Merge results of two meta-analyses on the same data set
This function can be used to merge results of two meta-analyses into a single meta-analysis object if they are based on the same data set. This is, for example, useful to produce a forest plot of a random-effects meta-analysis with different estimates of the between-study variance .
metamerge( meta1, meta2, common1 = meta1$common, random1 = meta1$random, prediction1 = meta1$prediction, common2 = meta2$common, random2 = meta2$random, prediction2 = meta2$prediction, label1 = NULL, label2 = NULL, label1.common = label1, label2.common = label2, label1.random = label1, label2.random = label2, label1.predict = label1, label2.predict = label2, label1.subgroup = label1, label2.subgroup = label2, hetlabel1 = label1.random, hetlabel2 = label2.random, taulabel1 = label1.random, taulabel2 = label2.random, text.pooled1 = NULL, text.pooled2 = NULL, text.w.pooled1 = NULL, text.w.pooled2 = NULL, text.common1 = text.pooled1, text.common2 = text.pooled2, text.random1 = text.pooled1, text.random2 = text.pooled2, text.predict1 = text.pooled1, text.predict2 = text.pooled2, text.w.common1 = text.w.pooled1, text.w.common2 = text.w.pooled2, text.w.random1 = text.w.pooled1, text.w.random2 = text.w.pooled2, keep = FALSE, keep.Q = keep, keep.I2 = keep.Q, keep.w = keep, common = common1 | common2, random = random1 | random2, overall = common | random, overall.hetstat = common | random, prediction = prediction1 | prediction2, backtransf, warn.deprecated = gs("warn.deprecated"), pooled1, pooled2 )
meta1: First meta-analysis object (see Details).meta2: Second meta-analysis object (see Details).common1: A logical indicating whether results of common effect model should be considered for first meta-analysis.random1: A logical indicating whether results of random effects model should be considered for first meta-analysis.prediction1: A logical indicating whether prediction interval should be considered for first meta-analysis.common2: A logical indicating whether results of common effect model should be considered for second meta-analysis.random2: A logical indicating whether results of random effects model should be considered for second meta-analysis.prediction2: A logical indicating whether prediction interval should be considered for second meta-analysis.label1: Default setting for arguments 'label1.common', 'label1.random', 'label1.predict' and 'label1.subgroup'.label2: Default setting for arguments 'label2.common', 'label2.random', 'label2.predict' and 'label2.subgroup'.label1.common: A character string ...label2.common: A character string ...label1.random: A character string ... (default label for arguments 'hetlabel1' and 'taulabel1').label2.random: A character string ... (default label for arguments 'hetlabel2' and 'taulabel2').label1.predict: A character string ...label2.predict: A character string ...label1.subgroup: A character string ...label2.subgroup: A character string ...hetlabel1: A character string used to label heterogeneity statistics of the first meta-analysis.hetlabel2: A character string used to label heterogeneity statistics of the second meta-analysis.taulabel1: A character string used to label estimate of between-study variance of the first meta-analysis.taulabel2: A character string used to label estimate of between-study variance of the second meta-analysis.text.pooled1: A character string used in printouts and forest plot to label the results from the first meta-analysis.text.pooled2: A character string used in printouts and forest plot to label the results from the second meta-analysis.text.w.pooled1: A character string used to label weights of the first meta-analysis; can be of same length as the number of pooled estimates requested in argument pooled1.text.w.pooled2: A character string used to label weights of the second meta-analysis; can be of same length as the number of pooled estimates requested in argument pooled1.text.common1: A character string used in printouts and forest plot to label results for common effect models from the first meta-analysis.text.common2: A character string used in printouts and forest plot to label results for common effect models from the second meta-analysis.text.random1: A character string used in printouts and forest plot to label results for random effects models from the first meta-analysis.text.random2: A character string used in printouts and forest plot to label results for random effects models from the second meta-analysis.text.predict1: A character string used in printouts and forest plot to label prediction interval from the first meta-analysis.text.predict2: A character string used in printouts and forest plot to label prediction interval from the second meta-analysis.text.w.common1: A character string used to label common effect weights of the first meta-analysis; can be of same length as the number of common effect estimates.text.w.common2: A character string used to label common effect weights of the second meta-analysis; can be of same length as the number of common effect estimates.text.w.random1: A character string used to label random effects weights of the first meta-analysis; can be of same length as the number of random effects estimates.text.w.random2: A character string used to label random effects weights of the second meta-analysis; can be of same length as the number of random effects estimates.keep: A logical indicating whether to keep additional information