metamean  R Documentation 
Calculation of an overall mean from studies reporting a single mean using the inverse variance method for pooling; inverse variance weighting is used for pooling.
metamean(
n,
mean,
sd,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
cluster = NULL,
rho = 0,
median,
q1,
q3,
min,
max,
method.mean = "Luo",
method.sd = "Shi",
approx.mean,
approx.sd,
sm = gs("smmean"),
method.ci = gs("method.ci.cont"),
level = gs("level"),
common = gs("common"),
random = gs("random")  !is.null(tau.preset),
overall = common  random,
overall.hetstat = if (is.null(gs("overall.hetstat"))) common  random else
gs("overall.hetstat"),
prediction = gs("prediction")  !missing(method.predict),
method.tau = gs("method.tau"),
method.tau.ci = gs("method.tau.ci"),
tau.preset = NULL,
TE.tau = NULL,
tau.common = gs("tau.common"),
level.ma = gs("level.ma"),
method.random.ci = gs("method.random.ci"),
adhoc.hakn.ci = gs("adhoc.hakn.ci"),
level.predict = gs("level.predict"),
method.predict = gs("method.predict"),
adhoc.hakn.pi = gs("adhoc.hakn.pi"),
seed.predict = NULL,
null.effect = NA,
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 = "",
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"),
seed.predict.subgroup = NULL,
byvar,
adhoc.hakn,
keepdata = gs("keepdata"),
warn = gs("warn"),
warn.deprecated = gs("warn.deprecated"),
control = NULL,
...
)
n 
Number of observations. 
mean 
Estimated mean. 
sd 
Standard deviation. 
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. 
rho 
Assumed correlation of estimates within a cluster. 
median 
Median (used to estimate the mean and standard deviation). 
q1 
First quartile (used to estimate the mean and standard deviation). 
q3 
Third quartile (used to estimate the mean and standard deviation). 
min 
Minimum (used to estimate the mean and standard deviation). 
max 
Maximum (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 
Approximation method to estimate means (see Details). 
approx.sd 
Approximation method to estimate standard deviations (see Details). 
sm 
A character string indicating which summary measure
( 
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. 
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. 
prediction 
A logical indicating whether a prediction interval should be printed. 
method.tau 
A character string indicating which method is
used to estimate the betweenstudy variance 
method.tau.ci 
A character string indicating which method is
used to estimate the confidence interval of 
tau.preset 
Prespecified value for the square root of the
betweenstudy variance 
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. 
level.ma 
The level used to calculate confidence intervals for metaanalysis estimates. 
method.random.ci 
A character string indicating which method
is used to calculate confidence interval and test statistic for
random effects estimate (see 
adhoc.hakn.ci 
A character string indicating whether an
ad hoc variance correction should be applied in the case
of an arbitrarily small HartungKnapp variance estimate (see

level.predict 
The level used to calculate prediction interval for a new study. 
method.predict 
A character string indicating which method is
used to calculate a prediction interval (see

adhoc.hakn.pi 
A character string indicating whether an
ad hoc variance correction should be applied for
prediction interval (see 
seed.predict 
A numeric value used as seed to calculate
bootstrap prediction interval (see 
null.effect 
A numeric value specifying the effect under the null hypothesis. 
method.bias 
A character string indicating which test is to
be used. Either 
backtransf 
A logical indicating whether results should be
back transformed in printouts and plots for 
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. 
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. 
seed.predict.subgroup 
A numeric vector providing seeds to calculate bootstrap prediction intervals within subgroups. Must be of same length as the number of subgroups. 
byvar 
Deprecated argument (replaced by 'subgroup'). 
adhoc.hakn 
Deprecated argument (replaced by 'adhoc.hakn.ci'). 
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 
... 
Additional arguments (to catch deprecated arguments). 
Common effect and random effects metaanalysis of single means to
calculate an overall mean; inverse variance weighting is used for
pooling. Note, you should use R function metacont
to
compare means of pairwise comparisons instead of using
metamean
for each treatment arm separately which will break
randomisation in randomised controlled trials.
A threelevel random effects metaanalysis model (Van den Noortgate
et al., 2013) is utilized if argument cluster
is used and at
least one cluster provides more than one estimate. Internally,
rma.mv
is called to conduct the analysis and
weights.rma.mv
with argument type =
"rowsum"
is used to calculate random effects weights.
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.
