 > y^2 # same result: y**2 R Calculate mean and standard deviance > x = 1: > sum(x) / length(x) [1] 5.5 > mean(x) [1] 5.5 > sqrt(sum((x-mean(x))^2)/(length(x)-1)) [1] > sd(x) [1] [1] Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

3 R Missing values Example: Aggressive Non-Hodgkin Lymphoma NA: Not Available > x = c(1:5, NA) > mean(x) [1] NA > # Getting help: > help(mean) # Show documentation on R command mean >?mean # Show documentation on R command mean > help.start() # Show documentation in webbrowser > help("+") # Show help on arithmetic operator + >?"+" # Show help on arithmetic operator + > mean(x, na.rm=true) Greb et al. (2008), Cochrane Database Syst Rev 1, CD004024: Cochrane Review including 15 randomised controlled trials (RCTs) Adult patients with aggressive non-hodgkin lymphoma First line treatment with high-dose chemotherapy (HDCT) versus conventional chemotherapy Primary outcome: Overall survival (14 RCTs, 2444 patients) Secondary outcome: Complete response (14 RCTs, 21 patients) [1] 3 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 Aggressive Non-Hodgkin Lymphoma Forestplot De Souza Gianni Gisselbrecht Haioun Intragumtornchai Kaiser Kluin Nelemans Martelli Martelli 2003 Milpied Rodriguez 2003 Santini Verdonck Vitolo Hazard Ratio Favours HDCT Favours control HR % CI [0.45; 1.89] [0.24; 1.11] [1.08; 1.93] [0.71; 1.30] [0.30; 1.36] [0.; 1.55] [0.72; 2.08] [0.29; 1.65] [0.59; 1.73] [0.40; 1.05] [0.68; 2.65] [0.48; 1.37] [0.73; 2.67] [0.82; 2.41] Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Meta-Analysis Calculate a Weighted Mean Weighted mean of estimated treatment effects in individual studies (Fleiss, 1993): Kk=1 w k ˆθ k ˆθ = Kk=1 w k Estimated treatment effect ˆθ k in study k (k = 1,..., K) Weight w k correspond to information of study k Methods of meta-analysis differ in definition of weights (especially fixed effect and random effects model) > args(weighted.mean) function (x, w,...) NULL > weighted.mean(1:2, c(0.2, 0.8)) [1] 1.8 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

4 Fixed effect model Inverse Variance Method Fixed effect model: ˆθ k = θ + ˆσ k ɛ k, ɛ k i.i.d. N(0, 1), k = 1,..., K (1) Maximum likelihood estimate under model (1) for given (ˆθ k, ˆσ k ): Kk=1 ˆθ k /ˆσ ˆθ 2 Kk=1 k w k ˆθ k F = Kk=1 = 1/ˆσ 2 Kk=1 w k k with weights w k = 1/ˆσ 2 k. Estimated variance of ˆθ F : Var (ˆθ F ) = (1-α) confidence interval for ˆθ F : 1 Kk=1 w k = 1 Kk=1 1/ˆσ 2 k ˆθ F ± z 1 α 2 S.E.(ˆθ F ) with S.E.(ˆθ F ) = Var(ˆθ F ) Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Fixed Effect Model Graphical Presentation True effect Odds ratio Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Aggressive Non-Hodgkin Lymphoma Overall Survival Hazard log(hr) SE(log(HR)) w k = 95%-CI Ratio (HR) (= ˆθ k ) (= ˆσ k ) 1/ˆσ 2 k De Souza Gianni Gisselbrecht Intragumtornchai Kaiser Kluin-Nelemans Martelli Martelli Milpied Rodriguez Santini Santini Verdonck Vitolo Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July R packages for meta-analysis on CRAN rmeta (Lumley, 2012) Fixed and random effects meta-analysis (Mantel-Haenszel, Peto, DerSimonian-Laird) metafor (Viechtbauer, 20) Tests for funnel plot asymmetry / Trim and fill method General linear (mixed-effects) model approach for meta-regression Multivariate meta-analysis meta (Schwarzer, 2007) Tests for funnel plot asymmetry / Trim and fill method Import data from RevMan 5 / Link to R package metafor mvmeta (Gasparrini, 2014) Multivariate meta-analysis and meta-regression on multiple outcomes metasens (Schwarzer et al., 2014; Carpenter et al., 2009) Advanced methods to model and adjust for bias in meta-analysis Add-on package to R package meta / replaces R package copas netmeta (Rücker et al., 2014) Network meta-analysis Add-on package to R package meta Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

