Description Usage Arguments Details Value Author(s) References See Also Examples
Calculation of an overall proportion from studies reporting a
single proportion. Inverse variance method and generalised linear
mixed model (GLMM) are available for pooling. For GLMMs, the
rma.glmm
function from R package
metafor (Viechtbauer 2010) is called internally.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  metaprop(
event,
n,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
method,
sm = gs("smprop"),
incr = gs("incr"),
allincr = gs("allincr"),
addincr = gs("addincr"),
method.ci = gs("method.ci.prop"),
level = gs("level"),
level.comb = gs("level.comb"),
comb.fixed = gs("comb.fixed"),
comb.random = gs("comb.random"),
overall = comb.fixed  comb.random,
overall.hetstat = comb.fixed  comb.random,
hakn = gs("hakn"),
adhoc.hakn = gs("adhoc.hakn"),
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"),
null.effect = NA,
method.bias = gs("method.bias"),
backtransf = gs("backtransf"),
pscale = 1,
text.fixed = gs("text.fixed"),
text.random = gs("text.random"),
text.predict = gs("text.predict"),
text.w.fixed = gs("text.w.fixed"),
text.w.random = gs("text.w.random"),
title = gs("title"),
complab = gs("complab"),
outclab = "",
byvar,
bylab,
print.byvar = gs("print.byvar"),
byseparator = gs("byseparator"),
test.subgroup = gs("test.subgroup"),
keepdata = gs("keepdata"),
warn = gs("warn"),
control = NULL,
...
)

event 
Number of events. 
n 
Number of observations. 
studlab 
An optional vector with study labels. 
data 
An optional data frame containing the study information, i.e., event and n. 
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. 
method 
A character string indicating which method is to be
used for pooling of studies. One of 
sm 
A character string indicating which summary measure
( 
incr 
A numeric which is added to event number and sample size of studies with zero or all events, i.e., studies with an event probability of either 0 or 1. 
allincr 
A logical indicating if 
addincr 
A logical indicating if 
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.comb 
The level used to calculate confidence intervals for pooled estimates. 
comb.fixed 
A logical indicating whether a fixed effect metaanalysis should be conducted. 
comb.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. 
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 for
transformed proportions (argument 
pscale 
A numeric defining a scaling factor for printing of single event probabilities. 
text.fixed 
A character string used in printouts and forest plot to label the pooled fixed 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.fixed 
A character string used to label weights of fixed 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. 
byvar 
An optional vector containing grouping information
(must be of same length as 
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. 
byseparator 
A character string defining the separator between label and levels of grouping variable. 
test.subgroup 
A logical value indicating whether to print results of test for subgroup differences. 
keepdata 
A logical indicating whether original data (set) should be kept in meta object. 
warn 
A logical indicating whether the addition of

control 
An optional list to control the iterative process to
estimate the betweenstudy variance τ^2. This argument
is passed on to 
... 
Additional arguments passed on to

