metacont  R Documentation 
Calculation of common and random effects estimates for metaanalyses with continuous outcome data; inverse variance weighting is used for pooling.
metacont( n.e, mean.e, sd.e, n.c, mean.c, sd.c, studlab, data = NULL, subset = NULL, exclude = NULL, cluster = NULL, median.e, q1.e, q3.e, min.e, max.e, median.c, q1.c, q3.c, min.c, max.c, method.mean = "Luo", method.sd = "Shi", approx.mean.e, approx.mean.c = approx.mean.e, approx.sd.e, approx.sd.c = approx.sd.e, sm = gs("smcont"), pooledvar = gs("pooledvar"), method.smd = gs("method.smd"), sd.glass = gs("sd.glass"), exact.smd = gs("exact.smd"), method.ci = gs("method.ci.cont"), level = gs("level"), level.ma = gs("level.ma"), common = gs("common"), random = gs("random")  !is.null(tau.preset), overall = common  random, overall.hetstat = common  random, hakn = gs("hakn"), adhoc.hakn = gs("adhoc.hakn"), method.tau = gs("method.tau"), method.tau.ci = gs("method.tau.ci"), tau.preset = NULL, TE.tau = NULL, tau.common = gs("tau.common"), prediction = gs("prediction"), level.predict = gs("level.predict"), method.bias = gs("method.bias"), backtransf = gs("backtransf"), text.common = gs("text.common"), text.random = gs("text.random"), text.predict = gs("text.predict"), text.w.common = gs("text.w.common"), text.w.random = gs("text.w.random"), 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"), subgroup, subgroup.name = NULL, print.subgroup.name = gs("print.subgroup.name"), sep.subgroup = gs("sep.subgroup"), test.subgroup = gs("test.subgroup"), prediction.subgroup = gs("prediction.subgroup"), byvar, id, keepdata = gs("keepdata"), warn = gs("warn"), warn.deprecated = gs("warn.deprecated"), control = NULL, ... )
n.e 
Number of observations in experimental group. 
mean.e 
Estimated mean in experimental group. 
sd.e 
Standard deviation in experimental group. 
n.c 
Number of observations in control group. 
mean.c 
Estimated mean in control group. 
sd.c 
Standard deviation in control group. 
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. 
exclude 
An optional vector specifying studies to exclude from metaanalysis, however, to include in printouts and forest plots. 
cluster 
An optional vector specifying which estimates come from the same cluster resulting in the use of a threelevel metaanalysis model. 
median.e 
Median in experimental group (used to estimate the mean and standard deviation). 
q1.e 
First quartile in experimental group (used to estimate the mean and standard deviation). 
q3.e 
Third quartile in experimental group (used to estimate the mean and standard deviation). 
min.e 
Minimum in experimental group (used to estimate the mean and standard deviation). 
max.e 
Maximum in experimental group (used to estimate the mean and standard deviation). 
median.c 
Median in control group (used to estimate the mean and standard deviation). 
q1.c 
First quartile in control group (used to estimate the mean and standard deviation). 
q3.c 
Third quartile in control group (used to estimate the mean and standard deviation). 
min.c 
Minimum in control group (used to estimate the mean and standard deviation). 
max.c 
Maximum in control group (used to estimate the mean and standard deviation). 
method.mean 
A character string indicating which method to use to approximate the mean from the median and other statistics (see Details). 
method.sd 
A character string indicating which method to use to approximate the standard deviation from sample size, median, interquartile range and range (see Details). 
approx.mean.e 
Approximation method to estimate means in experimental group (see Details). 
approx.mean.c 
Approximation method to estimate means in control group (see Details). 
approx.sd.e 
Approximation method to estimate standard deviations in experimental group (see Details). 
approx.sd.c 
Approximation method to estimate standard deviations in control group (see Details). 
sm 
A character string indicating which summary measure
( 
pooledvar 
A logical indicating if a pooled variance should
be used for the mean difference ( 
method.smd 
A character string indicating which method is
used to estimate the standardised mean difference
( 
sd.glass 
A character string indicating which standard
deviation is used in the denominator for Glass' method to
estimate the standardised mean difference. Either

exact.smd 
A logical indicating whether exact formulae should be used in estimation of the standardised mean difference and its standard error (see Details). 
method.ci 
A character string indicating which method is used to calculate confidence intervals for individual studies, see Details. 
level 
The level used to calculate confidence intervals for individual studies. 
level.ma 
The level used to calculate confidence intervals for metaanalysis estimates. 
