Package 'netmeta'

Description

R package netmeta (Balduzzi et al., 2023) provides frequentist methods for network meta-analysis and supports Schwarzer et al. (2015), Chapter 8 on network meta-analysis https://link.springer.com/book/10.1007/978-3-319-21416-0.

Details

R package netmeta is an add-on package for meta providing the following network meta-analysis models:

• frequentist network meta-analysis (function netmeta) based on Rücker (2012) and Rücker & Schwarzer (2014);

• additive network meta-analysis for combinations of treatments (netcomb for connected networks, discomb for disconnected networks) (Rücker et al., 2020a);

• network meta-analysis of binary data (netmetabin) using the Mantel-Haenszel or non-central hypergeometric distribution method (Efthimiou et al., 2019).

The following methods are available to present results of a network meta-analysis:

• network graphs (netgraph) described in Rücker & Schwarzer (2016);

• forest plots (forest.netmeta, forest.netcomb);

• league tables with network meta-analysis results (netleague);

• tables with network, direct and indirect estimates (nettable) looking similar to the statistical part of a GRADE table for a network meta-analysis (Puhan et al., 2014).

The following methods are implemented to rank treatments:

• rankograms (rankogram) (Salanti et al., 2011);

• ranking of treatments (netrank) based on P-scores (Rücker & Schwarzer, 2015) or the Surface Under the Cumulative RAnking curve (SUCRA) (Salanti et al., 2011);

• partial order of treatment rankings (netposet, plot.netposet) and Hasse diagram (hasse) according to Carlsen & Bruggemann (2014) and Rücker & Schwarzer (2017).

Available functions to evaluate network inconsistency:

• split direct and indirect evidence (netsplit) to check for consistency (Dias et al., 2010; Efthimiou et al., 2019);

• net heat plot (netheat) and design-based decomposition of Cochran's Q (decomp.design) described in Krahn et al. (2013).

Additional methods and functions:

• subgroup network meta-analysis (subgroup.netmeta);

• information on network connectivity (netconnection);

• contribution of direct comparisons to network estimates (netcontrib) (Papakonstantinou et al., 2018; Davies et al., 2022);

• importance of individual studies measured by reduction of precision if removed from network (netimpact) (Rücker et al., 2020b);

• ‘comparison-adjusted’ funnel plot (funnel.netmeta) to assess funnel plot asymmetry in network meta-analysis (Chaimani & Salanti, 2012);

• conduct pairwise meta-analyses for all comparisons with direct evidence in a network meta-analysis (netpairwise);

• results of several network meta-analyses can be combined with netbind to show these results in a forest plot (forest.netbind).

• measures characterizing the flow of evidence between two treatments (netmeasures) described in König et al. (2013);

• calculate comparison effects of two arbitrary complex interventions in component network meta-analysis (netcomparison);

• calculate effect of arbitrary complex interventions in component network meta-analysis (netcomplex).

Functions and datasets from netmeta are utilised in Schwarzer et al. (2015), Chapter 8 "Network Meta-Analysis", https://link.springer.com/book/10.1007/978-3-319-21416-0.

Type help(package = "netmeta") for a listing of all R functions available in netmeta.

Type citation("netmeta") on how to cite netmeta in publications.

To report problems and bugs

• type bug.report(package = "netmeta") if you do not use RStudio,

• send an email to Guido Schwarzer [email protected] if you use RStudio.

The development version of netmeta is available on GitHub https://github.com/guido-s/netmeta.

Author(s)

Guido Schwarzer [email protected], Gerta Rücker [email protected]

References

Balduzzi S, Rücker G, Nikolakopoulou A, Papakonstantinou T, Salanti G, Efthimiou O, Schwarzer G (2023): netmeta: An R Package for network meta-analysis using frequentist methods. Journal of Statistical Software, 106, 1–40

Carlsen L, Bruggemann R (2014): Partial order methodology: a valuable tool in chemometrics. Journal of Chemometrics, 28, 226–34

Chaimani A & Salanti G (2012): Using network meta-analysis to evaluate the existence of small-study effects in a network of interventions. Research Synthesis Methods, 3, 161–76

Davies AL, Papakonstantinou T, Nikolakopoulou A, Rücker G, Galla T (2022): Network meta-analysis and random walks. Statistics in Medicine, 41, 2091–2114

Dias S, Welton NJ, Caldwell DM, Ades AE (2010): Checking consistency in mixed treatment comparison meta-analysis. Statistics in Medicine, 29, 932–44

Efthimiou O, Rücker G, Schwarzer G, Higgins J, Egger M, Salanti G (2019): A Mantel-Haenszel model for network meta-analysis of rare events. Statistics in Medicine, 38, 2992–3012

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

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

Papakonstantinou, T., Nikolakopoulou, A., Rücker, G., Chaimani, A., Schwarzer, G., Egger, M., Salanti, G. (2018): Estimating the contribution of studies in network meta-analysis: paths, flows and streams. F1000Research

Puhan MA, Schünemann HJ, Murad MH, et al. (2014): A GRADE working group approach for rating the quality of treatment effect estimates from network meta-analysis. British Medical Journal, 349, g5630

Rücker G (2012): Network meta-analysis, electrical networks and graph theory. Research Synthesis Methods, 3, 312–24

Rücker G, Schwarzer G (2014): Reduce dimension or reduce weights? Comparing two approaches to multi-arm studies in network meta-analysis. Statistics in Medicine, 33, 4353–69

Rücker G, Schwarzer G (2015): Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Medical Research Methodology, 15, 58