This function provides methods for fixed effect and random effects
metaanalysis of single proportions to calculate an overall
proportion. Note, you should use R function metabin
to compare proportions of pairwise comparisons instead of using
metaprop
for each treatment arm separately which will break
randomisation in randomised controlled trials.
The following transformations of proportions are implemented to calculate an overall proportion:
Logit transformation (sm = "PLOGIT"
, default)
Arcsine transformation (sm = "PAS"
)
FreemanTukey Double arcsine transformation (sm = "PFT"
)
Log transformation (sm = "PLN"
)
Raw, i.e. untransformed, proportions (sm = "PRAW"
)
A generalised linear mixed model (GLMM)  more specific, a random
intercept logistic regression model  can be utilised for the
metaanalysis of proportions (Stijnen et al., 2010). This is the
default method for the logit transformation (argument sm =
"PLOGIT"
). Internally, the rma.glmm
function from R package metafor is called to fit a GLMM.
Classic metaanalysis (Borenstein et al., 2010) utilising the
(un)transformed proportions and corresponding standard errors in
the inverse variance method is conducted by calling the
metagen
function internally. This is the only
available method for all transformations but the logit
transformation. The classic metaanalysis model with logit
transformed proportions is used by setting argument method =
"Inverse"
.
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.
Contradictory recommendations on the use of transformations of proportions have been published in the literature. For example, Barendregt et al. (2013) recommend the use of the FreemanTukey double arcsine transformation instead of the logit transformation whereas Warton & Hui (2011) strongly advise to use generalised linear mixed models with the logit transformation instead of the arcsine transformation.
Schwarzer et al. (2019) describe seriously misleading results in a metaanalysis with very different sample sizes due to problems with the backtransformation of the FreemanTukey transformation which requires a single sample size (Miller, 1978). Accordingly, Schwarzer et al. (2019) also recommend to use GLMMs for the metaanalysis of single proportions, however, admit that individual study weights are not available with this method. Metaanalysts which require individual study weights should consider the inverse variance method with the arcsine or logit transformation.
In order to prevent misleading conclusions for the FreemanTukey double arcsine transformation, sensitivity analyses using other transformations or using a range of sample sizes should be conducted (Schwarzer et al., 2019).
If the summary measure is equal to "PLOGIT", "PLN", or "PRAW", a continuity correction is applied if any study has either zero or all events, i.e., an event probability of either 0 or 1.
By default, 0.5 is used as continuity correction (argument
incr
). This continuity correction is used both to calculate
individual study results with confidence limits and to conduct
metaanalysis based on the inverse variance method. For GLMMs no
continuity correction is used.
Various methods are available to calculate confidence intervals for individual study results (see Agresti & Coull 1998 and Newcombe 1988):
ClopperPearson interval also called 'exact' binomial
interval (method.ci = "CP"
, default)
Wilson Score interval (method.ci = "WS"
)
Wilson Score interval with continuity correction
(method.ci = "WSCC"
)
AgrestiCoull interval (method.ci = "AC"
)
Simple approximation interval (method.ci = "SA"
)
Simple approximation interval with continuity correction
(method.ci = "SACC"
)
Normal approximation interval based on summary measure,
i.e. defined by argument sm
(method.ci = "NAsm"
)
Note, with exception of the normal approximation based on the
summary measure, i.e. method.ci = "NAsm"
, the same
confidence interval is calculated for individual studies for any
summary measure (argument sm
) as only number of events and
observations are used in the calculation disregarding the chosen
transformation.
Results will be presented for transformed proportions if argument
backtransf = FALSE
in the print.meta
,
print.summary.meta
, or forest.meta
function. In this case, argument method.ci = "NAsm"
is used,
i.e. confidence intervals based on the normal approximation based
on the summary measure.
The following methods to estimate the betweenstudy variance τ^2 are available for the inverse variance method:
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. Note, the maximumlikelihood method is utilized for
GLMMs.
The following methods to calculate a confidence interval for τ^2 and τ are available.
Argument  Method 
method.tau.ci = "J"  Method by Jackson 
method.tau.ci = "BJ"  Method by Biggerstaff and Jackson 
method.tau.ci = "QP"  QProfile method 
See metagen
for more information on these
methods. For GLMMs, no confidence intervals for τ^2 and
τ are calculated. Likewise, no confidence intervals for
τ^2 and τ are calculated if method.tau.ci =
""
.
Hartung and Knapp (2001a,b) proposed an alternative method for random effects metaanalysis based on a refined variance estimator for the treatment estimate. Simulation studies (Hartung and Knapp, 2001a,b; 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 fixed 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) 
For GLMMs, a method similar to Knapp and Hartung (2003) is
implemented, see description of argument tdist
in
rma.glmm
, and the ad hoc variance
correction is not available.
A prediction interval for the proportion in a new study (Higgins et
al., 2009) is calculated if arguments prediction
and
comb.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 byvar
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.
Argument null.effect
can be used to specify the proportion
used under the null hypothesis in a test for an overall effect.
By default (null.effect = NA
), no hypothesis test is
conducted as it is unclear which value is a sensible choice for the
data at hand. An overall proportion of 50%, for example, could be
tested by setting argument null.effect = 0.5
.
Note, all tests for an overall effect are twosided with the
alternative hypothesis that the effect is unequal to
null.effect
.
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 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
.
Argument pscale
can be used to rescale proportions, e.g.
pscale = 1000
means that proportions are expressed as events
per 1000 observations. This is useful in situations with (very) low
event probabilities.
An object of class c("metaprop", "meta")
with corresponding
print
, summary
, and forest
functions. The
object is a list containing the following components:
event, n, studlab, exclude, 
As defined above. 
sm, incr, allincr, addincr, method.ci, 
As defined above. 
level, level.comb, 
As defined above. 
comb.fixed, comb.random, 
As defined above. 
overall, overall.hetstat, 
As defined above. 
hakn, adhoc.hakn, method.tau, method.tau.ci, 
As defined above. 
tau.preset, TE.tau, null.hypothesis, 
As defined above. 
method.bias, tau.common, title, complab, outclab, 
As defined above. 
byvar, bylab, print.byvar, byseparator, warn 
As defined above. 
TE, seTE 
Estimated (un)transformed proportion and its standard error for individual studies. 
lower, upper 
Lower and upper confidence interval limits for individual studies. 
zval, pval 
zvalue and pvalue 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 (un)transformed proportion and standard error (fixed effect model). 
lower.fixed, upper.fixed 
Lower and upper confidence interval limits (fixed effect model). 
statistic.fixed, pval.fixed 
zvalue and pvalue for test of overall effect (fixed effect model). 
TE.random, seTE.random 
Estimated overall (un)transformed proportion and standard error (random effects model). 
lower.random, upper.random 
Lower and upper confidence interval limits (random effects model). 
statistic.random, pval.random 
zvalue or tvalue and corresponding pvalue for test of overall 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 metaanalysis. 
Q 
Heterogeneity statistic Q. 
df.Q 
Degrees of freedom for heterogeneity statistic. 
pval.Q 
Pvalue of heterogeneity test. 
Q.LRT 
Heterogeneity statistic for likelihoodratio test
(only if 
df.Q.LRT 
Degrees of freedom for likelihoodratio test 
pval.Q.LRT 
Pvalue of likelihoodratio 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. 
method 
A character string indicating method used for
pooling: 
df.hakn 
Degrees of freedom for test of treatment effect for
HartungKnapp method (only if 
bylevs 
Levels of grouping variable  if 
TE.fixed.w, seTE.fixed.w 
Estimated treatment effect and
standard error in subgroups (fixed effect model)  if

