metafor (version 1.9-9)

regtest: Regression Test for Funnel Plot Asymmetry for 'rma' Objects

Description

The function can be used to carry out (various versions of) Egger's regression test for funnel plot asymmetry for objects of class "rma".

Usage

regtest(x, ...)
"regtest"(x, model="rma", predictor="sei", ret.fit=FALSE, ...)

Arguments

x

an object of class "rma".

model

either "rma" or "lm" to indicate the type of model to use for the regression test. See ‘Details’.

predictor

either "sei" "vi", "ni", "ninv", "sqrtni", or "sqrtninv" to indicate the type of independent variable to use for the regression test. See ‘Details’.

ret.fit

logical indicating whether the full results from the fitted model should also be returned.

...

other arguments.

Value

An object of class "regtest.rma". The object is a list containing the following components:The results are formated and printed with the print.regtest.rma function.

Details

Various tests for funnel plot asymmetry have been suggested in the literature, including the rank correlation test by Begg and Mazumdar (1994) and the regression test by Egger et al. (1997). Extensions, modifications, and further developments of the regression test are described (among others) by Macaskill, Walter, and Irwig (2001), Sterne and Egger (2005), Harbord, Egger, and Sterne (2006), Peters et al. (2006), Rücker, Schwarzer, and Carpenter (2008), and Moreno et al. (2009). The various versions of the regression test differ in terms of the model (either a regular weighted regression with a multiplicative dispersion term or one of the meta-analytic models is used), in terms of the independent variable that the observed outcomes are hypothesized to be related to when publication bias is present (suggested predictors include the standard error, the sampling variance, the sample size, and the inverse of the sample size), and in terms of the outcome measure used (e.g., for $2x2$ table data, one has the choice between various outcome measures). The idea behind the various tests is the same though: If there is a relationship between the observed outcomes and the chosen predictor, then this usually implies asymmetry in the funnel plot, which in turn may be an indication of publication bias.

The regtest.rma function can be used to carry out various versions of the regression test. The model is chosen via the model argument, with model="lm" for weighted regression with a multiplicative dispersion term or model="rma" for the meta-analytic models. In the latter case, arguments such as method, weighted, and test used during the initial model fitting are also used for the regression test. Therefore, if one wants to conduct the regression test with a random/mixed-effects model, one should first fit a random-effects model with the rma function and then use the regtest.rma function on the fitted model object.

The predictor is chosen via the predictor argument:

• predictor="sei" for the standard error,
• predictor="vi" for the sampling variance,
• predictor="ni" for the sample size,
• predictor="ninv" for the inverse of the sample size,
• predictor="sqrtni" for the square-root transformed sample size, and
• predictor="sqrtninv" for the inverse of the square-root transformed sample size.

For predictors based on the sample size, the object x obviously must contain the information about the sample sizes. This will automatically be the case when measure was not equal to "GEN" or the ni values were explicitly specified during the initial model fitting.

Finally, depending on what outcome measure was used for the model fitting will determine which outcome measure is used for the regression test.

References

Begg, C. B., & Mazumdar, M. (1994). Operating characteristics of a rank correlation test for publication bias. Biometrics, 50, 1088--1101.

Egger, M., Davey Smith, G., Schneider, M., & Minder, C. (1997). Bias in meta-analysis detected by a simple, graphical test. British Medical Journal, 315, 629--634.

Harbord, R. M., Egger, M., & Sterne, J. A. C. (2006). A modified test for small-study effects in meta-analyses of controlled trials with binary endpoints. Statistics in Medicine, 25, 3443--3457.

Macaskill, P., Walter, S. D., & Irwig, L. (2001). A comparison of methods to detect publication bias in meta-analysis. Statistics in Medicine, 20, 641--654.

Moreno, S. G., Sutton, A. J., Ades, A. E., Stanley, T. D., Abrams, K. R., Peters, J. L., & Cooper, N. J. (2009). Assessment of regression-based methods to adjust for publication bias through a comprehensive simulation study. BMC Medical Research Methodology, 9:2.

Peters, J. L., Sutton, A. J., Jones, D. R., Abrams, K. R., & Rushton, L. (2006). Comparison of two methods to detect publication bias in meta-analysis. Journal of the American Medical Association, 295, 676--680.

Rücker, G., Schwarzer, G., & Carpenter, J. (2008). Arcsine test for publication bias in meta-analyses with binary outcomes. Statistics in Medicine, 27, 746--763.

Sterne, J. A. C., & Egger, M. (2005). Regression methods to detect publication and other bias in meta-analysis. In H. R. Rothstein, A. J. Sutton, & M. Borenstein (Eds.) Publication bias in meta-analysis: Prevention, assessment, and adjustments (pp. 99--110). Chichester, England: Wiley.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. http://www.jstatsoft.org/v36/i03/.

See Also

ranktest

Examples

### calculate log relative risks and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

### fit random-effects model
res <- rma(yi, vi, data=dat)

### classical Egger test
regtest(res, model="lm")

### random/mixed-effects version of the Egger test
regtest(res)

### more examples
res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat)

regtest(res, model="lm", predictor="ni")
regtest(res, model="lm", predictor="ninv")

regtest(res, model="rma", predictor="ni")
regtest(res, model="rma", predictor="ninv")

### testing for asymmetry after accounting for the influence of a moderator
res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg,
           mods = ~ ablat, data=dat)
regtest(res, model="lm")
regtest(res)