5 R package meta Function Comment metabin Meta-analysis of binary outcome data metacont Meta-analysis of continuous outcome data metagen Generic inverse variance meta-analysis metacor Meta-analysis of correlations metainc Meta-analysis of incidence rates metaprop Meta-analysis of single proportions read.rm5 Import RevMan 5 data files (csv-files with special format) metacr Meta-analysis of outcome data from Cochrane review forest Forest plot funnel Plot to assess funnel plot asymmetry metabias Test for funnel plot asymmetry trimfill Trim and fill method for meta-analysis metareg Meta-regression (wrapper function to R package metafor)... Cumulative meta-analysis / Influence analysis in meta-analysis Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Meta-Analysis of Overall Survival > os = read.csv("hd-os.txt", as.is=true) > library(meta) > m1 = metagen(loghr, seloghr, + sm="hr", data=os, studlab=study, + comb.random=false) > str(m1) List of 62 $ TE : num [1:14] $ sete : num [1:14] $ studlab : chr [1:14] "De Souza" "Gianni" "Gisselbrecht" "Haioun". $ w.fixed : num [1:14] $ w.random : num [1:14] $ TE.fixed : num $ sete.fixed : num $ lower.fixed : num $ upper.fixed : num $ zval.fixed : num Carpenter/Krahn/Rücker/Schwarzer $ pval.fixed : num Session I: Introduction to Meta-Analysis Florence, 6 July Meta-Analysis of Survival Data Print Function > class(m1) [1] "metagen" "meta" > m1 # Calls R function print.meta HR 95%-CI %W(fixed) De Souza 0.92 [0.4491; 1.89] 3.21 Gianni [0.2448; 1.73] 2.92 Gisselbrecht [1.0799; ] Haioun [0.7129; 1.22] Intragumtornchai [0.3003; 1.93] 2.91 Kaiser [0.33; ] Kluin-Nelemans 1.22 [0.7222; ] 5.94 Martelli [0.2854; ] 2.16 Martelli [0.5887; ] 5.72 Milpied [0.3960; ] 7.02 Rodriguez [0.6768; ] 3.57 Santini [0.48; ] 5.94 Verdonck [0.7349; ] 3.99 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Meta-Analysis of Overall Survival Summary Function > summary(m1) # Calls summary.meta and print.summary.meta Number of studies combined: k=14 HR 95%-CI z p.value Fixed effect model [0.9187; ] Quantifying heterogeneity: tau^2 = ; H = 1.19 [1; 1.64]; I^2 = 29.9% [0%; 63%] Test of heterogeneity: Q d.f. p.value Details on meta-analytical method: - Inverse variance method Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

6 Overall Survival Forestplot > forest(m1, hetstat=false) # Calls function forest.meta Example: Aggressive Non-Hodgkin Lymphoma TE sete Hazard Ratio HR 95% CI W(fixed) De Souza Gianni Gisselbrecht Haioun Intragumtornchai Kaiser Kluin Nelemans Martelli Martelli 2003 Milpied Rodriguez 2003 Santini Verdonck Vitolo [0.45; 1.89] [0.24; 1.11] [1.08; 1.93] [0.71; 1.30] [0.30; 1.36] [0.; 1.55] [0.72; 2.08] [0.29; 1.65] [0.59; 1.73] [0.40; 1.05] [0.68; 2.65] [0.48; 1.37] [0.73; 2.67] [0.82; 2.41] 3.2% 2.9% 19.5% 18.5% 2.9% 12.9% 5.9% 2.2% 5.7% 7.0% 3.6% 5.9% 4.0% 5.7% Greb et al. (2008), Cochrane Database Syst Rev 1, CD004024: Cochrane Review including 15 randomised controlled trials (RCTs) Adult patients with aggressive non-hodgkin lymphoma First line treatment with high-dose chemotherapy (HDCT) versus conventional chemotherapy Primary outcome: Overall survival (14 RCTs, 2444 patients) Secondary outcome: Complete response (14 RCTs, 21 patients) Fixed effect model 1.05 [0.92; 1.19] 0% Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Aggressive Non-Hodgkin Lymphoma Complete Response HDCT Control Events Total Events Total De Souza Gianni Gisselbrecht Intragumtornchai 23 9 Kaiser Kluin-Nelemans Martelli Martelli Milpied Rodriguez Santini Santini Verdonck 38 Vitolo Milpied Complete Response (CR) CR no CR HDCT 74 (a) 24 (b) (a + b = n T ) Control (c) 43 (d) 99 (c + d = n C ) 130 (a + c) 67 (b + d) 197 (n) Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

