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

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.

A character string indicating underlying summary measure, e.g., "RD", "RR", "OR", "ASD", "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", or "EB", can be abbreviated.

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="ZCOR" are printed as correlations rather than Fisher's z transformed correlations, for example.

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

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).
bylevs: Levels of grouping variable - if byvar is not missing.
TE.fixed.w, seTE.fixed.w: Estimated treatment effect and standard error in subgroups (fixed effect model) - if byvar is not missing.
lower.fixed.w, upper.fixed.w: Lower and upper confidence interval limits in subgroups (fixed effect model) - if byvar is not missing.
zval.fixed.w, pval.fixed.w: z-value and p-value for test of treatment effect in subgroups (fixed effect model) - if byvar is not missing.
TE.random.w, seTE.random.w: Estimated treatment effect and standard error in subgroups (random effects model) - if byvar is not missing.
lower.random.w, upper.random.w: Lower and upper confidence interval limits in subgroups (random effects model) - if byvar is not missing.
zval.random.w, pval.random.w: z-value or t-value and corresponding p-value for test of treatment effect in subgroups (random effects model) - if byvar is not missing.
w.fixed.w, w.random.w: Weight of subgroups (in fixed and random effects model) - if byvar is not missing.
df.hakn.w: Degrees of freedom for test of treatment effect for Hartung-Knapp method in subgroups - if byvar is not missing and hakn=TRUE.
n.harmonic.mean.w: Harmonic mean of number of observations in subgroups (for back transformation of Freeman-Tukey Double arcsine transformation) - if byvar is not missing.
n.e.w: Number of observations in experimental group in subgroups - if byvar is not missing.
n.c.w: Number of observations in control group in subgroups - if byvar is not missing.
k.w: Number of studies combined within subgroups - if byvar is not missing.
k.all.w: Number of all studies in subgroups - if byvar is not missing.
Q.w: Heterogeneity statistics within subgroups - if byvar is not missing.
Q.w.fixed: Overall within subgroups heterogeneity statistic Q (based on fixed effect model) - if byvar is not missing.
Q.w.random: Overall within subgroups heterogeneity statistic Q (based on random effects model) - if byvar is not missing (only calculated if argument tau.common is TRUE).
df.Q.w: Degrees of freedom for test of overall within subgroups heterogeneity - if byvar is not missing.
Q.b.fixed: Overall between subgroups heterogeneity statistic Q (based on fixed effect model) - if byvar is not missing.
Q.b.random: Overall between subgroups heterogeneity statistic Q (based on random effects model) - if byvar is not missing.
df.Q.b: Degrees of freedom for test of overall between subgroups heterogeneity - if byvar is not missing.
tau.w: Square-root of between-study variance within subgroups - if byvar is not missing.
C.w: Scaling factor utilised internally to calculate common tau-squared across subgroups - if byvar is not missing.
H.w: Heterogeneity statistic H within subgroups - if byvar is not missing.
lower.H.w, upper.H.w: Lower and upper confidence limti for heterogeneity statistic H within subgroups - if byvar is not missing.
I2.w: Heterogeneity statistic I2 within subgroups - if byvar is not missing.
lower.I2.w, upper.I2.w: Lower and upper confidence limti for heterogeneity statistic I2 within subgroups - if byvar is not missing.
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.

Examples

Run this code

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"))

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