meta (version 3.8-0)

metagen: Generic inverse variance meta-analysis

Description

Fixed and random effects meta-analysis based on estimates (e.g. log hazard ratios) and their standard errors; inverse variance weighting is used for pooling.

Usage

metagen(TE, seTE, studlab, data=NULL, subset=NULL, sm="",
        level=.settings$level, level.comb=.settings$level.comb,
        comb.fixed=.settings$comb.fixed, comb.random=.settings$comb.random,
        hakn=.settings$hakn,
        method.tau=.settings$method.tau, tau.preset=NULL, TE.tau=NULL,
        tau.common=.settings$tau.common,
        prediction=.settings$prediction, level.predict=.settings$level.predict,
        method.bias=.settings$method.bias,
        n.e=NULL, n.c=NULL,
        backtransf=.settings$backtransf,
        title=.settings$title, complab=.settings$complab, outclab="",
        label.e=.settings$label.e, label.c=.settings$label.c,
        label.left=.settings$label.left, label.right=.settings$label.right,
        byvar, bylab, print.byvar=.settings$print.byvar,
        keepdata=.settings$keepdata,
        warn=.settings$warn)

Arguments

TE

Estimate of treatment effect.

seTE

Standard error of treatment estimate.

studlab

An optional vector with study labels.

data

An optional data frame containing the study information.

subset

An optional vector specifying a subset of studies to be used.

sm

A character string indicating underlying summary measure, e.g., "RD", "RR", "OR", "AS", "MD", "SMD".

level

The level used to calculate confidence intervals for individual studies.

level.comb

The level used to calculate confidence intervals for pooled estimates.

comb.fixed

A logical indicating whether a fixed effect meta-analysis should be conducted.

comb.random

A logical indicating whether a random effects meta-analysis should be conducted.

prediction

A logical indicating whether a prediction interval should be printed.

level.predict

The level used to calculate prediction interval for a new study.

n.e

Number of observations in experimental group.

n.c

Number of observations in control group.

hakn

A logical indicating whether method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.

method.tau

A character string indicating which method is used to estimate the between-study variance $\tau^2$. Either "DL", "PM", "REML", "ML", "HS", "SJ", "HE", o

tau.preset

Prespecified value for the square-root of the between-study variance $\tau^2$.

TE.tau

Overall treatment effect used to estimate the between-study variance tau-squared.

tau.common

A logical indicating whether tau-squared should be the same across subgroups.

method.bias

A character string indicating which test is to be used. Either "rank", "linreg", or "mm", can be abbreviated. See function metabias

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 and results for sm

title

Title of meta-analysis / systematic review.

complab

Comparison label.

outclab

Outcome label.

label.e

Label for experimental group.

label.c

Label for control group.

label.left

Graph label on left side of forest plot.

label.right

Graph label on right side of forest plot.

byvar

An optional vector containing grouping information (must be of same length as TE).

bylab

A character string with a label for the grouping variable.

print.byvar

A logical indicating whether the name of the grouping variable should be printed in front of the group labels.

keepdata

A logical indicating whether original data (set) should be kept in meta object.

warn

A logical indicating whether warnings should be printed (e.g., if studies are excluded from meta-analysis due to zero standard errors).

Value

• An object of class c("metagen", "meta") with corresponding print, summary, plot function. The object is a list containing the following components:
• TE, seTE, studlab, n.e, n.c
• sm, level, level.comb,
• comb.fixed, comb.random,
• hakn, method.tau, tau.preset, TE.tau, method.bias,
• tau.common, title, complab, outclab,
• label.e, label.c, label.left, label.right,
• byvar, bylab, print.byvar, warn
  As defined above.
• lower, upper
  Lower and upper confidence interval limits for individual studies.
• zval, pval
  z-value and p-value for test of treatment effect for individual studies.
• w.fixed, w.random
  Weight of individual studies (in fixed and random effects model).
• TE.fixed, seTE.fixed
  Estimated overall treatment effect and standard error (fixed effect model).
• lower.fixed, upper.fixed
  Lower and upper confidence interval limits (fixed effect model).
• zval.fixed, pval.fixed
  z-value and p-value for test of overall treatment effect (fixed effect model).
• TE.random, seTE.random
  Estimated overall treatment effect and standard error (random effects model).
• lower.random, upper.random
  Lower and upper confidence interval limits (random effects model).
• zval.random, pval.random
  z-value or t-value and corresponding p-value for test of overall treatment effect (random effects model).
• prediction, level.predict
  As defined above.
• seTE.predict
  Standard error utilised for prediction interval.
• lower.predict, upper.predict
  Lower and upper limits of prediction interval.
• k
  Number of studies combined in meta-analysis.
• Q
  Heterogeneity statistic.
• df.Q
  Degrees of freedom for heterogeneity statistic.
• tau
  Square-root of between-study variance.
• se.tau
  Standard error of square-root of between-study variance.
• C
  Scaling factor utilised internally to calculate common tau-squared across subgroups.
• method
  Pooling method: "Inverse".
• df.hakn
  Degrees of freedom for test of treatment effect for Hartung-Knapp method (only if hakn=TRUE).
• keepdata
  As defined above.
• data
  Original data (set) used in function call (if keepdata=TRUE).
• subset
  Information on subset of original data used in meta-analysis (if keepdata=TRUE).
• call
  Function call.
• version
  Version of R package meta used to create object.