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

statistic.fixed.w, pval.fixed.w 
zvalue and pvalue for test
of treatment effect in subgroups (fixed 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 
zvalue or tvalue and
corresponding pvalue for test of treatment effect in subgroups
(random effects model)  if 
w.fixed.w, w.random.w 
Weight of subgroups (in fixed and
random effects model)  if 
df.hakn.w 
Degrees of freedom for test of treatment effect
for HartungKnapp method in subgroups  if 
n.harmonic.mean.w 
Harmonic mean of number of observations in
subgroups (for back transformation of FreemanTukey Double
arcsine transformation)  if 
event.w 
Number of events in subgroups  if 
n.w 
Number of observations in subgroups  if 
k.w 
Number of studies combined within subgroups  if

k.all.w 
Number of all studies in subgroups  if 
Q.w.fixed 
Overall within subgroups heterogeneity statistic Q
(based on fixed 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.fixed 
Pvalue of within subgroups heterogeneity
statistic Q (based on fixed effect model)  if 
pval.Q.w.random 
Pvalue of within subgroups heterogeneity
statistic Q (based on random effects model)  if 
Q.b.fixed 
Overall between subgroups heterogeneity statistic
Q (based on fixed 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.fixed 
Pvalue of between subgroups heterogeneity
statistic Q (based on fixed 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 
incr.event 
Increment added to number of events. 
keepdata 
As defined above. 
data 
Original data (set) used in function call (if

subset 
Information on subset of original data used in
metaanalysis (if 
.glmm.fixed 
GLMM object generated by call of

