Test for funnel plot asymmetry
Description
Test for funnel plot asymmetry, based on rank correlation or linear regression method.
Usage
1 2 3 4 5 6 7 8 9 
Arguments
x 
An object of class 
seTE 
Standard error of estimated treatment effect (mandatory if

method.bias 
A character string indicating which test is to be
used. Either 
plotit 
A logical indicating whether a plot should be produced
for method.bias 
correct 
A logical indicating whether a continuity corrected
statistic is used for rank correlation methods 
k.min 
Minimum number of studies to perform test for funnel plot asymmetry. 
... 
Additional arguments (ignored at the moment). 
Details
Following recommendations by Sterne et al. (2011), by default, a
test for funnel plot asymmetry is only conducted if the number of
studies is ten or larger (argument k.min=10
). This behaviour
can be changed by setting a smaller value for argument
k.min
. Note, the minimum number of studies is three.
If argument method.bias
is "rank"
, the test statistic
is based on the rank correlation between standardised treatment
estimates and variance estimates of estimated treatment effects;
Kendall's tau is used as correlation measure (Begg & Mazumdar,
1994). The test statistic follows a standard normal distribution. By
default (if correct
is FALSE), no continuity correction is
utilised (Kendall & Gibbons, 1990).
If argument method.bias
is "linreg"
, the test
statistic is based on a weighted linear regression of the treatment
effect on its standard error (Egger et al., 1997). The test
statistic follows a t distribution with number of studies  2
degrees of freedom.
If argument method.bias
is "mm"
, the test statistic is
based on a weighted linear regression of the treatment effect on its
standard error using the method of moments estimator for the
additive betweenstudy variance component (method 3a in Thompson,
Sharp, 1999). The test statistic follows a t distribution with
number of studies  2
degrees of freedom.
If argument method.bias
is "peters"
, the test
statistic is based on a weighted linear regression of the treatment
effect on the inverse of the total sample size using the variance of
the average event rate as weights (Peters et al., 2006). The test
statistic follows a t distribution with number of studies  2
degrees of freedom. This test is available for metaanalyses
comparing two binary outcomes or combining single proportions, i.e.
generated with functions metabin
and metaprop
.
The following tests for funnel plot asymmetry are only available for
metaanalyses comparing two binary outcomes, i.e. metaanalyses
generated with the metabin
function.
If argument method.bias
is "count"
, the test statistic
is based on the rank correlation between a standardised cell
frequency and the inverse of the variance of the cell frequency;
Kendall's tau is used as correlation measure (Schwarzer et al.,
2007). The test statistic follows a standard normal distribution. By
default (if correct
is FALSE), no continuity correction is
utilised (Kendall & Gibbons, 1990).
If argument method.bias
is "score"
, the test statistic
is based on a weighted linear regression utilising efficient score
and score variance (Harbord et al., 2006). The test statistic
follows a t distribution with number of studies  2
degrees
of freedom.
In order to calculate an arcsine test for funnel plot asymmetry
(Rücker et al., 2008), one has to use the metabin
function
with argument sm="ASD"
as input to the metabias
command. The three arcsine tests described in Rücker et al. (2008)
can be calculated by setting method.bias
to "rank"
,
"linreg"
and "mm"
, respectively.
If argument method.bias
is missing, the Harbord test
(method.bias="score"
) is used for the odds ratio as effect
measure and the Egger test (method.bias="linreg"
) for other
effect measures (Sterne et al., 2011).
No test for funnel plot asymmetry is conducted in metaanalyses with subgroups.
Value
A list with class "htest"
containing the following components
if a test for funnel plot asymmetry is conducted:
estimate 
The estimated degree of funnel plot asymmetry, with
name 
statistic 
The value of the test statistic. 
parameters 
The degrees of freedom of the test statistic in the case that it follows a t distribution. 
p.value 
The pvalue for the test. 
alternative 
A character string describing the alternative hypothesis. 
method 
A character string indicating what type of test was used. 
data.name 
A character string giving the names of the data. 
title 
Title of Cochrane review. 
complab 
Comparison label. 
outclab 
Outcome label. 
version 
Version of R package meta used to create object. 
Or a list with the following elements if test is not conducted due to the number of studies:
k 
Number of studies in metaanalysis. 
k.min 
Minimum number of studies to perform test for funnel plot asymmetry. 
version 
Version of R package meta used to create object. 
Author(s)
Guido Schwarzer sc@imbi.unifreiburg.de
References
Begg CB & Mazumdar M (1994), Operating characteristics of a rank correlation test for publication bias. Biometrics, 50, 1088–1101.
Egger M, Smith GD, Schneider M & Minder C (1997), Bias in metaanalysis detected by a simple, graphical test. British Medical Journal, 315, 629–634.
Harbord RM, Egger M & Sterne J (2006), A modified test for smallstudy effects in metaanalyses of controlled trials with binary endpoints. Statistics in Medicine, 25, 3443–3457.
Kendall M & Gibbons JD (1990), Rank Correlation Methods. London: Edward Arnold.
Peters JL, Sutton AJ, Jones DR, Abrams KR & Rushton L (2006), Comparison of two methods to detect publication bias in metaanalysis. Journal of the American Medical Association, 295, 676–680.
Rücker G, Schwarzer G, Carpenter JR (2008) Arcsine test for publication bias in metaanalyses with binary outcomes. Statistics in Medicine, 27,746–763.
Schwarzer G, Antes G & Schumacher M (2007), A test for publication bias in metaanalysis with sparse binary data. Statistics in Medicine, 26, 721–733.
Sterne, JAC et al. (2011), Recommendations for Examining and Interpreting Funnel Plot Asymmetry in MetaAnalyses of Randomised Controlled Trials. BMJ (Clinical research ed.), 343, 1, doi: 10.1136/bmj.d4002 .
Thompson SG & Sharp, SJ (1999), Explaining heterogeneity in metaanalysis: A comparison of methods, Statistics in Medicine, 18, 2693–2708.
See Also
funnel
, funnel.meta
, metabin
, metacont
, metagen
Examples
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  data(Olkin95)
meta1 < metabin(event.e, n.e, event.c, n.c,
data=Olkin95, subset=1:10,
sm="RR", method="I")
metabias(meta1)
metabias(meta1, plotit=TRUE)
metabias(meta1, method.bias="rank")
metabias(meta1, method.bias="rank", correct=TRUE)
metabias(meta1, method.bias="count")
metabias(meta1, method.bias="linreg")$p.value
#
# Arcsine test (based on linear regression):
#
meta1.as < metabin(event.e, n.e, event.c, n.c,
data=Olkin95, subset=1:10,
sm="ASD", method="I")
metabias(meta1.as)
#
# Same result (using function metabias.default):
#
metabias(meta1.as$TE, meta1.as$seTE)
#
# No test for funnel plot asymmetry calculated:
#
meta2 < metabin(event.e, n.e, event.c, n.c,
data=Olkin95, subset=1:5,
sm="RR", method="I")
metabias(meta2)
meta3 < metabin(event.e, n.e, event.c, n.c,
data=Olkin95, subset=1:2,
sm="RR", method="I")
metabias(meta3)
# Test for funnel plot asymmetry calculated
# (use of argument k.min):
#
metabias(meta2, k.min=5)