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

Rücker G, Schwarzer G (2017): Resolve conflicting rankings of outcomes in network meta-analysis: Partial ordering of treatments. Research Synthesis Methods, 8, 526–36

Rücker G, Petropoulou M, Schwarzer G (2020a): Network meta-analysis of multicomponent interventions. Biometrical Journal, 62, 808–21

Rücker G, Nikolakopoulou A, Papakonstantinou T, Salanti G, Riley RD, Schwarzer G (2020b): The statistical importance of a study for a network meta-analysis estimate. BMC Medical Research Methodology, 20, 190

Salanti G, Ades AE, Ioannidis JP (2011): Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. Journal of Clinical Epidemiology, 64, 163–71

Schwarzer G, Carpenter JR and Rücker G (2015): Meta-Analysis with R (Use R!). Springer International Publishing, Switzerland.

See Also

Useful links:

• https://github.com/guido-s/netmeta https://link.springer.com/book/10.1007/978-3-319-21416-0

Description

The as.data.frame method returns a data frame containing information on membership of studies / pairwise comparisons to a (sub)network.

Usage

## S3 method for class 'netconnection'
as.data.frame(x, ...)

Arguments

Value

A data frame is returned by the function as.data.frame.

Author(s)

Guido Schwarzer [email protected]

See Also

netconnection

Examples

# Artificial example with two subnetworks
#
t1 <- c("G", "B", "B", "D", "A", "F")
t2 <- c("B", "C", "E", "E", "H", "A")
#
nc2 <- netconnection(t1, t2)
print(nc2, details = TRUE)

as.data.frame(nc2)

Description

The as.data.frame method returns a data frame containing information on individual studies, e.g., estimated treatment effect and its standard error.

Usage

## S3 method for class 'netmeta'
as.data.frame(x, row.names = NULL, optional = FALSE, details = FALSE, ...)

Arguments

Value

A data frame is returned by the function as.data.frame.

Author(s)

Guido Schwarzer [email protected]

See Also

netmeta

Examples

data(smokingcessation)

# Transform data from arm-based format to contrast-based format
#
p1 <- 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 and show data frame
#
net1 <- netmeta(p1, common = FALSE)
as.data.frame(net1)

## Not run: 
data(Senn2013)

# Conduct network meta-analysis
#
net2 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013, sm = "MD")

as.data.frame(net2)
as.data.frame(net2, details = TRUE)

## End(Not run)

Description

This dataset comes from a systematic review of randomized controlled trials on pharmacologic treatments for chronic obstructive pulmonary disease (COPD) (Baker et al., 2009).

The primary outcome, occurrence of one or more episodes of COPD exacerbation, is binary (yes / no). For this outcome, five drug treatments (fluticasone, budesonide, salmeterol, formoterol, tiotropium) and two combinations (fluticasone + salmeterol, budesonide + formoterol) were compared to placebo. The authors considered the two combinations as separate treatments instead of evaluating the individual components.

Format

A data frame with the following columns:

Source

Baker WL, Baker EL, Coleman CI (2009): Pharmacologic Treatments for Chronic Obstructive Pulmonary Disease: A Mixed-Treatment Comparison Meta-analysis. Pharmacotherapy: The Journal of Human Pharmacology and Drug Therapy, 29, 891–905

See Also

pairwise, metabin, netmetabin

Examples

data(Baker2009)
Baker2009

## Not run: 
# Transform data from long arm-based format to contrast-based
# format. Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, exac, total, studlab = paste(study, year),
  data = Baker2009, sm = "OR")

# Conduct network meta-analysis
#
net1 <- netmeta(p1, ref = "plac")

# Conduct component network meta-analysis
#
cnet1 <- netcomb(net1)
cnet1

## End(Not run)

Description

Auxiliary functions to (i) create a combination / C matrix with information on treatment combinations and interaction terms and (ii) a vector with all combinations in a component network meta-analysis.

Usage

createC(x, ...)

## S3 method for class 'matrix'
createC(
  x,
  comb.ia,
  inactive = NULL,
  sep.comps = gs("sep.comps"),
  sep.ia = gs("sep.ia"),
  ...
)

## S3 method for class 'netcomb'
createC(x, comb.ia = NULL, inactive = NULL, sep.ia = x$sep.ia, ...)

## S3 method for class 'netmeta'
createC(x, inactive = NULL, sep.comps = gs("sep.comps"), ...)

## S3 method for class 'netconnection'
createC(x, inactive = NULL, sep.comps = gs("sep.comps"), ...)

## Default S3 method:
createC(x, n = 1, ...)

combinations(x, n = NULL)

Arguments

Value

R function createC returns a combination matrix / C matrix with studies in rows and component and interaction terms in columns.

R function combinations returns a character vector with combinations.

