Function to create forest plots for objects of class "rma".

# S3 method for rma
forest(x, annotate=TRUE, addfit=TRUE, addpred=FALSE,
       showweights=FALSE, header=FALSE,
       xlim, alim, olim, ylim, top=3, at, steps=5,
       level=x$level, refline=0, digits=2L, width,
       xlab, slab, mlab, ilab, ilab.xpos, ilab.pos,
       order, transf, atransf, targs, rows,
       efac=1, pch=15, psize, plim=c(0.5,1.5), colout,
       col, border, lty, fonts, cex, cex.lab, cex.axis, annosym, ...)

Arguments

x

an object of class "rma".

annotate

logical to specify whether annotations should be added to the plot (the default is TRUE).

addfit

logical to specify whether the summary estimate (for models without moderators) or fitted values (for models with moderators) should be added to the plot (the default is TRUE). See ‘Details’.

addpred

logical to specify whether the bounds of the prediction interval should be added to the plot (the default is FALSE). See ‘Details’.

showweights

logical to specify whether the annotations should also include the weights given to the observed outcomes during the model fitting (the default is FALSE). See ‘Details’.

header

logical to specify whether column headings should be added to the plot (the default is FALSE). Can also be a character vector to specify the left and right headings (or only the left one).

xlim

horizontal limits of the plot region. If unspecified, the function tries to set the horizontal plot limits to some sensible values.

alim

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

olim

optional argument to specify observation/outcome limits. If unspecified, no limits are used.

ylim

the y-axis limits of the plot. If unspecified, the function tries to set the y-axis limits to some sensible values.

top

the amount of space to leave empty at the top of the plot (e.g., for adding headers) (the default is 3 rows).

at

position of the x-axis tick marks and corresponding labels. If unspecified, the function tries to set the tick mark positions/labels to some sensible values.

steps

the number of tick marks for the x-axis (the default is 5). Ignored when the positions are specified via the at argument.

level

numeric value between 0 and 100 to specify the confidence interval level (the default is to take the value from the object).

refline

numeric value to specify the location of the vertical ‘reference’ line (the default is 0). The line can be suppressed by setting this argument to NA.

digits

integer to specify the number of decimal places to which the tick mark labels of the x-axis and the annotations should be rounded (the default is 2L). Can also be a vector of two integers, the first to specify the number of decimal places for the annotations, the second for the x-axis labels. When specifying an integer (e.g., 2L), trailing zeros after the decimal mark are dropped for the x-axis labels. When specifying a numeric value (e.g., 2), trailing zeros are retained.

width

optional integer to manually adjust the width of the columns for the annotations.

xlab

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

slab

optional vector with labels for the \(k\) studies. If unspecified, the labels are either taken from the object (if study labels were specified) or simple labels are created within the function. To suppress labels, set this argument to NA.

mlab

optional character string giving a label to the summary estimate from a fixed- or random-effects model. If unspecified, the label is created within the function.

ilab

optional vector, matrix, or data frame providing additional information about the studies that should be added to the plot.

ilab.xpos

numeric vector to specify the x-axis position(s) of the variable(s) given via ilab (must be specified if ilab is specified).

ilab.pos

integer(s) (either 1, 2, 3, or 4) to specify the alignment of the vector(s) given via ilab (2 means right, 4 mean left aligned). If unspecified, the default is to center the labels.

order

optional character string to specify how the studies should be ordered. Can also be a variable based on which the studies will be ordered. See ‘Details’.

transf

optional argument to specify a function that should be used to transform the observed outcomes, summary estimates, fitted values, and confidence interval bounds (e.g., transf=exp; see also transf). If unspecified, no transformation is used.

atransf

optional argument to specify a function that should be used to transform the x-axis labels and annotations (e.g., atransf=exp; see also transf). If unspecified, no transformation is used.

targs

optional arguments needed by the function specified via transf or atransf.

rows

optional vector to specify the rows (or more generally, the horizontal positions) for plotting the outcomes. Can also be a single value to specify the row (horizontal position) of the first outcome (the remaining outcomes are then plotted below this starting row). If unspecified, the function sets this value automatically.

efac

vertical expansion factor for confidence interval limits, arrows, and the symbol used to denote summary estimates. The default value of 1 should usually work okay. Can also be a vector of two numbers, the first for CI limits and arrows, the second for summary estimates. Can also be a vector of three numbers, the first for CI limits, the second for arrows, the third for summary estimates.

pch

plotting symbol to use for the observed outcomes. By default, a filled square is used. See points for other options. Can also be a vector of values.

psize

optional numeric value to specify the point sizes for the observed outcomes. If unspecified, the point sizes are a function of the model weights. Can also be a vector of values.

