netgraph.netmeta: Network graph

Description

This function generates a graph of the evidence network.

Usage

# S3 method for netmeta
netgraph(
  x,
  seq = x$seq,
  labels = x$trts,
  cex = 1,
  adj = NULL,
  srt.labels = 0,
  offset = if (!is.null(adj) && all(unique(adj) == 0.5)) 0 else 0.0175,
  scale = 1.1,
  col = gs("col.netgraph"),
  plastic = gs("plastic"),
  thickness = gs("thickness"),
  lwd = 5,
  lwd.min = lwd/2.5,
  lwd.max,
  rescale.thickness,
  dim = "2d",
  rotate = 0,
  highlight = NULL,
  col.highlight = "red2",
  scale.highlight = 1,
  multiarm = gs("multiarm"),
  col.multiarm = NULL,
  alpha.transparency = 0.5,
  points = !missing(cex.points),
  cex.points = 1,
  pch.points = 20,
  col.points = if (length(pch.points) == 1 && pch.points == 21) "black" else "red",
  bg.points = "red",
  points.min,
  points.max,
  rescale.pointsize,
  number.of.studies = gs("number.of.studies"),
  cex.number.of.studies = cex,
  col.number.of.studies = "white",
  bg.number.of.studies = "black",
  pos.number.of.studies = 0.5,
  start.layout = ifelse(dim == "2d", "circle", "eigen"),
  eig1 = 2,
  eig2 = 3,
  eig3 = 4,
  iterate = FALSE,
  tol = 1e-04,
  maxit = 500,
  allfigures = FALSE,
  A.matrix = x$A.matrix,
  N.matrix = sign(A.matrix),
  D.matrix = netdistance(N.matrix),
  xpos = NULL,
  ypos = NULL,
  zpos = NULL,
  figure = TRUE,
  ...
)

Value

A list containing two data frames with information on nodes and edges.

List element 'nodes'

trts: Treatment names.
labels: Treatment labels.
seq: Sequence of treatment labels.
srt: String rotation.
xpos: Position of treatment / edge on x-axis.
ypos: Position of treatment / edge on y-axis.
zpos: Position of treatment / edge on z-axis (for 3-D plots).
xpos.labels: Position of treatment labels on x-axis (for 2-D plots).
ypos.labels: Position of treatment labels on y-axis (for 2-D plots).
offset.x: Offset of treatment labels on x-axis (for 2-D plots).
offset.y: Offset of treatment labels on y-axis (for 2-D plots).
cex: Point size of treatments / edges.
col: Color for points.
pch: Point type.
bg: Background color for points.
adj.x: Adjustment for treatment label on x-axis.
adj.y: Adjustment for treatment label on y-axis.
adj.z: Adjustment for treatment label on z-axis (for 3-D plots).

List element 'edges'

treat1: Name of first treatment.
treat2: Name of second treatment.
n.stud: Number of studies directly comparing treatments.
xpos: Position of number of studies on x-axis.
ypos: Position of number of studies on y-axis.
adj: Adjustment of number of studies.
pos.number.of.studies: Position of number of studies on edge.
col: Color for edges.

