Test for funnel plot asymmetry, based on rank correlation or linear regression method.

```
# S3 method for meta
metabias(
x,
method.bias = x$method.bias,
plotit = FALSE,
correct = FALSE,
k.min = 10,
...
)
```# S3 method for metabias
print(x, ...)

metabias(x, ...)

# S3 method for default
metabias(
x,
seTE,
method.bias = "linreg",
plotit = FALSE,
correct = FALSE,
k.min = 10,
...
)

x

An object of class `meta`

or estimated treatment
effect in individual studies.

method.bias

A character string indicating which test is to
be used. Either `"rank"`

, `"linreg"`

, `"mm"`

,
`"count"`

, `"score"`

, `"peters"`

, or
`"deeks"`

, can be abbreviated.

plotit

A logical indicating whether a plot should be
produced for method.bias `"rank"`

, `"linreg"`

,
`"mm"`

, `"score"`

, or `"deeks"`

.

correct

A logical indicating whether a continuity corrected
statistic is used for rank correlation methods `"rank"`

and
`"count"`

.

k.min

Minimum number of studies to perform test for funnel plot asymmetry.

…

Additional arguments (ignored at the moment).

seTE

Standard error of estimated treatment effect (mandatory
if `x`

not of class `meta`

).

A list with class `htest`

containing the following components
if a test for funnel plot asymmetry is conducted:

The estimated degree of funnel plot asymmetry, with
name `"ks"`

or `"bias"`

corresponding to the method
employed, i.e., rank correlation or regression method.

The value of the test statistic.

The degrees of freedom of the test statistic in the case that it follows a t distribution.

The p-value for the test.

A character string describing the alternative hypothesis.

A character string indicating what type of test was used.

A character string giving the names of the data.

Title of Cochrane review.

Comparison label.

Outcome label.

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:

Number of studies in meta-analysis.

Minimum number of studies to perform test for funnel plot asymmetry.

Version of R package **meta** used to create
object.

Functions to conduct rank correlation or linear regression tests for funnel plot asymmetry.

The following tests are generic tests for funnel plot asymmetry
which only require estimates of the treatment effect and
corresponding standard errors. Accordingly, these are the only tests
provided by R function `metabias.default`

.

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 between-study variance component (method 3a in Thompson,
Sharp, 1999). The test statistic follows a t distribution with
`number of studies - 2`

degrees of freedom.

The following tests for funnel plot asymmetry are only available
for meta-analyses comparing two binary outcomes, i.e. meta-analyses
generated with the `metabin`

function. The only exception is
the test by Peters et al. (2006) which can also be used in a
meta-analysis of single proportions generated with `metaprop`

.

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,
2009). 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
(R<U+00FC>cker 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 R<U+00FC>cker et al. (2008)
can be calculated by setting `method.bias`

to `"rank"`

,
`"linreg"`

and `"mm"`

, respectively.

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.

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).

Finally, for meta-analysis of diagnostic test accuracy studies, if
argument `method.bias`

is `"deeks"`

, the test statistic
is based on a weighted linear regression of the log diagnostic odds
ratio on the inverse of the squared effective sample size using the
effective sample size as weights (Deeks et al., 2005). The test
statistic follows a t distribution with ```
number of studies -
2
```

degrees of freedom.

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 missing, the Harbord test
(`method.bias = "score"`

) is used in meta-analysis of binary
outcomes for the odds ratio as effect measure and the Egger test
(`method.bias = "linreg"`

) in all other settings (Sterne
et al., 2011).

No test for funnel plot asymmetry is conducted in meta-analyses with subgroups.

Begg CB & Mazumdar M (1994):
Operating characteristics of a rank correlation test for
publication bias.
*Biometrics*,
**50**, 1088--101

Deeks JJ, Macaskill P, Irwig L (2005):
The performance of tests of publication bias and other sample size
effects in systematic reviews of diagnostic test accuracy was
assessed.
*Journal of Clinical Epidemiology*,
**58**:882--93

Egger M, Smith GD, Schneider M & Minder C (1997):
Bias in meta-analysis detected by a simple, graphical test.
*British Medical Journal*,
**315**, 629--34

Harbord RM, Egger M & Sterne J (2006):
A modified test for small-study effects in meta-analyses of
controlled trials with binary endpoints.
*Statistics in Medicine*,
**25**, 3443--57

Harbord RM, Harris RJ, Sterne JAC (2009):
Updated tests for small-study effects in meta<U+2013>analyses.
*The Stata Journal*,
**9**, 197--210

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
meta-analysis.
*Journal of the American Medical Association*,
**295**, 676--80

R<U+00FC>cker G, Schwarzer G, Carpenter JR (2008):
Arcsine test for publication bias in meta-analyses with binary
outcomes.
*Statistics in Medicine*,
**27**, 746--63

Schwarzer G, Antes G & Schumacher M (2007):
A test for publication bias in meta-analysis with sparse binary
data.
*Statistics in Medicine*,
**26**, 721--33

Sterne, JAC et al. (2011):
Recommendations for examining and interpreting funnel plot
asymmetry in meta-analyses of randomised controlled trials.
*BMJ (Clinical research ed.)*,
**343**, 1

Thompson SG & Sharp, SJ (1999):
Explaining heterogeneity in meta-analysis: a comparison of methods,
*Statistics in Medicine*,
**18**, 2693--708

```
# NOT RUN {
data(Olkin1995)
m1 <- metabin(ev.exp, n.exp, ev.cont, n.cont,
data = Olkin1995, subset = 1:10,
sm = "RR", method = "I")
metabias(m1)
metabias(m1, plotit = TRUE)
metabias(m1, method.bias = "rank")
metabias(m1, method.bias = "rank", correct = TRUE)
metabias(m1, method.bias = "count")
metabias(m1, method.bias = "linreg")$p.value
# Arcsine test (based on linear regression)
#
m1.as <- update(m1, sm = "ASD")
metabias(m1.as)
# Same result (using function metabias.default)
metabias(m1.as$TE, m1.as$seTE)
# No test for funnel plot asymmetry calculated
#
m2 <- update(m1, subset = 1:5)
metabias(m2)
m3 <- update(m1, subset = 1:2)
metabias(m3)
# Test for funnel plot asymmetry calculated (use of argument k.min)
#
metabias(m2, k.min = 5)
# }
```

Run the code above in your browser using DataCamp Workspace