Author(s)

Guido Schwarzer [email protected], Gerta Rücker [email protected]

See Also

netcomb, discomb

Examples

data(Linde2016)

# Only consider studies including Face-to-face PST (to reduce
# runtime of example)
#
face <- subset(Linde2016, id %in% c(16, 24, 49, 118))

# Conduct random effects network meta-analysis
#
net1 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = face, ref = "placebo", sm = "OR", common = FALSE)

# Additive component network meta-analysis (with placebo as inactive
# treatment)
#
nc1 <- netcomb(net1, inactive = "placebo")

# Available combinations in CNMA
combinations(nc1)

# Create C matrix with all available interactions, i.e., one interaction
# for each combination
createC(nc1)

# Run interaction CNMA model with all available interactions
# (same result as standard NMA)
netcomb(net1, C.matrix = createC(nc1))

## Not run: 
# Conduct random effects network meta-analysis on full dataset
#
net2 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = Linde2016, ref = "placebo", sm = "OR", common = FALSE)

# Additive component network meta-analysis (with placebo as inactive
# treatment)
#
nc2 <- netcomb(net2, inactive = "placebo")

# Available combinations in CNMA
combinations(nc2)

# Create C matrix with all available interactions, i.e., one interaction
# for each combination
head(createC(nc2))

# Run interaction CNMA model with all available interactions
# (same result as standard NMA)
netcomb(net2, C.matrix = createC(nc2))

## End(Not run)

Description

This function performs a design-based decomposition of Cochran's Q for assessing the homogeneity in the whole network, the homogeneity within designs, and the homogeneity/consistency between designs. It allows also an assessment of the consistency assumption after detaching the effect of single designs.

Usage

decomp.design(
  x,
  tau.preset = x$tau.preset,
  warn = gs("warn"),
  nchar.trts = x$nchar.trts
)

Arguments

Details

In the context of network meta-analysis and the assessment of the homogeneity and consistency assumption, a generalized Cochran's Q statistic for multivariate meta-analysis can be used as shown in Krahn et al. (2013). This Q statistic can be decomposed in a sum of within-design Q statistics and one between-designs Q statistic that incorporates the concept of design inconsistency, see Higgins et al. (2012).

For assessing the inconsistency in a random effects model, the between-designs Q statistic can be calculated based on a full design-by-treatment interaction random effects model (see Higgins et al., 2012). This Q statistic will be automatically given in the output ($\tau^2$ estimated by the method of moments (see Jackson et al., 2012). Alternatively, the square-root of the between-study variance can be prespecified by argument tau.preset to obtain a between-designs Q statistic (in Q.inc.random), its design-specific contributions Q.inc.design.random.preset) as well as residuals after detaching of single designs (residuals.inc.detach.random.preset).

Since an inconsistent treatment effect of one design can simultaneously inflate several residuals, Krahn et al. (2013) suggest for locating the inconsistency in a network to fit a set of extended models allowing for example for a deviating effect of each study design in turn. The recalculated between-designs Q statistics are given in list component Q.inc.detach. The change of the inconsistency contribution of single designs can be investigated in more detail by a net heat plot (see function netheat). Designs where only one treatment is involved in other designs of the network or where the removal of corresponding studies would lead to a splitting of the network do not contribute to the inconsistency assessment. These designs are not included in Q.inc.detach.

Value

Network meta-analysis with a single design: NULL. Otherwise, a list containing the following components:

Author(s)

Ulrike Krahn [email protected], Jochem König [email protected]

References

Higgins JPT, Jackson D, Barrett JK, Lu G, Ades AE, White IR (2012): Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Research Synthesis Methods, 3, 98–110

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

Jackson D, White IR and Riley RD (2012): Quantifying the impact of between-study heterogeneity in multivariate meta-analyses. Statistics in Medicine, 31, 3805–20

See Also

netmeta, netheat

Examples

data(Senn2013)

# Only consider first five studies (to reduce runtime of example)
#
studies <- unique(Senn2013$studlab)
Senn2013.5 <- subset(Senn2013, studlab %in% studies[1:5])

# Conduct network meta-analysis with placebo as reference treatment
#
net1 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013.5, sm = "MD", reference = "plac")

# Decomposition of Cochran's Q
#
decomp.design(net1)

Description

Network meta-analysis comparing the effects of two diets to control on mortality.

The data are rates, given as the number of deaths and person-years. These data are used as an example in the supplemental material of Dias et al. (2013).

Format

A data frame with the following columns:

Source

Dias S, Sutton AJ, Ades AE and Welton NJ (2013): Evidence synthesis for decision making 2: A generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Medical Decision Making, 33, 607–17

See Also

pairwise, metainc, netmeta, netgraph.netmeta

Examples

data(dietaryfat)

# Transform data from arm-based format to contrast-based format
# Using incidence rate ratios (sm = "IRR") as effect measure.
# Note, the argument 'sm' is not necessary as this is the default
# in R function metainc() called internally
#
p1 <- pairwise(list(treat1, treat2, treat3),
  list(d1, d2, d3), time = list(years1, years2, years3),
  studlab = ID, data = dietaryfat, sm = "IRR")
p1

# Conduct network meta-analysis
#
net1 <- netmeta(p1)
net1

# Conduct network meta-analysis using incidence rate differences
# (sm = "IRD")
#
p2 <- pairwise(list(treat1, treat2, treat3),
  list(d1, d2, d3), time = list(years1, years2, years3),
  studlab = ID, data = dietaryfat, sm = "IRD")
net2 <- netmeta(p2)
net2

# Draw network graph
#
netgraph(net1, points = TRUE, cex.points = 3, cex = 1.25)

netgraph(net1, points = TRUE, cex.points = 3, cex = 1.25,
  labels = c("Control","Diet", "Diet 2"))

Description

Some treatments in a network meta-analysis may be combinations of other treatments or have common components. The influence of individual components can be evaluated in an additive network meta-analysis model assuming that the effect of treatment combinations is the sum of the effects of its components. This function implements this additive model in a frequentist way and is particularly intended for disconnected networks.