common 
A logical indicating whether a common effect metaanalysis should be conducted. 
random 
A logical indicating whether a random effects metaanalysis should be conducted. 
overall 
A logical indicating whether overall summaries should be reported. This argument is useful in a metaanalysis with subgroups if overall results should not be reported. 
overall.hetstat 
A logical value indicating whether to print heterogeneity measures for overall treatment comparisons. This argument is useful in a metaanalysis with subgroups if heterogeneity statistics should only be printed on subgroup level. 
hakn 
A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals. 
adhoc.hakn 
A character string indicating whether an ad hoc variance correction should be applied in the case of an arbitrarily small HartungKnapp variance estimate, see Details. 
method.tau 
A character string indicating which method is
used to estimate the betweenstudy variance τ^2 and its
square root τ. Either 
method.tau.ci 
A character string indicating which method is
used to estimate the confidence interval of τ^2 and
τ. Either 
tau.preset 
Prespecified value for the square root of the betweenstudy variance τ^2. 
TE.tau 
Overall treatment effect used to estimate the betweenstudy variance tausquared. 
tau.common 
A logical indicating whether tausquared should be the same across subgroups. 
prediction 
A logical indicating whether a prediction interval should be printed. 
level.predict 
The level used to calculate prediction interval for a new study. 
method.bias 
A character string indicating which test is to
be used. Either 
backtransf 
A logical indicating whether results for ratio of
means ( 
text.common 
A character string used in printouts and forest plot to label the pooled common effect estimate. 
text.random 
A character string used in printouts and forest plot to label the pooled random effects estimate. 
text.predict 
A character string used in printouts and forest plot to label the prediction interval. 
text.w.common 
A character string used to label weights of common effect model. 
text.w.random 
A character string used to label weights of random effects model. 
title 
Title of metaanalysis / 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. 
subgroup 
An optional vector to conduct a metaanalysis with subgroups. 
subgroup.name 
A character string with a name for the subgroup variable. 
print.subgroup.name 
A logical indicating whether the name of the subgroup variable should be printed in front of the group labels. 
sep.subgroup 
A character string defining the separator between name of subgroup variable and subgroup label. 
test.subgroup 
A logical value indicating whether to print results of test for subgroup differences. 
prediction.subgroup 
A logical indicating whether prediction intervals should be printed for subgroups. 
byvar 
Deprecated argument (replaced by 'subgroup'). 
id 
Deprecated argument (replaced by 'cluster'). 
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 metaanalysis due to zero standard deviations). 
warn.deprecated 
A logical indicating whether warnings should be printed if deprecated arguments are used. 
control 
An optional list to control the iterative process to
estimate the betweenstudy variance τ^2. This argument
is passed on to 
... 
Additional arguments (to catch deprecated arguments). 
Calculation of common and random effects estimates for metaanalyses with continuous outcome data; inverse variance weighting is used for pooling.
Three different types of summary measures are available for continuous outcomes:
mean difference (argument sm = "MD"
)
standardised mean difference (sm = "SMD"
)
ratio of means (sm = "ROM"
)
Default settings are utilised for several arguments (assignments
using gs
function). These defaults can be changed for
the current R session using the settings.meta
function.
Furthermore, R function update.meta
can be used to
rerun a metaanalysis with different settings.
For the standardised mean difference three methods are implemented:
Hedges' g (default, method.smd = "Hedges"
)  see
Hedges (1981)
Cohen's d (method.smd = "Cohen"
)  see Cohen (1988)
Glass' delta (method.smd = "Glass"
)  see Glass (1976)
Hedges (1981) calculated the exact bias in Cohen's d which is a
ratio of gamma distributions with the degrees of freedom,
i.e. total sample size minus two, as argument. By default (argument
exact.smd = FALSE
), an accurate approximation of this bias
provided in Hedges (1981) is utilised for Hedges' g as well as its
standard error; these approximations are also used in RevMan
5. Following Borenstein et al. (2009) these approximations are not
used in the estimation of Cohen's d. White and Thomas (2005) argued
that approximations are unnecessary with modern software and
accordingly promote to use the exact formulae; this is possible
using argument exact.smd = TRUE
. For Hedges' g the exact
formulae are used to calculate the standardised mean difference as
well as the standard error; for Cohen's d the exact formula is only
used to calculate the standard error. In typical applications (with
sample sizes above 10), the differences between using the exact
formulae and the approximation will be minimal.
