netmeasures: Measures for characterizing a network meta-analysis

Description

This function provides measures for quantifying the direct evidence proportion, the mean path length and the minimal parallelism (the latter on aggregated and study level) of mixed treatment comparisons (network estimates) as well as the evidence flow per design, see König et al. (2013). These measures support the critical evaluation of the network meta-analysis results by rendering transparent the process of data pooling.

Usage

netmeasures(
  x,
  random = x$random | !missing(tau.preset),
  tau.preset = x$tau.preset,
  warn = gs("warn"),
  warn.deprecated = gs("warn.deprecated"),
  ...
)

Value

A list containing the following components:

random, tau.preset: As defined above.
proportion: A named vector of the direct evidence proportion of each network estimate.
meanpath: A named vector of the mean path length of each network estimate.
minpar: A named vector of the minimal parallelism on aggregated level of each network estimate.
minpar.study: A named vector of the minimal parallelism on study level of each network estimate.
H.tilde: Design-based hat matrix with information on absolute evidence flow per design. The number of rows is equal to the number of possible pairwise treatment comparisons and the number of columns is equal to the number of designs.

Arguments

x: An object of class netmeta.
random: A logical indicating whether random effects model should be used to calculate network measures.
tau.preset: An optional value for the square-root of the between-study variance \(\tau^2\).
warn: A logical indicating whether warnings should be printed.
warn.deprecated: A logical indicating whether warnings should be printed if deprecated arguments are used.
...: Additional arguments (to catch deprecated arguments).

Author

Ulrike Krahn ulrike.krahn@bayer.com, Jochem König koenigjo@uni-mainz.de

Details

The direct evidence proportion gives the absolute contribution of direct effect estimates combined for two-arm and multi-arm studies to one network estimate.

Concerning indirectness, comparisons with a mean path length beyond two should be interpreted with particular caution, as more than two direct comparisons have to be combined serially on average.

Large indices of parallelism, either on study-level or on aggregated level, can be considered as supporting the validity of a network meta-analysis if there is only a small amount of heterogeneity.

The network estimates for two treatments are linear combinations of direct effect estimates comparing these or other treatments. The linear coefficients can be seen as the generalization of weights known from classical meta-analysis. These coefficients are given in the projection matrix \(H\) of the underlying model. For multi-arm studies, the coefficients depend on the choice of the study-specific baseline treatment, but the absolute flow of evidence can be made explicit for each design as shown in König et al. (2013) and is given in H.tilde.

All measures are calculated based on the common effects meta-analysis by default. In the case that in function netmeta the argument random = TRUE, all measures are calculated for a random effects model. The value of the square-root of the between-study variance \(\tau^2\) can also be prespecified by argument tau.preset in function netmeta.

References

König J, Krahn U, Binder H (2013): Visualizing the flow of evidence in network meta-analysis and characterizing mixed treatment comparisons. Statistics in Medicine, 32, 5414--29

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 network meta-analysis
#
net1 <- netmeta(pw1)

# Calculate measures based on a common effects model
#        
nm1 <- netmeasures(net1)

# Plot of minimal parallelism versus mean path length
#
plot(nm1$meanpath, nm1$minpar, type = "n",
  xlab = "Mean path length", ylab = "Minimal parallelism")
text(nm1$meanpath, nm1$minpar, names(nm1$meanpath), cex = 0.8)

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