Arguments

x: An object of class netmeta (mandatory).
seq: A character or numerical vector specifying the sequence of treatments arrangement (anticlockwise if start.layout = "circle").
labels: An optional vector with treatment labels.
cex: The magnification to be used for treatment labels.
adj: One, two, or three values in [0, 1] (or a vector / matrix with length / number of rows equal to the number of treatments) specifying the x (and optionally y and z) adjustment for treatment labels.
srt.labels: The character string "orthogonal" (can be abbreviated), a single numeric or numerical vector with value(s) between -180 and 180 specifying the angle to rotate treatment labels (see Details).
offset: Distance between edges (i.e. treatments) in graph and treatment labels for 2-D plots (value of 0.0175 corresponds to a difference of 1.75% of the range on x- and y-axis).
scale: Additional space added outside of edges (i.e. treatments). Increase this value for larger treatment labels (value of 1.10 corresponds to an additional space of 10% around the network graph).
col: A single color (or vector of colors) for lines connecting treatments (edges) if argument plastic = FALSE. Length of the vector must be equal to the number of edges (see list element 'comparisons' in netmeta).
plastic: A logical indicating whether the appearance of the comparisons should be in '3D look' (not to be confused with argument dim).
thickness: Either a character variable to determine the method to plot line widths (see Details) or a matrix of the same dimension and row and column names as argument A.matrix with information on line width.
lwd: A numeric for scaling the line width of comparisons.
lwd.min: Minimum line width in network graph. All connections with line widths below this values will be set to lwd.min.
lwd.max: Maximum line width in network graph. The connection with the largest value according to argument thickness will be set to this value.
rescale.thickness: A logical value or R function to scale the thickness of lines (see Details).
dim: A character string indicating whether a 2- or 3-dimensional plot should be produced, either "2d" or "3d".
rotate: A single numeric with value between -180 and 180 specifying the angle to rotate nodes in a circular network.
highlight: A character vector identifying comparisons that should be marked in the network graph, e.g. highlight = "treat1:treat2".
col.highlight: Color(s) to highlight the comparisons given by highlight.
scale.highlight: Scaling factor(s) for the line width(s) to highlight the comparisons given by highlight.
multiarm: A logical indicating whether multi-arm studies should be marked in plot.
col.multiarm: Either a function from R package colorspace or grDevice to define colors for multi-arm studies or a character vector with colors to highlight multi-arm studies.
alpha.transparency: The alpha transparency of colors used to highlight multi-arm studies (0 means transparent and 1 means opaque).
points: A logical indicating whether points should be printed at nodes (i.e. treatments) of the network graph.
cex.points, pch.points, col.points, bg.points: Corresponding size, type, color, and background color for points. Can be a vector with length equal to the number of treatments.
points.min: Minimum point size. All points with size below this values will be set to points.min.
points.max: Maximum point size in network graph. The node with the largest value according to argument cex.points will be set to this value.
rescale.pointsize: A logical value or R function to scale the point size (see Details).
number.of.studies: A logical indicating whether number of studies should be added to network graph.
cex.number.of.studies: The magnification to be used for number of studies.
col.number.of.studies: Color for number of studies.
bg.number.of.studies: Color for shadow around number of studies.
pos.number.of.studies: A single value (or vector of values) in [0, 1] specifying the position of the number of studies on the lines connecting treatments (edges). Length of the vector must be equal to the number of edges.
start.layout: A character string indicating which starting layout is used if iterate = TRUE. If "circle" (default), the iteration starts with a circular ordering of the vertices; if "eigen", eigenvectors of the Laplacian matrix are used, calculated via generic function eigen (spectral decomposition); if "prcomp", eigenvectors of the Laplacian matrix are calculated via generic function prcomp (principal component analysis); if "random", a random layout is used, drawn from a bivariate normal.
eig1: A numeric indicating which eigenvector is used as x coordinate if start = "eigen" or "prcomp" and iterate = TRUE. Default is 2, the eigenvector to the second-smallest eigenvalue of the Laplacian matrix.
eig2: A numeric indicating which eigenvector is used as y-coordinate if start = "eigen" or "prcomp" and iterate = TRUE. Default is 3, the eigenvector to the third-smallest eigenvalue of the Laplacian matrix.
eig3: A numeric indicating which eigenvector is used as z-coordinate if start = "eigen" or "prcomp" and iterate = TRUE. Default is 4, the eigenvector to the fourth-smallest eigenvalue of the Laplacian matrix.
iterate: A logical indicating whether the stress majorization algorithm is carried out for optimization of the layout.
tol: A numeric for the tolerance for convergence if iterate = TRUE.
maxit: An integer defining the maximum number of iteration steps if iterate = TRUE.
allfigures: A logical indicating whether all iteration steps are shown if iterate = TRUE. May slow down computations if set to TRUE (especially if plastic = TRUE).
A.matrix: Adjacency matrix (nxn) characterizing the structure of the network graph. Row and column names must be the same set of values as provided by argument seq.
N.matrix: Neighborhood matrix (nxn) replacing A.matrix if neighborhood is to be specified differently from node adjacency in the network graph, for example content-based. Row and column names must be the same set of values as provided by argument seq.
D.matrix: Distance matrix (nxn) replacing A.matrix and N.matrix if distances should be provided directly. Row and column names must be the same set of values as provided by argument seq.
xpos: Vector (n) of x coordinates.
ypos: Vector (n) of y coordinates.
zpos: Vector (n) of z coordinates.
figure: A logical indicating whether network graph should be shown.
...: Additional graphical arguments (passed on to plot.default).

