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.
metagen(TE, seTE, studlab,
data=NULL, subset=NULL, exclude=NULL, sm="",
level=gs("level"), level.comb=gs("level.comb"),
comb.fixed=gs("comb.fixed"), comb.random=gs("comb.random"),
hakn=gs("hakn"),
method.tau=gs("method.tau"), tau.preset=NULL, TE.tau=NULL,
tau.common=gs("tau.common"),
prediction=gs("prediction"), level.predict=gs("level.predict"),
null.effect=0,
method.bias=gs("method.bias"),
n.e=NULL, n.c=NULL,
backtransf=gs("backtransf"),
pscale=1, irscale = 1, irunit = "person-years",
title=gs("title"), complab=gs("complab"), outclab="",
label.e=gs("label.e"), label.c=gs("label.c"),
label.left=gs("label.left"), label.right=gs("label.right"),
byvar, bylab, print.byvar=gs("print.byvar"),
byseparator = gs("byseparator"),
keepdata=gs("keepdata"),
warn=gs("warn"))Estimate of treatment effect, e.g., log hazard ratio or risk difference.
Standard error of treatment estimate.
An optional vector with study labels.
An optional data frame containing the study information.
An optional vector specifying a subset of studies to be used.
An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots.
A character string indicating underlying summary measure,
e.g., "RD", "RR", "OR", "ASD",
"HR", "MD", "SMD", or "ROM".
The level used to calculate confidence intervals for individual studies.
The level used to calculate confidence intervals for pooled estimates.
A logical indicating whether a fixed effect meta-analysis should be conducted.
A logical indicating whether a random effects meta-analysis should be conducted.
A logical indicating whether a prediction interval should be printed.
The level used to calculate prediction interval for a new study.
A numeric value specifying the effect under the null hypothesis.
Number of observations in experimental group.
Number of observations in control group.
A logical indicating whether method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.
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.
Prespecified value for the square-root of the between-study variance \(\tau^2\).
Overall treatment effect used to estimate the between-study variance tau-squared.
A logical indicating whether tau-squared should be the same across subgroups.
A character string indicating which test is to be
used. Either "rank", "linreg", or "mm", can
be abbreviated. See function metabias
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.
A numeric giving scaling factor for printing of single
event probabilities or risk differences, i.e. if argument
sm is equal to "PLOGIT", "PLN",
"PRAW", "PAS", "PFT", or "RD".
A numeric defining a scaling factor for printing of
single incidence rates or incidence rate differences, i.e. if
argument sm is equal to "IR", "IRLN",
"IRS", "IRFT", or "IRD".
A character specifying the time unit used to calculate rates, e.g. person-years.
Title of meta-analysis / systematic review.
Comparison label.
Outcome label.
Label for experimental group.
Label for control group.
Graph label on left side of forest plot.
Graph label on right side of forest plot.
An optional vector containing grouping information (must
be of same length as TE).
A character string with a label for the grouping variable.
A logical indicating whether the name of the grouping variable should be printed in front of the group labels.
A character string defining the separator between label and levels of grouping variable.
A logical indicating whether original data (set) should be kept in meta object.
A logical indicating whether warnings should be printed (e.g., if studies are excluded from meta-analysis due to zero standard errors).
An object of class c("metagen", "meta") with corresponding
print, summary, and forest functions. The
object is a list containing the following components:
As defined above.
Lower and upper confidence interval limits for individual studies.
z-value and p-value for test of treatment effect for individual studies.
Weight of individual studies (in fixed and random effects model).
Estimated overall treatment effect and standard error (fixed effect model).
Lower and upper confidence interval limits (fixed effect model).
z-value and p-value for test of overall treatment effect (fixed effect model).
Estimated overall treatment effect and standard error (random effects model).
Lower and upper confidence interval limits (random effects model).
z-value or t-value and corresponding p-value for test of overall treatment effect (random effects model).
As defined above.
Standard error utilised for prediction interval.
Lower and upper limits of prediction interval.
As defined above.
Number of studies combined in meta-analysis.
Heterogeneity statistic.
Degrees of freedom for heterogeneity statistic.
Square-root of between-study variance.
Standard error of square-root of between-study variance.
Scaling factor utilised internally to calculate common tau-squared across subgroups.
Pooling method: "Inverse".
Degrees of freedom for test of treatment effect for
Hartung-Knapp method (only if hakn=TRUE).
Levels of grouping variable - if byvar is not
missing.
Estimated treatment effect and
standard error in subgroups (fixed effect model) - if byvar
is not missing.
Lower and upper confidence
interval limits in subgroups (fixed effect model) - if
byvar is not missing.
z-value and p-value for test of
treatment effect in subgroups (fixed effect model) - if
byvar is not missing.
Estimated treatment effect and
standard error in subgroups (random effects model) - if
byvar is not missing.
Lower and upper confidence
interval limits in subgroups (random effects model) - if
byvar is not missing.
z-value or t-value and
corresponding p-value for test of treatment effect in subgroups
(random effects model) - if byvar is not missing.
Weight of subgroups (in fixed and
random effects model) - if byvar is not missing.
Degrees of freedom for test of treatment effect for
Hartung-Knapp method in subgroups - if byvar is not missing
and hakn=TRUE.
Harmonic mean of number of observations in
subgroups (for back transformation of Freeman-Tukey Double arcsine
transformation) - if byvar is not missing.
Number of observations in experimental group in
subgroups - if byvar is not missing.
Number of observations in control group in subgroups -
if byvar is not missing.
Number of studies combined within subgroups - if
byvar is not missing.
Number of all studies in subgroups - if byvar
is not missing.
Heterogeneity statistics within subgroups - if
byvar is not missing.
Overall within subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Overall within subgroups heterogeneity statistic Q
(based on random effects model) - if byvar is not missing
(only calculated if argument tau.common is TRUE).
Degrees of freedom for test of overall within
subgroups heterogeneity - if byvar is not missing.
Overall between subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Overall between subgroups heterogeneity statistic
Q (based on random effects model) - if byvar is not
missing.
Degrees of freedom for test of overall between
subgroups heterogeneity - if byvar is not missing.
Square-root of between-study variance within subgroups
- if byvar is not missing.
Scaling factor utilised internally to calculate common
tau-squared across subgroups - if byvar is not missing.
Heterogeneity statistic H within subgroups - if
byvar is not missing.
Lower and upper confidence limti for
heterogeneity statistic H within subgroups - if byvar is
not missing.
Heterogeneity statistic I2 within subgroups - if
byvar is not missing.
Lower and upper confidence limti for
heterogeneity statistic I2 within subgroups - if byvar is
not missing.
As defined above.
Original data (set) used in function call (if
keepdata=TRUE).
Information on subset of original data used in
meta-analysis (if keepdata=TRUE).
Function call.
Version of R package meta used to create object.
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.
For several arguments defaults settings are utilised (assignments
using gs function). 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 DerSimonian-Laird estimate (1986) is used in the random effects
model if method.tau="DL". 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 <s.ellison at lgc.co.uk>.
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.
Argument pscale can be used to rescale single proportions or
risk differences, e.g. pscale=1000 means that proportions are
expressed as events per 1000 observations. This is useful in
situations with (very) low event probabilities.
Argument irscale can be used to rescale single rates or rate
differences, e.g. irscale=1000 means that rates are expressed
as events per 1000 time units, e.g. person-years. This is useful in
situations with (very) low rates. Argument irunit can be used
to specify the time unit used in individual studies (default:
"person-years"). This information is printed in summaries and forest
plots if argument irscale is not equal to 1.
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.
# NOT RUN {
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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