7 Binary Data Effect Measures Let p T : Experimental event rate ˆp T = a/(a + b) p C : Control event rate ˆp C = c/(c + d) Risk Ratio φ: Odds ratio ψ: Risk Difference η: ( p T 1 p T ψ = ( p C 1 p C φ = p T p C ) ˆφ = ˆp T ˆp C ) = φ 1 p C ˆψ = a d 1 p T b c (2) Binary Data Effect Measures > cr = read.csv("hd-cr.txt", as.is=true) > library(meta) > mil = metabin(crhdct, nhdct, crcontrol, ncontrol, + sm="or", data=cr, studlab=study, + subset=study=="milpied") > round(exp(mil$te), 2) [1] 2.37 η = p T p C ˆη = ˆp T ˆp C Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 Binary Effect Measures Confidence Interval Binary Effect Measures Confidence Interval Large sample variance estimates (Fleiss, 1993): Var(log ˆφ) = 1 a + 1 c 1 a + b 1 c + d Var(log ˆψ) = 1 a + 1 b + 1 c + 1 d Var(ˆη) = a b (a + b) 3 + c d (c + d) 3 (1 α)-confidence interval (on log scale for risk ratio and odds ratio): ˆθ ± z 1 α 2 S.E.(ˆθ) with standard error S.E.(ˆθ) = Var(ˆθ). (3) Large sample variance estimates (Fleiss, 1993): Var(log ˆφ) = Var(log ˆψ) = Var(ˆη) = 1 a c a + b c + d a b c d (a + 0.5) (b + 0.5) (c + 0.5) (d + 0.5) (a + b + 1) 3 + (c + d + 1) 3 Add 0.5 if any cell counts are zero (Gart and Zweifel, 1967; Pettigrew et al., 16) Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

8 Binary Effect Measures Confidence Interval Aggressive Non-Hodgkin Lymphoma Forestplot > mil = metabin(crhdct, nhdct, crcontrol, ncontrol, + sm="or", data=cr, studlab=study, + subset=study=="milpied") > # Print variance estimate > mil$sete^2 [1] > ## Print confidence interval > print(mil, digits=2) OR 95%-CI z p.value 2.37 [1.29; 4.] De Souza Gianni Gisselbrecht Intragumtornchai Kaiser Kluin Nelemans Martelli Martelli 2003 Milpied Rodriguez 2003 Santini Santini 2 Verdonck Vitolo HDCT Control Events Total Events Total Odds Ratio OR 95% CI 1.60 [0.54; 4.73] 9.86 [2.11; 45.96] 0.95 [0.62; 1.45] 1.37 [0.43; 4.36] 1. [0.84; 2.16] 1.54 [0.86; 2.78] 0.91 [0.18; 4.57] 1.49 [0.73; 3.06] 2.37 [1.29; 4.] 1.87 [0.84; 4.14] 2.15 [1.01; 4.] 1.07 [0.61; 1.87] 0.67 [0.24; 1.83] 0.61 [0.29; 1.27] Details: - Inverse variance method Favours control Favours HDCT Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Naive Pooling Fictitious Example Inverse Variance Method Odds ratio Definition 1 2 CR no CR ˆp T ˆp C RR [95%-CI] HDCT 4 Control % 7.3% 0.91 [0.30; 2.74] HDCT Control % 24.0% 0.93 [0.53; 1.63] Overall odds ratio ˆψ IV (Fleiss, 1993): K w k log ˆψ k k=1 ˆψ IV = exp K w k k=1 (4) index: k = 1,..., K 1&2 HDCT Control % 11.5% 1.59 [1.00; 2.55] Weights: w k = 1 / Var(log ˆψ k ) ( fixed effect model) See formulae (2) and (3) for definition of ˆψ k and Var(log ˆψ k ) Appropriate meta-analysis 0.92 [0.; 1.52] Analogous for risk ratio as effect measure: log ˆφ k For risk difference: ˆη k (without exp function in equation (4)) Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

