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 2014 2 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 2014 3 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 4
What is R? General purpose statistical package (http://www.r-project.org/) 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 (http://www.r-project.org/doc/r-fda.pdf) More than 5000 add-on packages available on CRAN (http://cran.at.r-project.org/) Short introductions / reviews of add-on packages in The R Journal (http://journal.r-project.org/) successor of R News Mailing lists: http://stat.ethz.ch/mailman/listinfo/ (R-help) R Used as an overgrown calculator > 2 + 2 [1] 4 > 4 - + 1 [1] 3 > exp(1) [1] 2.718282 > x = 2. > x + x [1] 4.5 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 5 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 6 R Working with vectors > 1: [1] 1 2 3 4 5 6 7 8 9 > c(1:4, 6:) [1] 1 2 3 4 6 7 8 9 > y = c(1,4,9,16) > sqrt(y) [1] 1 2 3 4 > 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] 3.02765 > sd(x) [1] 3.02765 [1] 1 16 81 6 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 7 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 8
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 2014 9 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 0.5 1 2 Favours HDCT Favours control HR 0.92 0.52 1.45 0.96 0.64 1.08 1.23 0.69 1.01 0.64 1.34 0.81 1.40 1.41 95% 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 2014 11 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 2014 12
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 2014 13 Fixed Effect Model Graphical Presentation True effect 1 2 3 4 5 0.1 0.2 0.5 1 2 5 Odds ratio Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 14 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 0.92 0.45-1.89-0.0807 0.3672 7.42 Gianni 0.52 0.24-1.11-0.6527 0.3850 6. Gisselbrecht 1.45 1.08-1.93 0.3683 0.1487 45.22 Intragumtornchai 0.96 0.71-1.30-0.0387 0.1529 42.77 Kaiser 0.64 0.30-1.36-0.4480 0.3852 6.74 Kluin-Nelemans 1.08 0. - 1.55 0.0761 0.1834 29.73 Martelli 1996 1.23 0.72-2.08 0.2031 0.97 13. Martelli 2003 0.69 0.29-1.65-0.3773 0.4473 5.00 Milpied 1.01 0.59-1.73 0.0087 0.2748 13.24 Rodriguez 2003 0.64 0.40-1.05-0.4402 0.2481 16. Santini 19 1.34 0.68-2.65 0.2921 0.3482 8. Santini-2 0.81 0.48-1.37-0.2141 0.97 13. Verdonck 1.40 0.73-2.67 0.3368 0.3290 9.24 Vitolo 1.41 0.82-2.41 0.3412 0.2749 13.23 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 15 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 2014 16
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 2014 17 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] -0.0807-0.6527 0.3683-0.0387-0.448... $ sete : num [1:14] 0.367 0.385 0.149 0.153 0.385... $ studlab : chr [1:14] "De Souza" "Gianni" "Gisselbrecht" "Haioun". $ w.fixed : num [1:14] 7.42 6. 45.22 42.77 6.74... $ w.random : num [1:14] 6.18 5.71 20.34 19.83 5.7... $ TE.fixed : num 0.0441 $ sete.fixed : num 0.0657 $ lower.fixed : num -0.0848 $ upper.fixed : num 0.173 $ zval.fixed : num 0.671 Carpenter/Krahn/Rücker/Schwarzer $ pval.fixed : num 0.502 Session I: Introduction to Meta-Analysis Florence, 6 July 2014 18 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 0.5206 [0.2448; 1.73] 2.92 Gisselbrecht 1.4453 [1.0799; 1.9343] 19.55 Haioun 0.9620 [0.7129; 1.22] 18.49 Intragumtornchai 0.6389 [0.3003; 1.93] 2.91 Kaiser 1.0791 [0.33; 1.5458] 12.85 Kluin-Nelemans 1.22 [0.7222; 2.0786] 5.94 Martelli 0.6857 [0.2854; 1.6477] 2.16 Martelli 2003 1.0087 [0.5887; 1.7286] 5.72 Milpied 0.6439 [0.3960; 1.0471] 7.02 Rodriguez 2003 1.3392 [0.6768; 2.6500] 3.57 Santini 0.8073 [0.48; 1.3696] 5.94 Verdonck 1.4005 [0.7349; 2.6688] 3.99 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 19 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 1.0451 [0.9187; 1.1888] 0.6709 0.5023 Quantifying heterogeneity: tau^2 = 0.0270; H = 1.19 [1; 1.64]; I^2 = 29.9% [0%; 63%] Test of heterogeneity: Q d.f. p.value 18.55 13 0.1379 Details on meta-analytical method: - Inverse variance method Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 20
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 0.08 0.3672 0.65 0.3850 0.37 0.1487 0.04 0.1529 0.45 0.3852 0.08 0.1834 0.20 0.97 0.38 0.4473 0.01 0.2748 0.44 0.2481 0.29 0.3482 0.21 0.97 0.34 0.3290 0.34 0.2749 0.92 0.52 1.45 0.96 0.64 1.08 1.23 0.69 1.01 0.64 1.34 0.81 1.40 1.41 [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% 0.5 1 2 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 21 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 22 Aggressive Non-Hodgkin Lymphoma Complete Response HDCT Control Events Total Events Total De Souza 14 28 Gianni 48 50 Gisselbrecht 119 189 116 181 Intragumtornchai 23 9 Kaiser 1 158 97 154 Kluin-Nelemans 67 96 Martelli 1996 3 22 4 27 Martelli 2003 57 51 Milpied 74 99 Rodriguez 2003 39 55 30 53 Santini 19 63 34 61 Santini-2 80 117 71 6 Verdonck 38 Vitolo 60 66 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 2014 23 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 24