Usage

discomb(
  TE,
  seTE,
  treat1,
  treat2,
  studlab,
  data = NULL,
  subset = NULL,
  inactive = NULL,
  sep.comps = gs("sep.comps"),
  C.matrix,
  sm,
  level = gs("level"),
  level.ma = gs("level.ma"),
  common = gs("common"),
  random = gs("random") | !is.null(tau.preset),
  reference.group,
  baseline.reference = gs("baseline.reference"),
  seq = gs("sep"),
  tau.preset = NULL,
  tol.multiarm = gs("tol.multiarm"),
  tol.multiarm.se = gs("tol.multiarm.se"),
  details.chkmultiarm = gs("details.chkmultiarm"),
  details.chkident = FALSE,
  sep.trts = gs("sep.trts"),
  nchar.comps = gs("nchar.comps"),
  sep.ia = gs("sep.ia"),
  func.inverse = invmat,
  n1 = NULL,
  n2 = NULL,
  event1 = NULL,
  event2 = NULL,
  incr = NULL,
  overall.hetstat = gs("overall.hetstat"),
  backtransf = gs("backtransf"),
  na.unident = gs("na.unident"),
  title = gs("title"),
  keepdata = gs("keepdata"),
  warn = gs("warn"),
  warn.deprecated = gs("warn.deprecated"),
  nchar.trts = nchar.comps,
  ...
)

Arguments

Details

Treatments in network meta-analysis (NMA) can be complex interventions. Some treatments may be combinations of others or have common components. The standard analysis provided by netmeta is a NMA where all existing (single or combined) treatments are considered as different nodes in the network. Exploiting the fact that some treatments are combinations of common components, an additive component network meta-analysis (CNMA) model can be used to evaluate the influence of individual components. This model assumes that the effect of a treatment combination is the sum of the effects of its components which implies that common components cancel out in comparisons.

This R function can be used for disconnected networks. Use netmeta and netcomb for connected networks.

The additive CNMA model has been implemented using Bayesian methods (Mills et al., 2012; Welton et al., 2013). This function implements the additive model in a frequentist way (Rücker et al., 2020).

The underlying multivariate model is given by

$\bold{\delta} = \bold{B} \bold{\theta}, \bold{\theta} = \bold{C} \bold{\beta}$

with

$\bold{\delta}$

vector of true treatment effects (differences) from individual studies,

$\bold{B}$

design matrix describing the structure of the network,

$\bold{\theta}$

parameter vector that represents the existing combined treatments,

$\bold{C}$

matrix describing how the treatments are composed,

$\bold{\beta}$

parameter vector representing the treatment components.

All parameters are estimated using weighted least squares regression.

Argument inactive can be used to specify a single component that does not have any therapeutic value. Accordingly, it is assumed that the treatment effect of the combination of this component with an additional treatment component is equal to the treatment effect of the additional component alone.

Argument sep.comps can be used to specify the separator between individual components. By default, the matrix C is calculated internally from treatment names. However, it is possible to specify a different matrix using argument C.matrix.

By default, component names are not abbreviated in printouts. However, in order to get more concise printouts, argument nchar.comps can be used to define the minimum number of characters for abbreviated component names (see abbreviate, argument minlength). R function treats is utilised internally to create abbreviated component names.

Value

An object of classes discomb and netcomb with corresponding print, summary, and forest functions. The object is a list containing the following components:

Note

This function calculates effects for individual components and complex interventions present in the network.

R function netcomplex can be used to calculate the effect for arbitrary complex interventions in a component network meta-analysis. Furthermore, R function netcomparison can be used to calculate the effect for comparisons of two arbitrary complex intervention in a component network meta-analysis.

Author(s)

Gerta Rücker [email protected], Guido Schwarzer [email protected]

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

Mills EJ, Thorlund K, Ioannidis JP (2012): Calculating additive treatment effects from multiple randomized trials provides useful estimates of combination therapies. Journal of Clinical Epidemiology, 65, 1282–8

Rücker G, Petropoulou M, Schwarzer G (2020): Network meta-analysis of multicomponent interventions. Biometrical Journal, 62, 808–21

Welton NJ, Caldwell DM, Adamopoulos E, Vedhara K (2009): Mixed treatment comparison meta-analysis of complex interventions: psychological interventions in coronary heart disease. American Journal of Epidemiology, 169: 1158–65

See Also

netcomb, forest.netcomb, summary.netcomb, netmeta, netconnection, netcomplex, netcomparison

Examples

# Artificial dataset
#
t1 <- c("A + B", "A + C", "A"    , "A"    , "D", "D", "E")
t2 <- c("C"    , "B"    , "B + C", "A + D", "E", "F", "F")
#
mean    <- c(4.1, 2.05, 0, 0, 0.1, 0.1, 0.05)
se.mean <- rep(0.1, 7)
#
study <- paste("study", c(1:4, 5, 5, 5))
#
dat <- data.frame(mean, se.mean, t1, t2, study,
  stringsAsFactors = FALSE)
#
trts <- c("A", "A + B", "A + C", "A + D",
  "B", "B + C", "C", "D", "E", "F")
#
comps <- LETTERS[1:6]

# Use netconnection() to display network information
#
netconnection(t1, t2, study)

dc1 <- discomb(mean, se.mean, t1, t2, study, seq = trts)
dc1

forest(dc1, ref = "F")