Details

Generic method for meta-analysis, only treatment estimates and their standard error are needed. The method is useful, e.g., for pooling of survival data (using log hazard ratio and standard errors as input). The inverse variance method is used for pooling. By default, the DerSimonian-Laird estimate (1986) is used in the random effects model (method.tau="DL").

For several arguments defaults settings are utilised (assignments with .settings$). These defaults can be changed using the settings.meta function.

Internally, both fixed effect and random effects models are calculated regardless of values choosen for arguments comb.fixed and comb.random. Accordingly, the estimate for the random effects model can be extracted from component TE.random of an object of class "meta" even if argument comb.random=FALSE. However, all functions in R package meta will adequately consider the values for comb.fixed and comb.random. E.g. function print.meta will not print results for the random effects model if comb.random=FALSE.

A prediction interval for treatment effect of a new study is calculated (Higgins et al., 2009) if arguments prediction and comb.random are TRUE.

R function update.meta can be used to redo the meta-analysis of an existing metagen object by only specifying arguments which should be changed.

For the random effects, the method by Hartung and Knapp (2003) is used to adjust test statistics and confidence intervals if argument hakn=TRUE. The iterative Paule-Mandel method (1982) to estimate the between-study variance is used if argument method.tau="PM". Internally, R function paulemandel is called which is based on R function mpaule.default from R package metRology from S.L.R. Ellison . If R package metafor (Viechtbauer 2010) is installed, the following methods to estimate the between-study variance $\tau^2$ (argument method.tau) are also available:

• Restricted maximum-likelihood estimator (method.tau="REML")
• Maximum-likelihood estimator (method.tau="ML")
• Hunter-Schmidt estimator (method.tau="HS")
• Sidik-Jonkman estimator (method.tau="SJ")
• Hedges estimator (method.tau="HE")
• Empirical Bayes estimator (method.tau="EB").

For these methods the R function rma.uni of R package metafor is called internally. See help page of R function rma.uni for more details on these methods to estimate between-study variance.

References

Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: Russell Sage Foundation.

DerSimonian R & Laird N (1986), Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177--188.

Higgins JPT, Thompson SG, Spiegelhalter DJ (2009), A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A, 172, 137--159.

Knapp G & Hartung J (2003), Improved Tests for a Random Effects Meta-regression with a Single Covariate. Statistics in Medicine, 22, 2693--2710, doi: 10.1002/sim.1482 .

Paule RC & Mandel J (1982), Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87, 377--385.

Viechtbauer W (2010), Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48.

See Also

update.meta, metabin, metacont, print.meta

Examples

data(Fleiss93)
meta1 <- metabin(event.e, n.e, event.c, n.c, data=Fleiss93, sm="RR", method="I")
meta1

#
# Identical results by using the following commands:
#
meta1
metagen(meta1$TE, meta1$seTE, sm="RR")

forest(metagen(meta1$TE, meta1$seTE, sm="RR"))


#
# Meta-analysis with prespecified between-study variance
#
summary(metagen(meta1$TE, meta1$seTE, sm="RR", tau.preset=sqrt(0.1)))


#
# Meta-analysis of survival data:
#
logHR <- log(c(0.95, 1.5))
selogHR <- c(0.25, 0.35)

metagen(logHR, selogHR, sm="HR")


#
# Paule-Mandel method to estimate between-study variance
# Data from Paule & Mandel (1982)
#
average <- c(27.044, 26.022, 26.340, 26.787, 26.796)
variance <- c(0.003, 0.076, 0.464, 0.003, 0.014)
#
summary(metagen(average, sqrt(variance), sm="MD", method.tau="PM"))