plim

numeric vector of length 2 to scale the point sizes (ignored when psize is specified). See ‘Details’.

colout

optional character string to specify the name of a color to use for plotting the observed outcomes ("black" is used by default if not specified). Can also be a vector of color names.

col

optional character string to specify the name of a color to use for the summary polygon or fitted values. If unspecified, the function sets a default color.

border

optional character string to specify the name of a color to use for the border of the summary polygon or fitted values. If unspecified, the function sets a default color.

lty

optional character string to specify the line type for the confidence intervals. If unspecified, the function sets this to "solid" by default.

fonts

optional character string to specify the font to use for the study labels, annotations, and the extra information (if specified via ilab). If unspecified, the default font is used.

cex

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

cex.lab

optional expansion factor for the x-axis title. If unspecified, the function tries to set this to a sensible value.

cex.axis

optional expansion factor for the x-axis labels. If unspecified, the function tries to set this to a sensible value.

annosym

optional vector of length 3 to change the left bracket, separation, and right bracket symbols for the annotations.

...

other arguments.

Details

The plot shows the observed effect sizes or outcomes with corresponding confidence intervals.

For fixed- and random-effects models (i.e., for models without moderators), a four-sided polygon, sometimes called a summary ‘diamond’, is added to the bottom of the forest plot, showing the summary estimate based on the model (with the center of the polygon corresponding to the estimate and the left/right edges indicating the confidence interval limits). The col and border arguments can be used to adjust the (border) color of the polygon. Drawing of the polgyon can be suppressed by setting addfit=FALSE.

For random-effects models and if addpred=TRUE, a dotted line is added to the summary polygon which indicates the (approximate) bounds of the prediction interval (the interval indicates where level % of the true outcomes are expected to fall) (Riley et al., 2011). For random-effects models of class "rma.mv" (see rma.mv) with multiple \(\tau^2\) values, the addpred argument can be used to specify for which level of the inner factor the prediction interval should be provided (since the intervals differ depending on the \(\tau^2\) value). If the model should also contain multiple \(\gamma^2\) values, the addpred argument should then be of length 2 to specify the levels of both inner factors. See also predict.rma, which is used to compute these interval bounds.

For models involving moderators, the fitted value for each study is added as a polygon to the plot. By default, the width of the polygons corresponds to the confidence interval limits for the fitted values. By setting addpred=TRUE, the width reflects the prediction interval limits. Again, the col and border arguments can be used to adjust the (border) color of the polygons. These polygons can be suppressed by setting addfit=FALSE.

With the transf argument, the observed outcomes, summary estimate, fitted values, confidence interval bounds, and prediction interval bounds can be transformed with some suitable function. For example, when plotting log odds ratios, one could use transf=exp to obtain a forest plot showing the odds ratios. Alternatively, one can use the atransf argument to transform the x-axis labels and annotations (e.g., atransf=exp). See also transf for some other useful transformation functions in the context of a meta-analysis. The examples below illustrate the use of these arguments.

By default, the studies are ordered from top to bottom (i.e., the first study in the dataset will be placed in row \(k\), the second study in row \(k-1\), and so on, until the last study, which is placed in the first row). The studies can be reordered with the order argument:

  • order="obs": the studies are ordered by the observed outcomes,

  • order="fit": the studies are ordered by the fitted values,

  • order="prec": the studies are ordered by their sampling variances,

  • order="resid": the studies are ordered by the size of their residuals,

  • order="rstandard": the studies are ordered by the size of their standardized residuals,

  • order="abs.resid": the studies are ordered by the size of their absolute residuals,

  • order="abs.rstandard": the studies are ordered by the size of their absolute standardized residuals.

Alternatively, it is also possible to set order equal to a variable based on which the studies will be ordered (see ‘Examples’).

Additional columns with information about the studies can be added to the plot via the ilab argument. This can either be a single variable or an entire matrix / data frame (with as many rows as there are studies in the forest plot). The ilab.xpos argument must then also be specified to indicate the x-axis position of the variables specified via ilab.

The figure below illustrates how the elements in a forest plot can be arranged and the meaning of the some of the arguments such as xlim, alim or at, ilab, and ilab.xpos.

The figure corresponds to the following code:

   dat <- dat.bcg
   dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat)
   res <- rma(yi, vi, data=dat, slab=paste(author, year, sep=", "))
   forest(res, addpred=TRUE, xlim=c(-16,7), at=seq(-3,2,by=1),
          ilab=cbind(dat$tpos, dat$tneg, dat$cpos, dat$cneg),
          ilab.xpos=c(-9.5,-8,-6,-4.5), cex=.75, header="Author(s) and Year")
   text(c(-9.5,-8,-6,-4.5), 15, c("TB+", "TB-", "TB+", "TB-"), cex=.75, font=2)
   text(c(-8.75,-5.25),     16, c("Vaccinated", "Control"),    cex=.75, font=2)

Additional summary estimates can be added to the plot with the addpoly function. See the documentation for that function for examples.