# Define C matrix manually (which will produce the same results)
#
C <- rbind(c(1, 0, 0, 0, 0, 0),  # A
  c(1, 1, 0, 0, 0, 0),  # A + B
  c(1, 0, 1, 0, 0, 0),  # A + C
  c(1, 0, 0, 1, 0, 0),  # A + D
  c(0, 1, 0, 0, 0, 0),  # B
  c(0, 1, 1, 0, 0, 0),  # B + C
  c(0, 0, 1, 0, 0, 0),  # C
  c(0, 0, 0, 1, 0, 0),  # D
  c(0, 0, 0, 0, 1, 0),  # E
  c(0, 0, 0, 0, 0, 1))  # F
#                  
colnames(C) <- comps
rownames(C) <- trts
#
dc2 <- discomb(mean, se.mean, t1, t2, study, seq = trts,
  C.matrix = C)
#
# Compare C matrices
#
all.equal(dc1$C.matrix, dc2$C.matrix)

Description

This dataset comes from a systematic review aiming to determine the effects of eight antithrombotic treatments in reducing the incidence of major thrombotic events in patients with non-valvular atrial fibrillation (Dogliotti et al., 2014). The review included 20 studies (79,808 participants), four of which were three-arm studies. The primary outcome is stroke reduction.

Format

A data frame with the following columns:

Source

Dogliotti A, Paolasso E, Giugliano RP (2014): Current and new oral antithrombotics in non-valvular atrial fibrillation: a network meta-analysis of 79 808 patients. Heart, 100, 396–405

See Also

pairwise, metabin, netmetabin

Examples

data(Dogliotti2014)
Dogliotti2014

## Not run: 
# Transform data from long arm-based format to contrast-based
# format. Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, stroke, total, studlab = study,
  data = Dogliotti2014, sm = "OR")

# Conduct Mantel-Haenszel network meta-analysis
#
netmetabin(p1, ref = "plac")

## End(Not run)

Description

Network meta-analysis comparing inhaled medications in patients with chronic obstructive pulmonary disease.

Format

A data frame with the following columns:

Source

Dong Y-H, Lin H-H, Shau W-Y, Wu Y-C, Chang C-H, Lai M-S (2013): Comparative safety of inhaled medications in patients with chronic obstructive pulmonary disease: systematic review and mixed treatment comparison meta-analysis of randomised controlled trials. Thorax, 68, 48–56

See Also

pairwise, metabin, netmetabin

Examples

data(Dong2013)

# Transform data from long arm-based format to contrast-based
# format. Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, death, randomized, studlab = id,
  data = Dong2013, sm = "OR")

# Only consider first ten studies (to reduce runtime of example)
#
p1.10 <- subset(p1, id <= 10)

# Conduct Mantel-Haenszel network meta-analysis
#
netmetabin(p1.10, ref = "plac")

## Not run: 
# Conduct Mantel-Haenszel network meta-analysis for the whole
# dataset
#
p2 <- pairwise(treatment, death, randomized, studlab = id,
  data = Dong2013, sm = "OR")
netmetabin(p2, ref = "plac")

## End(Not run)

Description

Forest plot to show network estimates of two or more network meta-analyses.

Usage

## S3 method for class 'netbind'
forest(
  x,
  pooled = ifelse(x$x$random, "random", "common"),
  equal.size = gs("equal.size"),
  leftcols = "studlab",
  leftlabs = "Treatment",
  rightcols = c("effect", "ci"),
  rightlabs = NULL,
  subset.treatments,
  digits = gs("digits.forest"),
  digits.prop = max(gs("digits.pval") - 2, 2),
  backtransf = x$backtransf,
  lab.NA = gs("lab.NA"),
  smlab,
  ...
)

## S3 method for class 'netbind'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window.

The arguments leftcols and rightcols can be used to specify columns which are plotted on the left and right side of the forest plot, respectively. If argument rightcols is FALSE, no columns will be plotted on the right side.

For more information see help page of forest.meta function.

Author(s)

Guido Schwarzer [email protected]

See Also

netbind, netcomb, forest.meta

Examples

data(Linde2016)

# Only consider studies including Face-to-face PST (to reduce
# runtime of example)
#
face <- subset(Linde2016, id %in% c(16, 24, 49, 118))

# Standard random effects NMA model (with placebo as reference
# treatment)
#
net1 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = face, reference.group = "placebo",
  sm = "OR", common = FALSE)

# Additive CNMA model with placebo as inactive component and
# reference
#
nc1 <- netcomb(net1, inactive = "placebo")

# Combine results of standard NMA and CNMA
#
nb1 <- netbind(nc1, net1,
  name = c("Additive CNMA", "Standard NMA"),
  col.study = c("red", "black"),
  col.square = c("red", "black"))
forest(nb1,
  col.subgroup = "black", addrow.subgroups = FALSE,
  fontsize = 10, spacing = 0.7, squaresize = 0.9,
  label.left = "Favours Placebo",
  label.right = "Favours other")

Description

Draws a forest plot in the active graphics window (using grid graphics system).

Usage

## S3 method for class 'netcomb'
forest(
  x,
  pooled = ifelse(x$random, "random", "common"),
  reference.group = x$reference.group,
  baseline.reference = x$baseline.reference,
  equal.size = gs("equal.size"),
  leftcols = "studlab",
  leftlabs = "Treatment",
  rightcols = c("effect", "ci"),
  rightlabs = NULL,
  digits = gs("digits.forest"),
  smlab = NULL,
  sortvar = x$seq,
  overall.hetstat = gs("overall.hetstat"),
  backtransf = x$backtransf,
  lab.NA = gs("lab.NA"),
  add.data,
  addrows.below.overall = if (x$overall.hetstat) 2 else gs("addrows.below.overall"),
  drop.reference.group = gs("drop.reference.group"),
  ...
)

## S3 method for class 'netcomb'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window.

Argument sortvar can be either a numeric or character vector with length of number of treatments. If sortvar is numeric the order function is utilised internally to determine the order of values. If sortvar is character it must be a permutation of the treatment names. It is also possible to to sort by treatment comparisons (sortvar = TE, etc.), standard error (sortvar = seTE), and number of studies with direct treatment comparisons (sortvar = k).

