plot.copas {metasens}

Display results of Copas selection modelling

Description

Four plots (selectable by 'which') are currently available: (1) funnel plot, (2) contour plot, (3) treatment effect plot, (4) p-value for residual publication bias plot. By default, all plots are provided.

Usage

## S3 method for class 'copas'
plot(
  x,
  which = 1:4,
  main = c("Funnel plot", "Contour plot", "Treatment effect plot",
    "P-value for residual selection bias"),
  xlim.pp,
  orthogonal.line = TRUE,
  lines = FALSE,
  warn = -1,
  ...
)

Arguments

x

An object of class copas, generated by the copas function

which

Specify plots required: 1:4 produces all plots (default); 3 produces plot 3 etc; c(1,3) produces plots 1 and 3, and so on.

main

Specify plot captions. Must be of same length as argument which.

xlim.pp

A vector of x-axis limits for plots 3 and 4, i.e. for the probability of publishing the study with largest standard deviation. E.g. to specify limits between 0.3 and 0.1 set xlim.pp=c(0.3,0.1).

orthogonal.line

A logical indicating whether the orthogonal line should be displayed in plot 2 (contour plot).

lines

(Diagnostic use only) A logical indicating whether regression lines should be plotted in contour plot. These regression lines attempt to summarise each contour of constant treatment effect by a straight line, prior to calculating the orthogonal line. Regression lines with a positive adjusted R^2 will be printed in green color, others will be printed in red color.

warn

A number setting the handling of warning messages. It is not uncommon for numerical problems to be encountered during estimation over the grid of (gamma0, gamma1) values. Usually this does not indicate a serious problem. This option specifies what to do with warning messages. warn=-1: ignore all warnings; warn=0 (the default): store warnings till function finishes; if there are less than 10, print them, otherwise print a message saying warning messages were generated; warn=1: print warnings as they occur; warn=2: stop the function when the first warning is generated. For further details see help(options).

...

Other arguments (to check for deprecated argument 'caption').

Details

Takes an object created by the copas function and draws up to four plots to display the results of the Copas selection modelling.

The argument which specifies the plots to be drawn; plot numbers below will be produced by setting which=1, etc.

Plot 1: Funnel plot of studies in meta-analysis. Vertical grey line is usual random effects estimate (DerSimonian-Laird method); vertical broken line is common effects estimate.

Plot 2: Plot of contours of treatment effect (estimated by the Copas model) as the selection probability varies (the selection probability is a function of gamma0 and gamma1 - see help(copas) or the reference below).

Plot 3: Assuming the contours of treatment effect in Plot 2 are locally parallel, the results can be summarised in terms of the probability of publishing the study with the largest standard error. This plot displays the results of doing this, showing how the estimated treatment effect (and 100*level% confidence interval) vary as the probability of publishing the study with the largest standard error decreases.

The three horizontal grey lines are the usual random effects treatment estimate (center) +/- the 100*level% confidence interval (upper/lower grey lines).

Plot 4: For any degree of selection (i.e. probability of the study with largest SE being published), we can calculate a p-value for the hypothesis that no further selection remains unexplained in the data. These plot displays these p-values against the probability that the study with the largest SE is published.

Under the copas selection model, probabilities of the smallest study being published which correspond to p-values for residual selection bias that are larger than 0.1 are more plausible. The corresponding treatment effect in plot 3 is thus the most plausible under the copas selection model.

Note

In the current version, fine control of the graphics parameters for the individual panels is not possible. However, all the data used to create the plots can be extracted manually from the object created by the copas function (see attributes list for copas) and used to create tailor-made plots.

Author(s)

James Carpenter [e-mail], Guido Schwarzer [e-mail]

References

Carpenter JR, Schwarzer G, Rücker G, Künstler R (2009): Empirical evaluation showed that the Copas selection model provided a useful summary in 80% of meta-analyses. Journal of Clinical Epidemiology, 62, 624–31

Schwarzer G, Carpenter J, Rücker G (2010): Empirical evaluation suggests Copas selection model preferable to trim-and-fill method for selection bias in meta-analysis. Journal of Clinical Epidemiology, 63, 282–8

See Also

copas, summary.copas, metabias, metagen

Examples

data(Fleiss1993bin, package = "meta")

# Perform meta-analysis (outcome measure is OR = odds ratio)
#
m1 <- metabin(d.asp, n.asp, d.plac, n.plac, data = Fleiss1993bin, sm = "OR")

# Perform Copas analysis
#
cop1 <- copas(m1)

# Plot results
#
plot(cop1)

# Only show plots 1 and 2 (without orthogonal line)
#
plot(cop1, which = 1:2, orth = FALSE)

# Another example showing use of more arguments
# Note the use of "\n" to create a new line in the caption
#
plot(cop1, which = 3, xlim.pp = c(1, 0.5),
  main = "Variation in estimated treatment\n effect with selection")