When showweights=TRUE, the annotations will include information about the weights given to the observed outcomes during the model fitting. For simple models (such as those fitted with the rma.uni function), these weights correspond to the ‘inverse-variance weights’ (but are given in percent). For models fitted with the rma.mv function, the weights are based on the diagonal of the weight matrix. Note that the weighting structure is typically more complex in such models (i.e., the weight matrix is usually not just a diagonal matrix) and the weights shown therefore do not reflect this complexity. See weights.rma for more details.

By default (i.e., when psize is not specified), the size of the points is a function of the square root of the model weights. This way, their area is proportional to the the weights. However, the point sizes are rescaled so that the smallest point size is plim[1] and the largest point size is plim[2]. As a result, their relative sizes (i.e., areas) no longer exactly correspond to their relative weights. If exactly relative point sizes are desired, one can set plim[2] to NA, in which case the points are rescaled so that the smallest point size corresponds to plim[1] and all other points are scaled accordingly. As a result, the largest point may be very large. Alternatively, one can set plim[1] to NA, in which case the points are rescaled so that the largest point size corresponds to plim[2] and all other points are scaled accordingly. As a result, the smallest point may be very small and essentially indistinguishable from the confidence interval line. To avoid the latter, one can also set plim[3], which enforces a minimal point size.

Note

The function tries to set some sensible values for the optional arguments, but it may be necessary to adjust these in certain circumstances.

The function actually returns some information about the chosen defaults invisibly. Printing this information is useful as a starting point to make adjustments to the plot (see ‘Examples’).

If the number of studies is quite large, the labels, annotations, and symbols may become quite small and impossible to read. Stretching the plot window vertically may then provide a more readable figure (one should call the function again after adjusting the window size, so that the label/symbol sizes can be properly adjusted). Also, the cex, cex.lab, and cex.axis arguments are then useful to adjust the symbol and text sizes.

If the horizontal plot and/or x-axis limits are set manually, then the horizontal plot limits (xlim) must be at least as wide as the x-axis limits (alim). This restriction is enforced inside the function.

If the outcome measure used for creating the plot is bounded (e.g., correlations are bounded between -1 and +1, proportions are bounded between 0 and 1), one can use the olim argument to enforce those limits (the observed outcomes and confidence/prediction intervals cannot exceed those bounds then).

The models without moderators, the col argument can also be a vector of two elements, the first for specifying the color of the summary polygon, the second for specifying the color of the line for the prediction interval.

The lty argument can also be a vector of up to three elements, the first for specifying the line type of the individual CIs ("solid" by default), the second for the line type of the prediction interval ("dotted" by default), the third for the line type of the horizontal lines that are automatically added to the plot ("solid" by default; set to "blank" to remove them).

Author

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

References

Lewis, S., & Clarke, M. (2001). Forest plots: Trying to see the wood and the trees. British Medical Journal, 322(7300), 1479--1480. https://doi.org/10.1136/bmj.322.7300.1479

Riley, R. D., Higgins, J. P. T., & Deeks, J. J. (2011). Interpretation of random effects meta-analyses. British Medical Journal, 342, d549. https://doi.org/10.1136/bmj.d549