.glmm.random 
GLMM object generated by call of

call 
Function call. 
version 
Version of R package meta used to create object. 
version.metafor 
Version of R package metafor used for GLMMs. 
Guido Schwarzer sc@imbi.unifreiburg.de
Agresti A & Coull BA (1998): Approximate is better than "exact" for interval estimation of binomial proportions. The American Statistician, 52, 119–26
Barendregt JJ, Doi SA, Lee YY, Norman RE, Vos T (2013): Metaanalysis of prevalence. Journal of Epidemiology and Community Health, 67, 974–8
Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2010): A basic introduction to fixedeffect and randomeffects models for metaanalysis. Research Synthesis Methods, 1, 97–111
DerSimonian R & Laird N (1986): Metaanalysis in clinical trials. Controlled Clinical Trials, 7, 177–88
Edward JM et al. (2006): Adherence to antiretroviral therapy in subsaharan Africa and North America  a metaanalysis. Journal of the American Medical Association, 296, 679–90
Freeman MF & Tukey JW (1950): Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607–11
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009): A reevaluation of randomeffects metaanalysis. Journal of the Royal Statistical Society: Series A, 172, 137–59
Hartung J, Knapp G (2001a): On tests of the overall treatment effect in metaanalysis with normally distributed responses. Statistics in Medicine, 20, 1771–82
Hartung J, Knapp G (2001b): A refined method for the metaanalysis of controlled clinical trials with binary outcome. Statistics in Medicine, 20, 3875–89
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
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
Miller JJ (1978): The inverse of the FreemanTukey double arcsine transformation. The American Statistician, 32, 138
Newcombe RG (1998): Twosided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine, 17, 857–72
Pettigrew HM, Gart JJ, Thomas DG (1986): The bias and higher cumulants of the logarithm of a binomial variate. Biometrika, 73, 425–35
Schwarzer G, Chemaitelly H, AbuRaddad LJ, Rücker G (2019): Seriously misleading results using inverse of FreemanTukey double arcsine transformation in metaanalysis of single proportions. Research Synthesis Methods, 10, 476–83
Stijnen T, Hamza TH, Ozdemir P (2010): Random effects metaanalysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046–67
Viechtbauer W (2010): Conducting metaanalyses in R with the metafor package. Journal of Statistical Software, 36, 1–48
Warton DI, Hui FKC (2011): The arcsine is asinine: the analysis of proportions in ecology. Ecology, 92, 3–10
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
, metacont
,
metagen
, print.meta
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152  # Metaanalysis using generalised linear mixed model
#
metaprop(4:1, 10 * 1:4)
# Apply various classic metaanalysis methods to estimate
# proportions
#
m1 < metaprop(4:1, 10 * 1:4, method = "Inverse")
m2 < update(m1, sm = "PAS")
m3 < update(m1, sm = "PRAW")
m4 < update(m1, sm = "PLN")
m5 < update(m1, sm = "PFT")
#
m1
m2
m3
m4
m5
#
forest(m1)
## Not run:
forest(m2)
forest(m3)
forest(m3, pscale = 100)
forest(m4)
forest(m5)
## End(Not run)
# Do not back transform results, e.g. print logit transformed
# proportions if sm = "PLOGIT" and store old settings
#
oldset < settings.meta(backtransf = FALSE)
#
m6 < metaprop(4:1, c(10, 20, 30, 40), method = "Inverse")
m7 < update(m6, sm = "PAS")
m8 < update(m6, sm = "PRAW")
m9 < update(m6, sm = "PLN")