For Glass' delta, by default (argument sd.glass =
"control"
), the standard deviation in the control group
(sd.c
) is used in the denominator of the standard mean
difference. The standard deviation in the experimental group
(sd.e
) can be used by specifying sd.glass =
"experimental"
.
Metaanalysis of ratio of means – also called response ratios –
is described in Hedges et al. (1999) and Friedrich et al. (2008).
Calculations are conducted on the log scale and list elements
TE
, TE.common
, and TE.random
contain the
logarithm of the ratio of means. In printouts and plots these
values are back transformed if argument backtransf = TRUE
.
Missing means in the experimental group (analogously for the control group) can be derived from
sample size, median, interquartile range and range (arguments
n.e
, median.e
, q1.e
, q3.e
,
min.e
, and max.e
),
sample size, median and interquartile range (arguments
n.e
, median.e
, q1.e
, and q3.e
), or
sample size, median and range (arguments n.e
,
median.e
, min.e
, and max.e
).
By default, methods described in Luo et al. (2018) are utilized
(argument method.mean = "Luo"
):
equation (15) if sample size, median, interquartile range and range are available,
equation (11) if sample size, median and interquartile range are available,
equation (7) if sample size, median and range are available.
Instead the methods described in Wan et al. (2014) are used if
argument method.mean = "Wan"
:
equation (10) if sample size, median, interquartile range and range are available,
equation (14) if sample size, median and interquartile range are available,
equation (2) if sample size, median and range are available.
By default, missing means are replaced successively using
interquartile ranges and ranges (if available), interquartile
ranges (if available) and finally ranges. Arguments
approx.mean.e
and approx.mean.c
can be used to
overwrite this behaviour for each individual study and treatment
arm:
use means directly (entry ""
in argument
approx.mean.e
or approx.mean.c
);
median, interquartile range and range ("iqr.range"
);
median and interquartile range ("iqr"
);
median and range ("range"
).
Missing standard deviations in the experimental group (analogously for the control group) can be derived from
sample size, median, interquartile range and range (arguments
n.e
, median.e
, q1.e
, q3.e
,
min.e
, and max.e
),
sample size, median and interquartile range (arguments
n.e
, median.e
, q1.e
and q3.e
), or
sample size, median and range (arguments n.e
,
median.e
, min.e
and max.e
).
Wan et al. (2014) describe methods to estimate the standard
deviation from the sample size, median and additional
statistics. Shi et al. (2020) provide an improved estimate of the
standard deviation if the interquartile range and range are
available in addition to the sample size and median. Accordingly,
equation (11) in Shi et al. (2020) is the default (argument
method.sd = "Shi"
), if the median, interquartile range and
range are provided. The method by Wan et al. (2014) is used if
argument method.sd = "Wan"
and, depending on the sample
size, either equation (12) or (13) is used. If only the
interquartile range or range is available, equations (15) / (16)
and (7) / (9) in Wan et al. (2014) are used, respectively.
By default, missing standard deviations are replaced successively
using these method, i.e., interquartile ranges and ranges are used
before interquartile ranges before ranges. Arguments
approx.sd.e
and approx.sd.c
can be used to overwrite
this default for each individual study and treatment arms:
sample size, median, interquartile range and range
("iqr.range"
);
sample size, median and interquartile range ("iqr"
);
sample size, median and range ("range"
).
For the mean difference (argument sm = "MD"
), the confidence
interval for individual studies can be based on the
standard normal distribution (method.ci = "z"
, default), or
tdistribution (method.ci = "t"
).
Note, this choice does not affect the results of the common effect and random effects metaanalysis.
The following methods to estimate the betweenstudy variance τ^2 are available:
DerSimonianLaird estimator (method.tau = "DL"
)
PauleMandel estimator (method.tau = "PM"
)
Restricted maximumlikelihood estimator (method.tau =
"REML"
)
Maximumlikelihood estimator (method.tau = "ML"
)
HunterSchmidt estimator (method.tau = "HS"
)
SidikJonkman estimator (method.tau = "SJ"
)
Hedges estimator (method.tau = "HE"
)
Empirical Bayes estimator (method.tau = "EB"
)
See metagen
for more information on these
estimators.
The following methods to calculate a confidence interval for τ^2 and τ are available.
Argument  Method 
method.tau.ci = "J"  Method by Jackson (2013) 
method.tau.ci = "BJ"  Method by Biggerstaff and Jackson (2008) 
method.tau.ci = "QP"  QProfile method (Viechtbauer, 2007) 
method.tau.ci = "PL"  ProfileLikelihood method for threelevel metaanalysis 
(Van den Noortgate et al., 2013)  
method.tau.ci = ""  No confidence interval 
See metagen
for more information on these methods.