from second meta-analysis.keep.Q: A logical indicating whether heterogeneity statistic Q of second meta-analysis should be kept or ignored.keep.I2: A logical indicating whether heterogeneity statistic I2 of second meta-analysis should be kept or ignored.keep.w: A logical indicating whether weights of the second meta-analysis should be kept or ignored.common: A logical indicating whether results of common effect meta-analyses should be reported.random: A logical indicating whether results of random effects meta-analyses should be reported.overall: A logical indicating whether overall summaries should be reported.overall.hetstat: A logical value indicating whether to print heterogeneity measures for overall treatment comparisons.prediction: A logical indicating whether prediction intervals should be reported.backtransf: A logical indicating whether results should be back transformed in printouts and plots. If backtransf=TRUE (default), results for sm="OR" are printed as odds ratios rather than log odds ratios, for example.warn.deprecated: A logical indicating whether warnings should be printed if deprecated arguments are used.pooled1: Deprecated argument (replaced by 'common1', 'random1', 'prediction1'). A character string indicating whether results of common effect or random effects model should be considered for first meta-analysis. Either "both", "common" or "random", can be abbreviated.pooled2: Deprecated argument (replaced by 'common2', 'random2', 'prediction2'). A character string indicating whether results of common effect or random effects model should be considered for second meta-analysis. Either "both", "common" or "random", can be abbreviated.An object of class "meta" and "metamerge" with corresponding generic functions (see meta-object).
The following list elements have a different meaning: - TE, seTE, studlab: Treatment estimate, standard error, and study labels (first meta-analyis).
lower, upper: Lower and upper confidence interval limits for individual studies (first meta-analysis).
statistic, pval: Statistic and p-value for test of treatment effect for individual studies (first meta-analysis.
w.common: Vector or matrix with common effect weights.
w.random: Vector or matrix with random effects weights.
k: Vector with number of estimates (same length as number of common effect and random effects estimates).
k.study: Vector with number of studies (same length as number of common effect and random effects estimates).
k.all: Vector with total number of studies (same length as number of common effect and random effects estimates).
k.TE: Vector with number of studies with estimable effects (same length as number of common effect and random effects estimates).
k.MH: Vector with number of studies combined with Mantel-Haenszel method (same length as number of common effect and random effects estimates).
TE.common: Vector with common effect estimates.
seTE.common: Vector with standard errors of common effect estimates.
lower.common: Vector with lower confidence limits (common effect model).
upper.common: Vector with upper confidence limits (common effect model).
statistic.common: Vector with test statistics for test of overall effect (common effect model).
pval.common: Vector with p-value of test for overall effect (common effect model).
TE.random: Vector with random effects estimates.
seTE.random: Vector with standard errors of random effects estimates.
lower.random: Vector with lower confidence limits (random effects model).
upper.random: Vector with upper confidence limits (random effects model).
statistic.random: Vector with test statistics for test of overall effect (random effects model).
pval.random: Vector with p-value of test for overall effect (random effects model).
Furthermore, meta-analysis results of common effect or random effects model are taken from first meta-analysis if only random effects or common effects models are selected from both meta-analyses (arguments pooled1 and pooled2).
In R package meta , objects of class "meta" contain results of both common effect and random effects meta-analyses. This function enables the user to merge the results of two meta-analysis object if they are based on the same data set.
Applications of this function include printing and plotting results of the common effect or random effects meta-analysis and the
trimfill),limitmeta from R package metasens ),copas from R package metasens ),robu from R package robumeta ).The first argument (meta1) must be an object created by a meta-analysis function (see meta-object). If an object created with limitmeta or copas is provided as the first argument, this object will be returned, i.e., argument meta2 will be ignored.
The second meta-analysis could be an object created by a meta-analysis function or with trimfill, limitmeta, copas, or robu.
The created meta-analysis object only contains the study results, i.e., estimated effects and confidence intervals, from the first meta-analysis which are shown in printouts and forest plots. This only makes a difference for meta-analysis methods where individual study results differ, e.g., Mantel-Haenszel and Peto method for binary outcomes (see metabin).
R function metaadd can be used to add pooled results from any (external) meta-analysis.
R function metabind can be used to print and plot the results of several meta-analyses without the restriction that the same data set has to be used. Accordingly, individual study results are ignored.