9 Meta-Analysis of CR Inverse Variance Method > cr = read.csv("hd-cr.txt", as.is=true) > library(meta) > m2 = metabin(crhdct, nhdct, crcontrol, ncontrol, + sm="or", data=cr, studlab=study, + comb.random=false, method="inverse") > summary(m2) Number of studies combined: k=14 OR 95%-CI z p.value Fixed effect model [1.0999; ] Quantifying heterogeneity: tau^2 = ; H = 1.3 [1; 1.78]; I^2 = 41% [0%; 68.6%] Test of heterogeneity: Q d.f. p.value Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Forest Plot CR Inverse Variance Method > forest(m2, hetstat=false, text.fixed="iv estimate") De Souza Gianni Gisselbrecht Intragumtornchai Kaiser Kluin Nelemans Martelli Martelli 2003 Milpied Rodriguez 2003 Santini Santini 2 Verdonck Vitolo IV estimate Experimental Control Events Total Events Total Odds Ratio OR 1.60 [0.54; 4.73] 9.86 [2.11; 45.96] 0.95 [0.62; 1.45] 1.37 [0.43; 4.36] 1. [0.84; 2.16] 1.54 [0.86; 2.78] 0.91 [0.18; 4.57] 1.49 [0.73; 3.06] 2.37 [1.29; 4.] 1.87 [0.84; 4.14] 2.15 [1.01; 4.] 1.07 [0.61; 1.87] 0.67 [0.24; 1.83] 0.61 [0.29; 1.27] 1.32 [1.; 1.59] 95% CI W(fixed) 2.9% 1.4% 19.0% 2.5% 15.3% 9.8% 1.3% 6.6% 9.2% 5.4% 6.0%.8% 3.3% 6.3% 0% Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Mantel-Haenszel Method Odds ratio Definition Mantel and Haenszel (1959): Estimator for common odds ratio in stratified case-control study Can be used in meta-analysis of RCTs Fixed effect method Mantel-Haenszel odds ratio ˆψ MH : ˆψ MH = k k=1 w k ˆψ k k k=1 w k (5) Meta-Analysis of CR Mantel-Haenszel Method > cr = read.csv("hd-cr.txt", as.is=true) > library(meta) > m3 = metabin(crhdct, nhdct, crcontrol, ncontrol, + sm="or", data=cr, studlab=study, + comb.random=false, method="mh") > # Same result (Mantel-Haenszel method is default) > m3 = metabin(crhdct, nhdct, crcontrol, ncontrol, + sm="or", data=cr, studlab=study, + comb.random=false) > # Same result (use of R function update.meta) > m3 = update(m2, method="mh") Weights: w k = b kc k n k Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July

10 Forest Plot CR Mantel-Haenszel Method > forest(m3, hetstat=false, text.fixed="mh estimate") De Souza Gianni Gisselbrecht Intragumtornchai Kaiser Kluin Nelemans Martelli Martelli 2003 Milpied Rodriguez 2003 Santini Santini 2 Verdonck Vitolo MH estimate Experimental Control Events Total Events Total Odds Ratio OR 1.60 [0.54; 4.73] 9.86 [2.11; 45.96] 0.95 [0.62; 1.45] 1.37 [0.43; 4.36] 1. [0.84; 2.16] 1.54 [0.86; 2.78] 0.91 [0.18; 4.57] 1.49 [0.73; 3.06] 2.37 [1.29; 4.] 1.87 [0.84; 4.14] 2.15 [1.01; 4.] 1.07 [0.61; 1.87] 0.67 [0.24; 1.83] 0.61 [0.29; 1.27] 1. [1.12; 1.61] 95% CI W(fixed) 2.6% 0.7% 21.8% 2.4% 14.8% 8.9% 1.5% 6.1% 6.8% 4.4% 4.6% 11.7% 4.6% 9.1% 0% Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July Summary Meta-analysis R Central to evidence based medicine (see, e.g. website of Cochrane Collaboration Only as good as the evidence that it relies on. Some important issues are: Heterogeneity of study results. The more you can explain, the better subgroup-analysis / meta-regression. Bias in contributing studies / non-representativeness of studies (e.g. due to publication bias). Binary data raises some special issues, especially if event rates are low. Modern statistical packages for data analysis, management & graphics Use of additional software easily possible, e.g. for meta-analysis Use of command line necessary Extended documentation available (Online, Use-R! books,...) Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July References Carpenter, J., Rücker, G., and Schwarzer, G. (2009). copas: An R package for fitting the Copas selection model. The R Journal, 1(2): Egger, M. and Smith, G. D. (1997). Meta-analysis: Potentials and promise. British Medical Journal, 315: Fleiss, J. L. (1993). The statistical basis of meta-analysis. Statistical Methods in Medical Research, 2: Gart, J. J. and Zweifel, J. R. (1967). On the bias of various estimators of the logit and its variance with application to quantal bioassay. Biometrika, 54: Gasparrini, A. (2014). mvmeta: Multivariate and univariate meta-analysis and meta-regression. R package version Greb, A., Bohlius, J., Schiefer, D., Schwarzer, G., Schulz, H., and Engert, A. (2008). High-dose chemotherapy with autologous stem cell transplantation in the first line treatment of aggressive non-hodgkin lymphoma (nhl) in adults. Cochrane Database Syst Rev, 1:CD DOI:.02/ CD pub2. Lumley, T. (2012). rmeta: Meta-analysis. R package version Mantel, N. and Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute, 22(4): Pettigrew, H. M., Gart, J. J., and Thomas, D. G. (16). The bias and higher cumulants of the logarithm of a binomial variate. Biometrika, 73:4 4. Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Rücker, G., Schwarzer, G., Krahn, U., and König, J. (2014). netmeta: Network meta-analysis with R. R package version Schwarzer, G. (2007). meta: An R package for meta-analysis. R News, 7(3): Schwarzer, G., Carpenter, J., and Rücker, G. (2014). metasens: Advanced statistical methods to model and adjust for bias in meta-analysis. R package version Viechtbauer, W. (20). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3):1 48. Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July