Hartung and Knapp (2001) proposed an alternative method for random effects metaanalysis based on a refined variance estimator for the treatment estimate. Simulation studies (Hartung and Knapp, 2001; IntHout et al., 2014; Langan et al., 2019) show improved coverage probabilities compared to the classic random effects method.
In rare settings with very homogeneous treatment estimates, the HartungKnapp variance estimate can be arbitrarily small resulting in a very narrow confidence interval (Knapp and Hartung, 2003; Wiksten et al., 2016). In such cases, an ad hoc variance correction has been proposed by utilising the variance estimate from the classic random effects model with the HK method (Knapp and Hartung, 2003; IQWiQ, 2020). An alternative approach is to use the wider confidence interval of classic common or random effects metaanalysis and the HK method (Wiksten et al., 2016; Jackson et al., 2017).
Argument adhoc.hakn
can be used to choose the ad hoc
method:
Argument  Ad hoc method 
adhoc.hakn = ""  not used 
adhoc.hakn = "se"  use variance correction if HK standard error is smaller 
than standard error from classic random effects  
metaanalysis (Knapp and Hartung, 2003)  
adhoc.hakn = "iqwig6"  use variance correction if HK confidence interval 
is narrower than CI from classic random effects model  
with DerSimonianLaird estimator (IQWiG, 2020)  
adhoc.hakn = "ci"  use wider confidence interval of classic random effects 
and HK metaanalysis  
(Hybrid method 2 in Jackson et al., 2017) 
A prediction interval for the proportion in a new study (Higgins et
al., 2009) is calculated if arguments prediction
and
random
are TRUE
. Note, the definition of
prediction intervals varies in the literature. This function
implements equation (12) of Higgins et al., (2009) which proposed a
t distribution with K2 degrees of freedom where
K corresponds to the number of studies in the metaanalysis.
Argument subgroup
can be used to conduct subgroup analysis for
a categorical covariate. The metareg
function can be
used instead for more than one categorical covariate or continuous
covariates.
Arguments subset
and exclude
can be used to exclude
studies from the metaanalysis. Studies are removed completely from
the metaanalysis using argument subset
, while excluded
studies are shown in printouts and forest plots using argument
exclude
(see Examples in metagen
).
Metaanalysis results are the same for both arguments.
Internally, both common effect and random effects models are
calculated regardless of values choosen for arguments
common
and 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 random = FALSE
. However, all functions in R
package meta will adequately consider the values for
common
and random
. E.g. function
print.meta
will not print results for the random
effects model if random = FALSE
.
An object of class c("metacont", "meta")
with corresponding
print
, summary
, and forest
functions. The
object is a list containing the following components:
n.e, mean.e, sd.e, 
As defined above. 
n.c, mean.c, sd.c, 
As defined above. 
studlab, exclude, cluster, sm, method.ci, 
As defined above. 
median.e, q1.e, q3.e, min.e, max.e, 
As defined above. 
median.c, q1.c, q3.c, min.c, max.c, 
As defined above. 
method.mean, method.sd, 
As defined above. 
approx.mean.e, approx.sd.e, approx.mean.c, approx.sd.c, 
As defined above. 
level, level.ma, 
As defined above. 
common, random, 
As defined above. 
overall, overall.hetstat, 
As defined above. 
pooledvar, method.smd, sd.glass, 
As defined above. 
hakn, adhoc.hakn, method.tau, method.tau.ci, 
As defined above. 
tau.preset, TE.tau, method.bias, 
As defined above. 
tau.common, title, complab, outclab, 
As defined above. 
label.e, label.c, label.left, label.right, 
As defined above. 
subgroup, subgroup.name, 
As defined above. 
print.subgroup.name, sep.subgroup, warn, 
As defined above. 
TE, seTE 
Estimated treatment effect and standard error of individual studies. 
lower, upper 
Lower and upper confidence interval limits for individual studies. 
statistic, pval 
Statistic and pvalue for test of treatment effect for individual studies. 
w.common, w.random 
Weight of individual studies (in common effect and random effects model). 
TE.common, seTE.common 
Estimated overall treatment effect and standard error (common effect model). 
lower.common, upper.common 
Lower and upper confidence interval limits (common effect model). 
statistic.common, pval.common 
Statistic and pvalue for test of overall treatment effect (common 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). 
statistic.random, pval.random 
Statistic and pvalue 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 estimates combined in metaanalysis. 
k.study 
Number of studies combined in metaanalysis. 
k.all 
Number of all studies. 
k.TE 
Number of studies with estimable effects. 