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

See also

Examples

### 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, slab=paste(author, year, sep=", ")) ### default forest plot of the log risk ratios and summary estimate forest(res, header=TRUE)
### summary estimate in row -1; studies in rows k=13 through 1; horizontal ### lines in rows 0 and k+1; two extra lines of space at the top for headings, ### and other annotations; headings (if requested) in line k+2 op <- par(xpd=TRUE) text(x=-8.4, y=-1:16, -1:16, pos=4, cex=.6)
par(op) ### can also inspect defaults chosen defaults <- forest(res)
defaults
#> $xlim #> [1] -8.00 7.26 #> #> $alim #> [1] -3 2 #> #> $at #> [1] -3 -2 -1 0 1 2 #> #> $ylim #> [1] -1.5 16.0 #> #> $rows #> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 #> #> $cex #> [1] 1 #> #> $cex.lab #> [1] 1 #> #> $cex.axis #> [1] 1 #>
### several forest plots illustrating the use of various arguments forest(res, cex=.8)
forest(res, cex=.8, addpred=TRUE)
forest(res, cex=.8, alim=c(-3,3))
forest(res, cex=.8, order="prec", alim=c(-3,3))
forest(res, cex=.8, order=dat.bcg$ablat, addpred=TRUE)
### adjust xlim values to see how that changes the plot forest(res)
par("usr")[1:2] ### this shows what xlim values were chosen by default
#> [1] -8.00 7.26
forest(res, xlim=c(-16,14))
forest(res, xlim=c(-18,10))
forest(res, xlim=c(-10,10))
### illustrate transf argument forest(res, transf=exp, at=0:7, xlim=c(-8,12), cex=.8, refline=1, header=TRUE)
### illustrate atransf argument forest(res, atransf=exp, at=log(c(.05,.25,1,4,20)), xlim=c(-8,7), cex=.8, header=TRUE)
### showweights argument forest(res, atransf=exp, at=log(c(.05,.25,1,4,20)), xlim=c(-8,8), order="prec", showweights=TRUE, cex=.8)
### forest plot with extra annotations ### note: may need to widen plotting device to avoid overlapping text forest(res, atransf=exp, at=log(c(.05, .25, 1, 4)), xlim=c(-16,6), ilab=cbind(dat.bcg$tpos, dat.bcg$tneg, dat.bcg$cpos, dat.bcg$cneg), ilab.xpos=c(-9.5,-8,-6,-4.5), cex=.75, header="Author(s) and Year")
op <- par(cex=.75, font=2) text(c(-9.5,-8,-6,-4.5), 15, c("TB+", "TB-", "TB+", "TB-"))
text(c(-8.75,-5.25), 16, c("Vaccinated", "Control"))
par(op) ### mixed-effects model with absolute latitude in the model res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, mods = ~ ablat, data=dat.bcg, slab=paste(author, year, sep=", ")) ### forest plot with observed and fitted values forest(res, xlim=c(-9,5), order="fit", cex=.8, ilab=dat.bcg$ablat, ilab.xpos=-4, atransf=exp, at=log(c(.05,.25,1,4)), header="Author(s) and Year")
text(-4, 15, "Latitude", cex=.8, font=2)
### meta-analysis of the log risk ratios using a random-effects model res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg, slab=paste(author, year, sep=", ")) ### for more complicated plots, the ylim and rows arguments may be useful forest(res)
forest(res, ylim=c(-1.5, 16)) ### the default
forest(res, ylim=c(-1.5, 20)) ### extra space in plot
forest(res, ylim=c(-1.5, 20), rows=c(17:15, 12:6, 3:1)) ### set positions
### forest plot with subgrouping of studies ### note: may need to widen plotting device to avoid overlapping text forest(res, xlim=c(-16, 4.6), at=log(c(.05, .25, 1, 4)), atransf=exp, ilab=cbind(dat.bcg$tpos, dat.bcg$tneg, dat.bcg$cpos, dat.bcg$cneg), ilab.xpos=c(-9.5,-8,-6,-4.5), cex=.75, ylim=c(0.5, 21), order=dat.bcg$alloc, rows=c(1:2,5:11,14:17), header="Author(s) and Year")
op <- par(cex=0.75, font=2) text(c(-9.5,-8,-6,-4.5), 20, c("TB+", "TB-", "TB+", "TB-"))
text(c(-8.75,-5.25), 21, c("Vaccinated", "Control"))
op <- par(font=4) text(-16, c(18,12,3), c("Systematic Allocation", "Random Allocation", "Alternate Allocation"), pos=4)
par(op) ### see also the addpoly.rma function for an example where summaries ### for the three subgroups are added to such a forest plot ### illustrate use of olim argument with a meta-analysis of raw correlation ### coefficients (data from Pritz, 1997); without olim=c(0,1), some of the ### CIs would have upper bounds larger than 1 dat <- escalc(measure="PR", xi=xi, ni=ni, data=dat.pritz1997) res <- rma(yi, vi, data=dat, slab=paste0(study, ") ", authors)) forest(res, xlim=c(-0.8,1.6), alim=c(0,1), psize=1, refline=coef(res), olim=c(0,1), header=TRUE)
### an example of a forest plot where the data have a multilevel structure and ### we want to reflect this by grouping together estimates from the same cluster dat <- dat.konstantopoulos2011 res <- rma.mv(yi, vi, random = ~ 1 | district/school, data=dat, slab=paste0("District ", district, ", School: ", school)) dd <- c(0,diff(dat$district)) dd[dd > 0] <- 1 rows <- (1:res$k) + cumsum(dd) par(tck=-.01, mgp = c(1.6,.2,0)) forest(res, cex=0.5, header=TRUE, rows=rows, ylim=c(0.5,max(rows)+3))
abline(h = rows[c(1,diff(rows)) == 2] - 1, lty="dotted")