The following transformations of means are implemented to calculate an overall mean:
Raw, i.e. untransformed, means (sm = "MRAW"
, default)
Log transformed means (sm = "MLN"
)
Calculations are conducted on the log scale if sm =
"ROM"
. Accordingly, list elements TE
, TE.common
, and
TE.random
contain the logarithm of means. In printouts and
plots these values are back transformed if argument
backtransf = TRUE
(default).
Missing means can be derived from
sample size, median, interquartile range and range (arguments
n
, median
, q1
, q3
, min
, and
max
),
sample size, median and interquartile range (arguments
n
, median
, q1
, and q3
), or
sample size, median and range (arguments n
,
median
, min
, and max
).
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.
The following methods are also available to estimate means from quantiles or ranges if R package estmeansd is installed:
Method for Unknown NonNormal Distributions (MLN) approach
(Cai et al. (2021), argument method.mean = "Cai"
),
Quantile Estimation (QE) method (McGrath et al. (2020),
argument method.mean = "QEMcGrath"
)),
BoxCox (BC) method (McGrath et al. (2020),
argument method.mean = "BCMcGrath"
)).
By default, missing means are replaced successively using
interquartile ranges and ranges (if available), interquartile
ranges (if available) and finally ranges. Argument
approx.mean
can be used to overwrite this behaviour for each
individual study and treatment arm:
use means directly (entry ""
in argument
approx.mean
);
median, interquartile range and range ("iqr.range"
);
median and interquartile range ("iqr"
);
median and range ("range"
).
Missing standard deviations can be derived from
sample size, median, interquartile range and range (arguments
n
, median
, q1
, q3
, min
, and
max
),
sample size, median and interquartile range (arguments
n
, median
, q1
and q3
), or
sample size, median and range (arguments n
,
median
, min
and max
).
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.
The following methods are also available to estimate standard deviations from quantiles or ranges if R package estmeansd is installed:
Method for Unknown NonNormal Distributions (MLN) approach
(Cai et al. (2021), argument method.mean = "Cai"
),
Quantile Estimation (QE) method (McGrath et al. (2020),
argument method.mean = "QEMcGrath"
)),
BoxCox (BC) method (McGrath et al. (2020),
argument method.mean = "BCMcGrath"
)).
By default, missing standard deviations are replaced successively
using these method, i.e., interquartile ranges and ranges are used
before interquartile ranges before ranges. Argument
approx.sd
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 untransformed means (argument sm = "MRAW"
), the
confidence interval for individual studies can be based on the
standard normal distribution (method.ci = "z"
, default), or
tdistribution (method.ci = "t"
).
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. functions
print.meta
and forest.meta
will not
print results for the random effects model if random =
FALSE
.
A prediction interval will only be shown if prediction =
TRUE
.
An object of class c("metamean", "meta")
with corresponding
generic functions (see metaobject
).
The function metagen
is called internally to
calculate individual and overall treatment estimates and standard
errors.
Guido Schwarzer guido.schwarzer@uniklinikfreiburg.de
Cai S, Zhou J, Pan J (2021): Estimating the sample mean and standard deviation from order statistics and sample size in metaanalysis. Statistical Methods in Medical Research, 30, 2701–2719
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
McGrath S, Zhao X, Steele R, et al. and the DEPRESsion Screening Data (DEPRESSD) Collaboration (2020): Estimating the sample mean and standard deviation from commonly reported quantiles in metaanalysis. Statistical Methods in Medical Research, 29, 2520–2537
Shi J, Luo D, Weng H, Zeng XT, Lin L, Chu H, et al. (2020): Optimally estimating the sample standard deviation from the fivenumber summary. Research Synthesis Methods.
Van den Noortgate W, LópezLópez JA, MarínMartínez F, SánchezMeca J (2013): Threelevel metaanalysis of dependent effect sizes. Behavior Research Methods, 45, 576–94
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
metapackage
, update.meta
,
metamean
, metagen
m1 < metamean(rep(100, 3), 1:3, rep(1, 3))
m1
m2 < update(m1, sm = "MLN")
m2
# With test for overall mean equal to 2
#
update(m1, null.effect = 2)
update(m2, null.effect = 2)
# Print results without backtransformation
#
update(m1, backtransf = FALSE)
update(m2, backtransf = FALSE)
update(m1, null.effect = 2, backtransf = FALSE)
update(m2, null.effect = 2, backtransf = FALSE)
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