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$te), 2) [1] 2.37 η = p T p C ˆη = ˆp T ˆp C Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 Binary Effect Measures Confidence Interval Binary Effect Measures Confidence Interval Large sample variance estimates (Fleiss, 1993): Var(log ˆφ) = 1 a + 1 c 1 a + b 1 c + d Var(log ˆψ) = 1 a + 1 b + 1 c + 1 d Var(ˆη) = a b (a + b) 3 + c d (c + d) 3 (1 α)-confidence interval (on log scale for risk ratio and odds ratio): ˆθ ± z 1 α 2 S.E.(ˆθ) with standard error S.E.(ˆθ) = Var(ˆθ). (3) Large sample variance estimates (Fleiss, 1993): Var(log ˆφ) = Var(log ˆψ) = Var(ˆη) = 1 a + 0.5 + 1 c + 0.5 1 a + b + 0.5 1 c + d + 0.5 1 a + 0.5 + 1 b + 0.5 + 1 c + 0.5 + 1 d + 0.5 (a + 0.5) (b + 0.5) (c + 0.5) (d + 0.5) (a + b + 1) 3 + (c + d + 1) 3 Add 0.5 if any cell counts are zero (Gart and Zweifel, 1967; Pettigrew et al., 16) Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 27 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 28
Binary Effect Measures Confidence Interval Aggressive Non-Hodgkin Lymphoma Forestplot > mil = metabin(crhdct, nhdct, crcontrol, ncontrol, + sm="or", data=cr, studlab=study, + subset=study=="milpied") > # Print variance estimate > mil$sete^2 [1] 0.09629314 > ## Print confidence interval > print(mil, digits=2) OR 95%-CI z p.value 2.37 [1.29; 4.] 2.78 0.0055 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 14 119 1 67 3 57 74 39 80 28 48 189 23 158 22 55 63 117 38 60 116 9 97 4 51 30 34 71 50 181 154 96 27 99 53 61 6 66 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 0.1 0.5 1 2 Favours control Favours HDCT Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 29 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 30 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 11 139 6.7% 7.3% 0.91 [0.30; 2.74] HDCT 40 140 Control 12 38 22.2% 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 44 196 Control 23 177 18.3% 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 2014 31 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 32
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 1.3228 [1.0999; 1.5909] 2.9713 0.003 Quantifying heterogeneity: tau^2 = 0.0897; H = 1.3 [1; 1.78]; I^2 = 41% [0%; 68.6%] Test of heterogeneity: Q d.f. p.value 22.03 13 0.0549 Carpenter/Krahn/Rücker/Schwarzer Session I: Introduction to Meta-Analysis Florence, 6 July 2014 33 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 14 119 1 67 3 57 74 39 80 28 48 189 23 158 22 55 63 117 38 60 72 116 9 97 4 51 30 34 71 50 181 154 96 27 99 53 61 6 66 54 Odds Ratio 0.1 0.5 1 2 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 2014 34 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 2014 36
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 14 119 1 67 3 57 74 39 80 28 48 189 23 158 22 55 63 117 38 60 72 116 9 97 4 51 30 34 71 50 181 154 96 27 99 53 61 6 66 54 Odds Ratio 0.1 0.5 1 2 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 2014 37 Summary Meta-analysis R Central to evidence based medicine (see, e.g. website of Cochrane Collaboration http://www.cochrane.org/). 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 2014 38 References Carpenter, J., Rücker, G., and Schwarzer, G. (2009). copas: An R package for fitting the Copas selection model. The R Journal, 1(2):31 36. Egger, M. and Smith, G. D. (1997). Meta-analysis: Potentials and promise. British Medical Journal, 315:1371 1374. Fleiss, J. L. (1993). The statistical basis of meta-analysis. Statistical Methods in Medical Research, 2:121 145. 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, 54:181 187. Gasparrini, A. (2014). mvmeta: Multivariate and univariate meta-analysis and meta-regression. R package version 0.4.3. 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:CD004024. DOI:.02/151858.CD004024.pub2. Lumley, T. (2012). rmeta: Meta-analysis. R package version 2.16. 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):719 748. 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 2014 38 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 0.5-0. Schwarzer, G. (2007). meta: An R package for meta-analysis. R News, 7(3):40 45. Schwarzer, G., Carpenter, J., and Rücker, G. (2014). metasens: Advanced statistical methods to model and adjust for bias in meta-analysis. R package version 0.1-0. 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 2014 38