Q 
Heterogeneity statistic Q. 
df.Q 
Degrees of freedom for heterogeneity statistic. 
pval.Q 
Pvalue of heterogeneity test. 
tau2 
Betweenstudy variance τ^2. 
se.tau2 
Standard error of τ^2. 
lower.tau2, upper.tau2 
Lower and upper limit of confidence interval for τ^2. 
tau 
Squareroot of betweenstudy variance τ. 
lower.tau, upper.tau 
Lower and upper limit of confidence interval for τ. 
H 
Heterogeneity statistic H. 
lower.H, upper.H 
Lower and upper confidence limit for heterogeneity statistic H. 
I2 
Heterogeneity statistic I^2. 
lower.I2, upper.I2 
Lower and upper confidence limit for heterogeneity statistic I^2. 
Rb 
Heterogeneity statistic R_b. 
lower.Rb, upper.Rb 
Lower and upper confidence limit for heterogeneity statistic R_b. 
df.hakn 
Degrees of freedom for test of treatment effect for
HartungKnapp method (only if 
method 
Pooling method: 
bylevs 
Levels of grouping variable  if 
TE.common.w, seTE.common.w 
Estimated treatment effect and
standard error in subgroups (common effect model)  if

lower.common.w, upper.common.w 
Lower and upper confidence
interval limits in subgroups (common effect model)  if

statistic.common.w, pval.common.w 
Statistics and pvalues for
test of treatment effect in subgroups (common effect model)  if

TE.random.w, seTE.random.w 
Estimated treatment effect and
standard error in subgroups (random effects model)  if

lower.random.w, upper.random.w 
Lower and upper confidence
interval limits in subgroups (random effects model)  if

statistic.random.w, pval.random.w 
Statistics and pvalues
for test of treatment effect in subgroups (random effects model)
 if 
w.common.w, w.random.w 
Weight of subgroups (in common effect
and random effects model)  if 
df.hakn.w 
Degrees of freedom for test of treatment effect
for HartungKnapp method in subgroups  if 
n.e.w 
Number of observations in experimental group in
subgroups  if 
n.c.w 
Number of observations in control group in subgroups 
if 
k.w 
Number of studies combined within subgroups  if

k.all.w 
Number of all studies in subgroups  if 
Q.w.common 
Overall within subgroups heterogeneity statistic Q
(based on common effect model)  if 
Q.w.random 
Overall within subgroups heterogeneity statistic
Q (based on random effects model)  if 
df.Q.w 
Degrees of freedom for test of overall within
subgroups heterogeneity  if 
pval.Q.w.common 
Pvalue of within subgroups heterogeneity
statistic Q (based on common effect model)  if 
pval.Q.w.random 
Pvalue of within subgroups heterogeneity
statistic Q (based on random effects model)  if 
Q.b.common 
Overall between subgroups heterogeneity statistic
Q (based on common effect model)  if 
Q.b.random 
Overall between subgroups heterogeneity statistic
Q (based on random effects model)  if 
df.Q.b 
Degrees of freedom for test of overall between
subgroups heterogeneity  if 
pval.Q.b.common 
Pvalue of between subgroups heterogeneity
statistic Q (based on common effect model)  if 
pval.Q.b.random 
Pvalue of between subgroups heterogeneity
statistic Q (based on random effects model)  if 
tau.w 
Squareroot of betweenstudy variance within subgroups
 if 
H.w 
Heterogeneity statistic H within subgroups  if

lower.H.w, upper.H.w 
Lower and upper confidence limit for
heterogeneity statistic H within subgroups  if 
I2.w 
Heterogeneity statistic I^2 within subgroups  if

lower.I2.w, upper.I2.w 
Lower and upper confidence limit for
heterogeneity statistic I^2 within subgroups  if 
keepdata 
As defined above. 
data 
Original data (set) used in function call (if

subset 
Information on subset of original data used in
metaanalysis (if 
call 
Function call. 
version 
Version of R package meta used to create object. 
The function metagen
is called internally to
calculate individual and overall treatment estimates and standard
errors.