# Print results with more significant digits and do not show confidence # intervals for tau^2 and tau oldset <- settings.meta(digits = 6, digits.stat = 4, digits.pval = 6, digits.Q = 6, digits.I2 = 4, digits.H = 4, print.tau2.ci = FALSE, print.tau.ci = FALSE) oldopts <- options(width = 120) data(Fleiss1993bin) # Mantel-Haenszel method m1 <- metabin(d.asp, n.asp, d.plac, n.plac, data = Fleiss1993bin, studlab = paste(study, year), sm = "OR") # Peto method m2 <- update(m1, method = "Peto") # Inverse variance method (only common effect model) m3 <- update(m2, method = "Inverse", random = FALSE) # Merge results from MH and Peto method # - show individual results for MH method # (as this is the first meta-analysis) # - keep all additional information from Peto meta-analysis (i.e., # weights, Q statistic and I2 statistic) m12 <- metamerge(m1, m2, label1 = "REML", label2 = "REML-Peto", label1.common = "MH", label2.common = "Peto", text.common1 = "Mantel-Haenszel method", text.common2 = "Peto method", text.w.random1 = "REML", text.w.random2 = "REML-Peto", hetlabel1 = "MH/IV", hetlabel2 = "Peto", keep = TRUE) # Add common effect results from inverse variance method # - keep weights from IV meta-analysis # - Q and I2 statistic are identical for sm = "MH" and sm = "Inverse" # as inverse variance method is used for sm = "MH" under random # effects model m123 <- metamerge(m12, m3, label2 = "IV", text.common2 = "Inverse variance method", keep.w = TRUE) summary(m123) ## Not run: forest(m123, digits = 6) # Merge results (show individual results for Peto method) m21 <- metamerge(m2, m1, label1 = "REML-Peto", label2 = "REML", label1.common = "Peto", label2.common = "MH", hetlabel1 = "Peto", hetlabel2 = "MH/IV", text.common1 = "Peto method", text.common2 = "Mantel-Haenszel method", keep = TRUE) # Add results from inverse variance method # - keep weights from IV meta-analysis # - Q and I2 statistic are identical for sm = "MH" and sm = "Inverse" # as inverse variance method is used for sm = "MH" under random # effects model m213 <- metamerge(m21, m3, label2 = "IV", text.common2 = "Inverse variance method", keep.w = TRUE) summary(m213) # Random effects method using ML estimator for between-study variance tau2 m4 <- update(m1, common = FALSE, method.tau = "ML") # Use DerSimonian-Laird estimator for tau2 m5 <- update(m4, method.tau = "DL") # Use Paule-Mandel estimator for tau2 m6 <- update(m4, method.tau = "PM") # Merge random effects results for ML and DL estimators # - keep weights for DL estimator (which are different from ML) m45 <- metamerge(m4, m5, label1 = "ML", label2 = "DL", text.w.random1 = "RE-ML", text.w.random2 = "RE-DL", keep.w = TRUE) summary(m45) # Add results for PM estimator # - keep weights m456 <- metamerge(m45, m6, label2 = "PM", text.w.random2 = "RE-PM", keep.w = TRUE) summary(m456) m123456 <- metamerge(m123, m456) m123456 # Use Hartung-Knapp confidence intervals # - do not keep information on Q, I2 and weights m7 <- update(m4, method.random.ci = "HK", text.random = "Hartung-Knapp method") m8 <- update(m5, method.random.ci = "HK", text.random = "Hartung-Knapp method") m9 <- update(m6, method.random.ci = "HK", text.random = "Hartung-Knapp method") # Merge results for Hartung-Knapp method (with REML and DL estimator) # - RE weights for REML estimator are shown m78 <- metamerge(m7, m8, label1 = "ML", label2 = "DL") summary(m78) m789 <- metamerge(m78, m9, label2 = "PM") summary(m789) # Merge everything m1to9 <- metamerge(metamerge(m123, m456, keep.w = TRUE), m789) summary(m1to9) m10 <- update(m1, method = "GLMM") m.all <- metamerge(m1to9, m10, keep.Q = TRUE, label2 = "GLMM", taulabel2 = "ML-GLMM") summary(m.all) forest(m.all, layout = "JAMA") forest(m.all, details = TRUE) ## End(Not run) settings.meta(oldset) options(oldopts)
metagen, metabind, metaadd
Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de