metabias: Test for funnel plot asymmetry

In meta: General Package for Meta-Analysis

Test for funnel plot asymmetry

Description

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

Usage

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

## S3 method for class 'metabias'
print(
  x,
  digits = gs("digits"),
  digits.stat = gs("digits.stat"),
  digits.pval = max(gs("digits.pval"), 2),
  digits.se = gs("digits.se"),
  digits.tau2 = gs("digits.tau2"),
  scientific.pval = gs("scientific.pval"),
  big.mark = gs("big.mark"),
  zero.pval = gs("zero.pval"),
  JAMA.pval = gs("JAMA.pval"),
  text.tau2 = gs("text.tau2"),
  ...
)

metabias(x, ...)

## Default S3 method:
metabias(
  x,
  seTE,
  method.bias = "Egger",
  plotit = FALSE,
  correct = FALSE,
  k.min = 10,
  ...
)

Arguments

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 (see Details), can be abbreviated.
plotit	A logical indicating whether a plot should be produced (see Details).
correct	A logical indicating whether a continuity corrected statistic is used for rank correlation tests.
k.min	Minimum number of studies to perform test for funnel plot asymmetry.
...	Additional arguments passed on to rma.uni.
digits	Minimal number of significant digits for estimates, see print.default.
digits.stat	Minimal number of significant digits for z- or t-value of test for test of funnel plot asymmetry, see print.default.
digits.pval	Minimal number of significant digits for p-value of test for test of funnel plot asymmetry, see print.default.
digits.se	Minimal number of significant digits for standard errors, see print.default.
digits.tau2	Minimal number of significant digits for residual heterogeneity variance, see print.default.
scientific.pval	A logical specifying whether p-values should be printed in scientific notation, e.g., 1.2345e-01 instead of 0.12345.
big.mark	A character used as thousands separator.
zero.pval	A logical specifying whether p-values should be printed with a leading zero.
JAMA.pval	A logical specifying whether p-values for test of overall effect should be printed according to JAMA reporting standards.
text.tau2	Text printed to identify residual heterogeneity variance \tau^2.
seTE	Standard error of estimated treatment effect (mandatory if x not of class meta).

Details

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

Classic generic tests

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 "Begg", 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 "Egger", 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 "Thompson", the test statistic is based on a weighted linear regression of the treatment effect on its standard error using an additive between-study variance component denoted as methods (3a) - (3d) in Thompson & Sharp (1999). The test statistic follows a t distribution with number of studies - 2 degrees of freedom.

Tests for meta-analysis with binary outcomes

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 "Harbord", 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 (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 "Begg", "Egger" and "Thompson", respectively.

If argument method.bias is "Macaskill", the test statistic is based on a weighted linear regression of the treatment effect on the total sample size with weights reciprocal to the variance of the average event probability (Macaskill et al., 2001, method FPV). 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 with weights reciprocal to the variance of the average event probability (Peters et al., 2006). The test statistic follows a t distribution with number of studies - 2 degrees of freedom. Note, this test is a variant of Macaskill et al. (2001), method FPV, using the inverse sample size as covariate.

If argument method.bias is "Schwarzer", 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.

Test for the standardised mean difference

If argument method.bias is "Pustejovsky", the test statistic is based on a weighted linear regression of the treatment effect on the square root of the sum of the inverse group sample sizes using the treatment effect variance as weights (Pustejovsky & Rodgers, 2019). The test statistic follows a t distribution with number of studies - 2 degrees of freedom.

Recommendations and default settings

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 = "Harbord") is used in meta-analysis of binary outcomes for the odds ratio as effect measure and the Egger test (method.bias = "Egger") in all other settings (Sterne et al., 2011).

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

If argument plotit = TRUE, a scatter plot is shown if argument method.bias is equal to "Begg", "Egger", "Thompson", "Harbord", or "Deeks".

Value

A list with class metabias containing the following components if a test for funnel plot asymmetry is conducted:

statistic	Test statistic.
df	The degrees of freedom of the test statistic in the case that it follows a t distribution.
pval	The p-value for the test.
estimate	Estimates used to calculate test statisic.
method	A character string indicating what type of test was used.
title	Title of Cochrane review.
complab	Comparison label.
outclab	Outcome label.
var.model	A character string indicating whether none, multiplicative, or additive residual heterogeneity variance was assumed.
method.bias	As defined above.
x	Meta-analysis object.
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 meta-analysis.
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 [e-mail]

References

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–analyses. The Stata Journal, 9, 197–210

Kendall M & Gibbons JD (1990): Rank Correlation Methods. London: Edward Arnold

Macaskill P, Walter SD, Irwig L (2001): A comparison of methods to detect publication bias in meta-analysis. Statistics in Medicine, 20, 641–54

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

Pustejovsky JE, Rodgers MA (2019): Testing for funnel plot asymmetry of standardized mean differences. Research Synthesis Methods, 10, 57–71

Rücker 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

See Also

funnel, funnel.meta, metabin, metacont, metagen

Examples

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 = "Begg")
metabias(m1, method.bias = "Begg", correct = TRUE)

metabias(m1, method.bias = "Schwarzer")
metabias(m1, method.bias = "Egger")$pval

# 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)

meta documentation built on June 7, 2023, 5:08 p.m.