Guido Schwarzer sc@imbi.unifreiburg.de
Borenstein M, Hedges LV, Higgins JPT, Rothstein HR (2009): Introduction to MetaAnalysis. Chichester: Wiley
Cohen J (1988): Statistical Power Analysis for the Behavioral Sciences (second ed.). Lawrence Erlbaum Associates
Cooper H & Hedges LV (1994): The Handbook of Research Synthesis. Newbury Park, CA: Russell Sage Foundation
DerSimonian R & Laird N (1986): Metaanalysis in clinical trials. Controlled Clinical Trials, 7, 177–88
Friedrich JO, Adhikari NK, Beyene J (2008): The ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in metaanalysis: A simulation study. BMC Medical Research Methodology, 8, 32
Glass G (1976): Primary, secondary, and metaanalysis of research. Educational Researcher, 5, 3–8
Hartung J & Knapp G (2001): On tests of the overall treatment effect in metaanalysis with normally distributed responses. Statistics in Medicine, 20, 1771–82
Hedges LV (1981): Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28
Hedges LV, Gurevitch J, Curtis PS (1999): The metaanalysis of response ratios in experimental ecology. Ecology, 80, 1150–6
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009): A reevaluation of randomeffects metaanalysis. Journal of the Royal Statistical Society: Series A, 172, 137–59
IntHout J, Ioannidis JPA, Borm GF (2014): The HartungKnappSidikJonkman method for random effects metaanalysis is straightforward and considerably outperforms the standard DerSimonianLaird method. BMC Medical Research Methodology, 14, 25
IQWiG (2020): General Methods: Version 6.0. https://www.iqwig.de/en/aboutus/methods/methodspaper/
Jackson D, Law M, Rücker G, Schwarzer G (2017): The HartungKnapp modification for randomeffects metaanalysis: A useful refinement but are there any residual concerns? Statistics in Medicine, 36, 3923–34
Knapp G & Hartung J (2003): Improved tests for a random effects metaregression with a single covariate. Statistics in Medicine, 22, 2693–710
Langan D, Higgins JPT, Jackson D, Bowden J, Veroniki AA, Kontopantelis E, et al. (2019): A comparison of heterogeneity variance estimators in simulated randomeffects metaanalyses. Research Synthesis Methods, 10, 83–98
Luo D, Wan X, Liu J, Tong T (2018): Optimally estimating the sample mean from the sample size, median, midrange, and/or midquartile range. Statistical Methods in Medical Research, 27, 1785–805
Review Manager (RevMan) [Computer program]. Version 5.4. The Cochrane Collaboration, 2020
Shi J, Luo D, Weng H, Zeng XT, Lin L, Chu H, Tong T (2020): Optimally estimating the sample standard deviation from the fivenumber summary. Research Synthesis Methods, 11, 641–54
Van den Noortgate W, LópezLópez JA, MarínMartínez F, SánchezMeca J (2013): Threelevel metaanalysis of dependent effect sizes. Behavior Research Methods, 45, 576–94
Viechtbauer W (2010): Conducting MetaAnalyses in R with the Metafor Package. Journal of Statistical Software, 36, 1–48
Wan X, Wang W, Liu J, Tong T (2014): Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Medical Research Methodology, 14, 135
White IR, Thomas J (2005): Standardized mean differences in individuallyrandomized and clusterrandomized trials, with applications to metaanalysis. Clinical Trials, 2, 141–51
Wiksten A, Rücker G, Schwarzer G (2016): HartungKnapp method is not always conservative compared with fixedeffect metaanalysis. Statistics in Medicine, 35, 2503–15
update.meta
, metabin
,
metagen
data(Fleiss1993cont) # Metaanalysis with Hedges' g as effect measure # m1 < metacont(n.psyc, mean.psyc, sd.psyc, n.cont, mean.cont, sd.cont, data = Fleiss1993cont, sm = "SMD") m1 forest(m1) # Use Cohen's d instead of Hedges' g as effect measure # update(m1, method.smd = "Cohen") # Use Glass' delta instead of Hedges' g as effect measure # update(m1, method.smd = "Glass") # Use Glass' delta based on the standard deviation in the experimental group # update(m1, method.smd = "Glass", sd.glass = "experimental") # Calculate Hedges' g based on exact formulae # update(m1, exact.smd = TRUE) data(amlodipine) m2 < metacont(n.amlo, mean.amlo, sqrt(var.amlo), n.plac, mean.plac, sqrt(var.plac), data = amlodipine, studlab = study) m2 # Use pooled variance # update(m2, pooledvar = TRUE) # Metaanalysis of response ratios (Hedges et al., 1999) # data(woodyplants) m3 < metacont(n.elev, mean.elev, sd.elev, n.amb, mean.amb, sd.amb, data = woodyplants, sm = "ROM") m3 print(m3, backtransf = FALSE)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.