Function to create radial (also called Galbraith) plots for objects of class "rma".

radial(x, …)
galbraith(x, …)

# S3 method for rma
radial(x, center=FALSE, xlim, zlim, xlab, zlab,
       atz, aty, steps=7, level=x$level, digits=2, back="lightgray",
       transf, targs, pch=19, arc.res=100, cex, …)

Arguments

x

an object of class "rma".

center

logical to indicate whether the plot should be centered horizontally at the model estimate (the default is FALSE).

xlim

x-axis limits. If unspecified, the function tries to set the x-axis limits to some sensible values.

zlim

z-axis limits. If unspecified, the function tries to set the z-axis limits to some sensible values (note that the z-axis limits are the actual vertical limit of the plotting region).

xlab

title for the x-axis. If unspecified, the function tries to set an appropriate axis title.

zlab

title for the z-axis. If unspecified, the function tries to set an appropriate axis title.

atz

position for the z-axis tick marks and labels. If unspecified, these values are set by the function.

aty

position for the y-axis tick marks and labels. If unspecified, these values are set by the function.

steps

the number of tick marks for the y-axis (the default is 7). Ignored when argument aty is used.

level

numerical value between 0 and 100 specifying the level of the z-axis error region (the default is to take the value from the object).

digits

integer specifying the number of decimal places to which the tick mark labels of the y-axis should be rounded (the default is 2).

back

color of the z-axis error region. Set to NA to suppress shading of the region.

transf

optional argument specifying the name of a function that should be used to transform the y-axis labels (e.g., transf=exp; see also transf). If unspecified, no transformation is used.

targs

optional arguments needed by the function specified via transf.

pch

plotting symbol. By default, a solid circle is used. See points for other options.

arc.res

integer specifying the number of line segments to use when drawing the y-axis and confidence interval arcs (the default is 100).

cex

optional character and symbol expansion factor. If unspecified, the function tries to set this to a sensible value.

other arguments.

Details

For a fixed-effects model, the plot shows the inverse of the standard errors on the horizontal axis against the individual observed effect sizes or outcomes standardized by their corresponding standard errors on the vertical axis. Since the vertical axis corresponds to standardized values, it is referred to as the z-axis within this function. On the right hand side of the plot, an arc is drawn (referred to as the y-axis within this function) corresponding to the individual observed effect sizes or outcomes. A line projected from (0,0) through a particular point within the plot onto this arc indicates the value of the individual observed effect size or outcome for that point.

For a random-effects model, the function uses \(1/\sqrt{v_i + \tau^2}\) for the horizontal axis, where \(v_i\) is the sampling variance of the observed effect size or outcome and \(\tau^2\) is the amount of heterogeneity as estimated based on the model. For the z-axis, \(\sqrt{v_i + \tau^2}\) is used to standardize the individual observed effect sizes or outcomes.

If the model contains moderators, the function returns an error.

Value

A data frame with components:

x

the x coordinates of the points that were plotted.

y

the y coordinates of the points that were plotted.

slab

study labels of the points that were plotted.

Note that the data frame is returned invisibly.

References

Galbraith, R. F. (1988). Graphical display of estimates having differing standard errors. Technometrics, 30, 271--281.

Galbraith, R. F. (1988). A note on graphical presentation of estimated odds ratios from several clinical trials. Statistics in Medicine, 7, 889--894.

Galbraith, R. F (1994). Some applications of radial plots. Journal of the American Statistical Association, 89, 1232--1242.

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

Examples

### meta-analysis of the log risk ratios using a fixed-effects model res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg, method="FE") radial(res)
### line from (0,0) with slope equal to the log risk ratio from the 4th study abline(a=0, b=-1.44155119, lty="dotted")
### meta-analysis of the log risk ratios using a random-effects model res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) radial(res)