Author

Gerta Rücker gerta.ruecker@uniklinik-freiburg.de, Ulrike Krahn ulrike.krahn@bayer.com, Jochem König koenigjo@uni-mainz.de, Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de

Details

This function generates a network graph for an R object created with netmeta. R function plot.default is used to create the network graph.

Layout of network graph

The network is laid out in the plane, where the nodes in the graph layout correspond to the treatments and edges display the observed treatment comparisons. For the default setting, nodes are placed on a circle. Other starting layouts are "eigen", "prcomp", and "random" (Rücker & Schwarzer 2015). If iterate = TRUE, the layout is further optimized using the stress majorization algorithm. This algorithm specifies an 'ideal' distance (e.g., the graph distance) between two nodes in the plane. In the optimal layout, these distances are best approximated in the sense of least squares. Starting from an initial layout, the optimum is approximated in an iterative process called stress majorization (Kamada and Kawai 1989, Michailidis and de Leeuw 2001, Hu 2012). The starting layout can be chosen as a circle or coming from eigenvectors of the Laplacian matrix (corresponding to Hall's algorithm, Hall 1970), calculated in different ways, or random. Moreover, it can be chosen whether the iteration steps are shown (argument allfigures = TRUE).

An optimized circular presentation which typically has a reduced (sometimes minimal) number of crossings can be achieved by using argument seq = "optimal" in combination with argument start.layout. Note, is is not possible of prespecify the best value for argument start.layout for any situation as the result depends on the network structure.

Definition of line widths

Argument thickness providing the line width of edges (comparisons) can be a matrix of the same dimension as argument A.matrix or any of the following character strings (which can be abbreviated):

Proportional to number of studies comparing two treatments (thickness = "number.of.studies", default)
Proportional to inverse standard error of common effects model comparing two treatments (thickness = "se.common")
Proportional to inverse standard error of random effects model comparing two treatments (thickness = "se.random")
Weight from common effects model comparing two treatments (thickness = "w.common")
Weight from random effects model comparing two treatments (thickness = "w.random")
Same line width for all comparisons (thickness = "equal")

Only evidence from direct treatment comparisons is considered to determine the line width if argument thickness is equal to any but the last method.

Line widths are determined by argument lwd if all lines have the same width. This is possible if either argument thickness = "equal", all pairwise comparisons have the same number of studies for thickness = "number.of.studies" or all direct comparisons are equally precise.

Otherwise, the line width of the thickest line is equal to the value of argument lwd.max and all lines with a thickness below the value of argument lwd.min are set to this value. Default for argument lwd.max is 4 * lwd.

Argument rescale.thickness can be used to provide a function to specify the relative line width of edges (comparisons). By default, the square root function sqrt is used in order to lessen differences in line widths. Argument rescale.thickness = FALSE or rescale.thickness = I, i.e., the identity function I, can be used to not rescale line widths.

Definition of point sizes

Points are printed at nodes (treatments) if argument points = TRUE or argument cex.points is provided.

Point sizes are equal to the value of argument cex.points if all points are of equal size.

Otherwise, the point size of the largest point is equal to the value of argument points.max and all points smaller than the value of argument points.min are set to this value. The default for argument points.max is equal to the largest value provided in argument cex.points if this largest value is below or equal to 25. Otherwise the default is points.max = 8.

Argument rescale.pointsize can be used to provide a function to specify relative point sizes. Point sizes are not rescaled at all if they are all equal or the largest cex.points value is below or equal to 25. Otherwise, the square root function sqrt is used in order to lessen the differences in point sizes. Argument rescale.pointsize = FALSE or rescale.pointsize = I, i.e., the identity function I, can be used to not rescale point sizes.

Other settings

Argument srt.labels can be used to specific the rotation (in degrees) of the treatment labels. If srt.labels is equal to "orthogonal", treatment labels are orthogonal to the circle. If srt.labels is a single numeric, all labels are rotated by this degree. If srt.labels is a numeric vector, it must be of the same length as the number of treatments and labels are rotated counter-clockwise starting on the right side. Finally, if srt.labels is a named numeric vector, it must be of the same length as the number of treatments and the names must be equal to the treatment names (and treatment labels are rotated according to the specified values).