Argument add.data can be used to add additional columns to the forest plot. This argument must be a data frame with the same row names as the treatment effects matrices in R object x, i.e., x$TE.common or x$TE.random.

For more information see help page of forest.meta function.

Author(s)

Guido Schwarzer [email protected]

See Also

netcomb, discomb, forest.meta

Examples

data(Linde2016)

# Only consider studies including Face-to-face PST (to reduce
# runtime of example)
#
face <- subset(Linde2016, id %in% c(16, 24, 49, 118))

# Conduct random effects network meta-analysis
#
net1 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = face, ref = "placebo", sm = "OR", common = FALSE)

# Additive model for treatment components (with placebo as inactive
# treatment)
#
nc1 <- netcomb(net1, inactive = "placebo")
#
forest(nc1)

## Not run: 
# Specify, order of treatments
#
trts <- c("TCA", "SSRI", "SNRI", "NRI", "Low-dose SARI", "NaSSa",
  "rMAO-A", "Ind drug", "Hypericum", "Face-to-face CBT",
  "Face-to-face PST", "Face-to-face interpsy", "Face-to-face psychodyn",
  "Other face-to-face", "Remote CBT", "Self-help CBT", "No contact CBT",
  "Face-to-face CBT + SSRI", "Face-to-face interpsy + SSRI",
  "Face-to-face PST + SSRI", "UC", "Placebo")
#
# Note, three treatments are actually combinations of 'SSRI' with
# other components:
# "Face-to-face CBT + SSRI",
# "Face-to-face interpsy + SSRI",
# "Face-to-face PST + SSRI"

# Conduct random effects network meta-analysis
#
net2 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = Linde2016, ref = "placebo",
  seq = trts, sm = "OR", common = FALSE)
#
net2

# Additive model for treatment components (with placebo as inactive
# treatment)
#
nc2 <- netcomb(net2, inactive = "placebo")
#
forest(nc2)

## End(Not run)

Description

Draws a forest plot in the active graphics window (using grid graphics system).

Usage

## S3 method for class 'netcomparison'
forest(
  x,
  pooled = ifelse(x$random, "random", "common"),
  leftcols = c("studlab", "treat1", "treat2"),
  leftlabs = c("Comparison", "Trt 1", "Trt 2"),
  rightcols = c("effect", "ci", "statistic", "pval"),
  rightlabs = c(NA, NA, "z", "p-value"),
  nchar.comps = x$nchar.trts,
  digits = gs("digits.forest"),
  digits.stat = gs("digits.stat"),
  digits.pval = gs("digits.pval"),
  smlab = NULL,
  backtransf = x$backtransf,
  lab.NA = gs("lab.NA"),
  equal.size = gs("equal.size"),
  ...
)

## S3 method for class 'netcomparison'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window. For more information see help page of forest.meta function.

Author(s)

Guido Schwarzer [email protected]

See Also

netcomparison, netcomb, discomb, forest.meta

Examples

data(Linde2016)

# Only consider studies including Face-to-face PST (to reduce
# runtime of example)
#
face <- subset(Linde2016, id %in% c(16, 24, 49, 118))

# Conduct random effects network meta-analysis
#
net1 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = face, ref = "placebo", sm = "OR", common = FALSE)

# Additive model for treatment components (with placebo as inactive
# treatment)
#
nc1 <- netcomb(net1, inactive = "placebo")

# Some comparisons
#
t1 <- c("F + TCA", "F + Plac", "SSRI + Plac + TCA")
t2 <- c("UC", "Plac", "UC")
#
netcomparison(nc1, t1, t2)
#
forest(netcomparison(nc1, t1, t2))
forest(netcomparison(nc1, t1, t2), nchar.comps = 4)
forest(netcomparison(nc1, c("F", "TCA"), "UC"), nchar.comps = 4)

Description

Draws a forest plot in the active graphics window (using grid graphics system).

Usage

## S3 method for class 'netcomplex'
forest(
  x,
  pooled = ifelse(x$random, "random", "common"),
  leftcols = "studlab",
  leftlabs = NULL,
  rightcols = c("effect", "ci", "statistic", "pval"),
  rightlabs = c(NA, NA, "z", "p-value"),
  nchar.comps = x$nchar.trts,
  digits = gs("digits.forest"),
  digits.stat = gs("digits.stat"),
  digits.pval = gs("digits.pval"),
  smlab = NULL,
  backtransf = x$backtransf,
  lab.NA = gs("lab.NA"),
  equal.size = gs("equal.size"),
  ...
)

## S3 method for class 'netcomplex'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window. For more information see help page of forest.meta function.

