The function can be used to carry out the rank correlation test for funnel plot asymmetry.

ranktest(x, vi, sei, subset, data, digits, ...)

## Arguments

x

a vector with the observed effect sizes or outcomes or an object of class "rma".

vi

vector with the corresponding sampling variances (ignored if x is an object of class "rma").

sei

vector with the corresponding standard errors (note: only one of the two, vi or sei, needs to be specified).

subset

optional (logical or numeric) vector to specify the subset of studies that should be included in the test (ignored if x is an object of class "rma").

data

optional data frame containing the variables given to the arguments above.

digits

optional integer to specify the number of decimal places to which the printed results should be rounded.

...

other arguments.

## Details

The function carries out the rank correlation test as described by Begg and Mazumdar (1994). The test can be used to examine whether the observed effect sizes or outcomes and the corresponding sampling variances are correlated. A high correlation would indicate that the funnel plot is asymmetric, which may be a result of publication bias.

One can either pass a vector with the observed effect sizes or outcomes (via x) and the corresponding sampling variances via vi (or the standard errors via sei) to the function or an object of class "rma".

## Value

An object of class "ranktest". The object is a list containing the following components:

tau

the estimated value of Kendall's tau rank correlation coefficient.

pval

the corresponding p-value for the test that the true tau value is equal to zero.

The results are formatted and printed with the print function.

## Note

The method does not depend on the model fitted. Therefore, regardless of the model passed to the function, the results of the rank test will always be the same. See regtest for tests of funnel plot asymmetry that are based on regression models and model dependent.

The function makes use of the cor.test function with method="kendall". If possible, an exact p-value is provided; otherwise, a large-sample approximation is used.

## Author

Wolfgang Viechtbauer wvb@metafor-project.org https://www.metafor-project.org

## References

Begg, C. B., & Mazumdar, M. (1994). Operating characteristics of a rank correlation test for publication bias. Biometrics, 50(4), 1088–1101. https://doi.org/10.2307/2533446

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. https://doi.org/10.18637/jss.v036.i03

regtest for the regression test, trimfill for the trim and fill method, tes for the test of excess significance, and selmodel for selection models.

## Examples

### calculate log risk ratios 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)

### carry out the rank correlation test
ranktest(res)
#>
#> Rank Correlation Test for Funnel Plot Asymmetry
#>
#> Kendall's tau = 0.0256, p = 0.9524
#>

### can also pass the observed outcomes and corresponding sampling variances to the function
ranktest(yi, vi, data=dat)
#>
#> Rank Correlation Test for Funnel Plot Asymmetry
#>
#> Kendall's tau = 0.0256, p = 0.9524
#>