Further, a couple of graphical parameters can be specified, such as color and appearance of the edges (treatments) and the nodes (comparisons), whether special comparisons should be highlighted and whether multi-arm studies should be indicated as colored polygons. By default, the sequential_hcl function is used to highlight multi-arm studies.

In order to generate 3-D plots (argument dim = "3d"), R package rgl is necessary. Note, under macOS the X.Org X Window System must be available (see https://www.xquartz.org).

References

Hall KM (1970): An r-dimensional quadratic placement algorithm. Management Science, 17, 219--29

Hu Y (2012): Combinatorial Scientific Computing, Chapter Algorithms for Visualizing Large Networks, pages 525--49. Chapman and Hall / CRC, Computational Science.

Kamada T, Kawai S (1989): An algorithm for drawing general undirected graphs. Information Processing Letters, 31, 7--15

Krahn U, Binder H, König J (2013): A graphical tool for locating inconsistency in network meta-analyses. BMC Medical Research Methodology, 13, 35

Michailidis G, de Leeuw J (2001): Data visualization through graph drawing. Computational Statistics, 16, 435--50

Rücker G, Schwarzer G (2016): Automated drawing of network plots in network meta-analysis. Research Synthesis Methods, 7, 94--107

Examples

Run this code

data(smokingcessation)

# Transform data from arm-based format to contrast-based format
#
pw1 <- pairwise(list(treat1, treat2, treat3),
  event = list(event1, event2, event3), n = list(n1, n2, n3),
  data = smokingcessation, sm = "OR")

# Conduct random effects network meta-analysis
#
net1 <- netmeta(pw1, common = FALSE)

# Network graph with default settings
#
netgraph(net1)

# \donttest{
data(Senn2013)

# Generation of an object of class 'netmeta' with reference
# treatment 'plac'
#
net2 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013, sm = "MD", reference = "plac")

# Network graph with default settings
#
netgraph(net2)

# Network graph with specified order of the treatments and one
# highlighted comparison
#
trts <- c("plac", "benf", "migl", "acar", "sulf",
  "metf", "rosi", "piog", "sita", "vild")
netgraph(net2, highlight = "rosi:plac", seq = trts)

# Same network graph using argument 'seq' in netmeta function
#
net3 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013, sm = "MD", reference = "plac", seq = trts)
netgraph(net3, highlight = "rosi:plac")

# Network graph optimized, starting from a circle, with multi-arm
# study colored
#
netgraph(net2, start = "circle", iterate = TRUE,
  multiarm = TRUE, col.multiarm = "purple")

# Network graph optimized, starting from a circle, with multi-arm
# study colored and all intermediate iteration steps visible
#
netgraph(net2, start = "circle", iterate = TRUE,
  multiarm = TRUE, col.multiarm = "purple",
  allfigures = TRUE)

# Network graph optimized, starting from Laplacian eigenvectors,
# with multi-arm study colored
#
netgraph(net2, start = "eigen",
  multiarm = TRUE, col.multiarm = "purple")

# Network graph optimized, starting from different Laplacian
# eigenvectors, with multi-arm study colored
#
netgraph(net2, start = "prcomp",
  multiarm = TRUE, col.multiarm = "purple")

# Network graph optimized, starting from random initial layout,
# with multi-arm study colored
#
netgraph(net2, start = "random",
  multiarm = TRUE, col.multiarm = "purple")

# Network graph without plastic look and one highlighted comparison
#
netgraph(net2, plastic = FALSE, highlight = "rosi:plac")

# Network graph with same thickness for all comparisons
#
netgraph(net2, thickness = "equal")

# Network graph with changed labels and specified order of the
# treatments
#
netgraph(net2, seq = c(1, 3, 5, 2, 9, 4, 7, 6, 8, 10),
  labels = LETTERS[1:10])

# Rotate treatment labels (orthogonal to circle)
#
netgraph(net2, srt.labels = "o")

# Network graph in 3-D (opens a new device, where you may rotate and
# zoom the plot using the mouse / the mouse wheel).
# The rgl package must be installed for 3-D plots.
#
if (requireNamespace("rgl", quietly = TRUE))
  netgraph(net2, dim = "3d")
# }

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