Author(s)

Guido Schwarzer [email protected]

See Also

netcomplex, netcomb, discomb, forest.meta

Examples

data(Linde2016)

# Only consider studies including Face-to-face PST (to reduce
# runtime of example)
#
face <- subset(Linde2016, id %in% c(16, 24, 49, 118))

# Conduct random effects network meta-analysis
#
net1 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = face, ref = "placebo", sm = "OR", common = FALSE)

# Additive model for treatment components (with placebo as inactive
# treatment)
#
nc1 <- netcomb(net1, inactive = "placebo")

# Some complex interventions
#
ints <- c("F + TCA", "F + Plac", "SSRI + Plac + TCA")
netcomplex(nc1, ints)
#
forest(netcomplex(nc1, ints))
forest(netcomplex(nc1, ints), nchar.comps = 4)

# Component effects
#
forest(netcomplex(nc1, nc1$comps))

Description

Draws a forest plot in the active graphics window (using grid graphics system).

Usage

## S3 method for class 'netmeta'
forest(
  x,
  pooled = ifelse(x$random, "random", "common"),
  reference.group = x$reference.group,
  baseline.reference = x$baseline.reference,
  labels = x$trts,
  equal.size = gs("equal.size"),
  leftcols = "studlab",
  leftlabs,
  rightcols = c("effect", "ci"),
  rightlabs,
  digits = gs("digits.forest"),
  small.values = x$small.values,
  nsim = gs("nsim"),
  digits.prop = 2,
  smlab = NULL,
  sortvar = x$seq,
  overall.hetstat = gs("overall.hetstat"),
  print.tau2 = gs("forest.tau2"),
  print.tau = gs("forest.tau"),
  print.I2 = gs("forest.I2"),
  backtransf = x$backtransf,
  lab.NA = gs("lab.NA"),
  add.data,
  addrows.below.overall = if (x$overall.hetstat) 2 else gs("addrows.below.overall"),
  drop.reference.group = gs("drop.reference.group"),
  col.subgroup = "black",
  print.subgroup.name = FALSE,
  ...
)

## S3 method for class 'netmeta'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window.

Argument sortvar can be either a numeric or character vector with length of number of treatments. If sortvar is numeric the order function is utilised internally to determine the order of values. If sortvar is character it must be a permutation of the treatment names. It is also possible to provide either sortvar = Pscore, sortvar = "Pscore", sortvar = -Pscore, or sortvar = "-Pscore" in order to sort treatments according to the ranking generated by netrank which is called internally. It is also possible to use "SUCRA" instead of "Pscore". Similar expressions are possible to sort by treatment comparisons (sortvar = TE, etc.), standard error (sortvar = seTE), number of studies with direct treatment comparisons (sortvar = k), and direct evidence proportion (sortvar = prop.direct, see also netmeasures).

The arguments leftcols and rightcols can be used to specify columns which are plotted on the left and right side of the forest plot, respectively. The following columns are available:

As a sidenote, the rather odd column name "studlab" to describe the treatment comparisons comes from internally calling forest.meta which uses study labels as the essential information.

Argument add.data can be used to add additional columns to the forest plot. This argument must be a data frame with row names equal to the treatment names in R object x, i.e., x$trts.

See help page of forest.meta for more information on the generation of forest plots and additional arguments.

Author(s)

Guido Schwarzer [email protected]

See Also

forest.meta

Examples

data(smokingcessation)

# Transform data from arm-based format to contrast-based format
#
p1 <- 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(p1, common = FALSE)

forest(net1)

## Not run: 
data(Senn2013)

# Conduct network meta-analysis
#
net2 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013, sm = "MD")

forest(net2, ref = "plac")
forest(net2, xlim = c(-1.5, 1), ref = "plac",
  xlab = "HbA1c difference", rightcols = FALSE)

# Random effects effect model
#
net3 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013, sm = "MD", common = FALSE)

forest(net3, xlim = c(-1.5, 1), ref = "plac",
  xlab = "HbA1c difference")

# Add column with P-Scores on right side of forest plot
#
forest(net3, xlim = c(-1.5, 1), ref = "plac",
  xlab = "HbA1c difference",
  rightcols = c("effect", "ci", "Pscore"),
  just.addcols = "right")

# Add column with P-Scores on left side of forest plot
#
forest(net3, xlim = c(-1.5, 1), ref = "plac",
  xlab = "HbA1c difference",
  leftcols = c("studlab", "Pscore"),
  just.addcols = "right")

# Sort forest plot by descending P-Score
#
forest(net3, xlim = c(-1.5, 1), ref = "plac",
  xlab = "HbA1c difference",
  rightcols = c("effect", "ci", "Pscore"),
  just.addcols = "right",
  sortvar = -Pscore)

# Drop reference group and sort by and print number of studies with
# direct treatment comparisons
#
forest(net3, xlim = c(-1.5, 1), ref = "plac",
  xlab = "HbA1c difference",
  leftcols = c("studlab", "k"),
  leftlabs = c("Contrast\nto Placebo", "Direct\nComparisons"),
  sortvar = -k,
  drop = TRUE,
  smlab = "Random Effects Model")

## End(Not run)

Description

Forest plot to show direct and indirect evidence in network meta-analysis. Furthermore, estimates from network meta-analysis as well as prediction intervals can be printed.