m10 < update(m6, sm = "PFT")
#
forest(m6)
## Not run:
forest(m7)
forest(m8)
forest(m8, pscale = 100)
forest(m9)
forest(m10)
## End(Not run)
# Use old settings
#
settings.meta(oldset)
# Examples with zero events
#
m1 < metaprop(c(0, 0, 10, 10), rep(100, 4), method = "Inverse")
m2 < metaprop(c(0, 0, 10, 10), rep(100, 4), incr = 0.1, method = "Inverse")
#
summary(m1)
summary(m2)
#
## Not run:
forest(m1)
forest(m2)
## End(Not run)
# Example from Miller (1978):
#
death < c(3, 6, 10, 1)
animals < c(11, 17, 21, 6)
#
m3 < metaprop(death, animals, sm = "PFT")
forest(m3)
# Data examples from Newcombe (1998)
#  apply various methods to estimate confidence intervals for
# individual studies
#
event < c(81, 15, 0, 1)
n < c(263, 148, 20, 29)
#
m1 < metaprop(event, n, method.ci = "SA", method = "Inverse")
m2 < update(m1, method.ci = "SACC")
m3 < update(m1, method.ci = "WS")
m4 < update(m1, method.ci = "WSCC")
m5 < update(m1, method.ci = "CP")
#
lower < round(rbind(NA, m1$lower, m2$lower, NA, m3$lower,
m4$lower, NA, m5$lower), 4)
upper < round(rbind(NA, m1$upper, m2$upper, NA, m3$upper,
m4$upper, NA, m5$upper), 4)
#
tab1 < data.frame(
scen1 = meta:::formatCI(lower[, 1], upper[, 1]),
scen2 = meta:::formatCI(lower[, 2], upper[, 2]),
scen3 = meta:::formatCI(lower[, 3], upper[, 3]),
scen4 = meta:::formatCI(lower[, 4], upper[, 4]),
stringsAsFactors = FALSE
)
names(tab1) < c("r=81, n=263", "r=15, n=148",
"r=0, n=20", "r=1, n=29")
row.names(tab1) < c("Simple", " SA", " SACC",
"Score", " WS", " WSCC",
"Binomial", " CP")
tab1[is.na(tab1)] < ""
# Newcombe (1998), Table I, methods 15:
tab1
# Same confidence interval, i.e. unaffected by choice of summary
# measure
#
print(metaprop(event, n, method.ci = "WS", method = "Inverse"), ma = FALSE)
print(metaprop(event, n, sm = "PLN", method.ci = "WS"), ma = FALSE)
print(metaprop(event, n, sm = "PFT", method.ci = "WS"), ma = FALSE)
print(metaprop(event, n, sm = "PAS", method.ci = "WS"), ma = FALSE)
print(metaprop(event, n, sm = "PRAW", method.ci = "WS"), ma = FALSE)
# Different confidence intervals as argument sm = "NAsm"
#
print(metaprop(event, n, method.ci = "NAsm", method = "Inverse"), ma = FALSE)
print(metaprop(event, n, sm = "PLN", method.ci = "NAsm"), ma = FALSE)
print(metaprop(event, n, sm = "PFT", method.ci = "NAsm"), ma = FALSE)
print(metaprop(event, n, sm = "PAS", method.ci = "NAsm"), ma = FALSE)
print(metaprop(event, n, sm = "PRAW", method.ci = "NAsm"), ma = FALSE)
# Different confidence intervals as argument backtransf = FALSE.
# Accordingly, method.ci = "NAsm" used internally.
#
print(metaprop(event, n, method.ci = "WS", method = "Inverse"),
ma = FALSE, backtransf = FALSE)
print(metaprop(event, n, sm = "PLN", method.ci = "WS"),
ma = FALSE, backtransf = FALSE)
print(metaprop(event, n, sm = "PFT", method.ci = "WS"),
ma = FALSE, backtransf = FALSE)
print(metaprop(event, n, sm = "PAS", method.ci = "WS"),
ma = FALSE, backtransf = FALSE)
print(metaprop(event, n, sm = "PRAW", method.ci = "WS"),
ma = FALSE, backtransf = FALSE)
# Same results (printed on original and log scale, respectively)
#
print(metaprop(event, n, sm = "PLN", method.ci = "NAsm"), ma = FALSE)
print(metaprop(event, n, sm = "PLN"), ma = FALSE, backtransf = FALSE)
# Results for first study (on log scale)
round(log(c(0.3079848, 0.2569522, 0.3691529)), 4)
# Print results as events per 1000 observations
#
print(metaprop(6:8, c(100, 1200, 1000), method = "Inverse"),
pscale = 1000, digits = 1)

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