Usage

## S3 method for class 'netsplit'
forest(
  x,
  pooled = ifelse(x$x$random, "random", "common"),
  show = x$show,
  subgroup = "comparison",
  overall = x$overall,
  direct = x$direct,
  indirect = x$indirect,
  prediction = x$prediction,
  only.reference = x$only.reference,
  sortvar = NULL,
  subset = NULL,
  text.overall = "Network estimate",
  text.direct = "Direct estimate",
  text.indirect = "Indirect estimate",
  text.predict = "Prediction interval",
  type.overall,
  type.direct,
  type.indirect,
  col.square = "gray",
  col.square.lines = col.square,
  col.inside = "white",
  col.diamond = "gray",
  col.diamond.lines = "black",
  col.predict = "red",
  col.predict.lines = "black",
  col.subgroup = "black",
  equal.size = TRUE,
  leftcols,
  leftlabs,
  rightcols = c("effect", "ci"),
  rightlabs = NULL,
  digits = gs("digits.forest"),
  digits.prop = max(gs("digits.pval") - 2, 2),
  backtransf = x$backtransf,
  lab.NA = "",
  smlab,
  ...
)

## S3 method for class 'netsplit'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window.

The arguments leftcols and rightcols can be used to specify columns which are plotted on the left and right side of the forest plot, respectively. If argument rightcols is FALSE, no columns will be plotted on the right side.

If direct estimates are included in the forest plot (direct = TRUE, default), the following columns will be printed on the left side of the forest plot: the comparisons (column "studlab" in forest.meta), number of pairwise comparisons ("k"), direct evidence proportion ("k"), and I$^2$ from pairwise comparison ("I2").

If direct estimates are not included in the forest plot (direct = FALSE), only the comparisons ("studlab") are printed on the left side of the forest plot.

For more information see help page of forest.meta function.

Argument show determines which comparisons are printed:

Author(s)

Guido Schwarzer [email protected]

See Also

forest.meta

Examples

data(Senn2013)

# Only consider first five studies (to reduce runtime of example)
#
studies <- unique(Senn2013$studlab)
Senn2013.5 <- subset(Senn2013, studlab %in% studies[1:5])

net1 <- netmeta(TE, seTE, treat1.long, treat2.long,
  studlab, data = Senn2013.5, common = FALSE, reference = "plac")
#
ns1 <- netsplit(net1)

# Forest plot showing comparisons contributing both direct and
# indirect evidence
#
forest(ns1, fontsize = 6, spacing = 0.5, addrow.subgroups = FALSE)

## Not run: 
# Forest plot showing comparisons contributing direct evidence
#
forest(ns1, fontsize = 6, spacing = 0.5, addrow.subgroups = FALSE,
  show = "with.direct")


# Forest plot only showing network estimates compared to reference
# group and prediction intervals
#
forest(ns1, fontsize = 8, spacing = 0.75, show = "all",
  only.reference = TRUE, prediction = TRUE,
  direct = FALSE, indirect = FALSE)

## End(Not run)

Description

Forest plot to show subgroup estimates of network meta-analysis.

Usage

## S3 method for class 'subgroup.netmeta'
forest(
  x,
  pooled = ifelse(x$x$random, "random", "common"),
  equal.size = gs("equal.size"),
  leftcols = c("studlab", "Q", "df.Q", "pval.Q"),
  leftlabs = c("Comparison /\nSubgroup", "Q", "d.f.", "p-value"),
  rightcols = c("effect", "ci", "k", if (pooled == "random") "tau"),
  rightlabs = c(NA, NA, "Number of\nStudies", if (pooled == "random") "Tau"),
  calcwidth.subgroup = gs("calcwidth.subgroup"),
  digits = gs("digits.forest"),
  digits.Q = gs("digits.Q"),
  digits.pval.Q = gs("digits.pval.Q"),
  digits.tau2 = gs("digits.tau2"),
  digits.tau = gs("digits.tau"),
  sep.trts = " vs ",
  backtransf = x$x$backtransf,
  lab.NA = ".",
  smlab,
  col.subgroup = "black",
  ...
)

## S3 method for class 'subgroup.netmeta'
plot(x, ...)

Arguments

Details

A forest plot, also called confidence interval plot, is drawn in the active graphics window.

The arguments leftcols and rightcols can be used to specify columns which are plotted on the left and right side of the forest plot, respectively. If argument rightcols is FALSE, no columns will be plotted on the right side.

For more information see help page of forest.meta function.

Author(s)

Guido Schwarzer [email protected]

See Also

subgroup.netmeta, netmeta, forest.meta

Examples

# Add examples

Description

Network meta-analysis comparing the effects of a number of treatments for Parkinson's disease.

The data are the mean lost work-time reduction in patients given dopamine agonists as adjunct therapy in Parkinson’s disease (Franchini et al. 2012). The data are given as sample size, mean and standard deviation in each trial arm. Treatments are placebo and four active drugs. These data are used as an example in the supplemental material of Dias et al. (2013) where placebo is coded as 1 and the four active drugs as 2 to 5.

Format

A data frame with the following columns:

Source

Dias S, Sutton AJ, Ades AE and Welton NJ (2013): Evidence synthesis for decision making 2: A generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Medical Decision Making, 33, 607–17

Franchini AJ, Dias S, Ades AE, Jansen JP, Welton NJ (2012): Accounting for correlation in network meta-analysis with multi-arm trials. Research Synthesis Methods, 3, 142–60

See Also

pairwise, metacont, netmeta, netgraph.netmeta

Examples

data(Franchini2012)

# Transform data from arm-based format to contrast-based format
#
p1 <- pairwise(list(Treatment1, Treatment2, Treatment3),
  n = list(n1, n2, n3),
  mean = list(y1, y2, y3), sd = list(sd1, sd2, sd3),
  data = Franchini2012, studlab = Study)
p1

# Conduct network meta-analysis
net1 <- netmeta(p1)
net1

# Draw network graphs
netgraph(net1, points = TRUE, cex.points = 3, cex = 1.5,
  thickness = "se.common")
netgraph(net1, points = TRUE, cex.points = 3, cex = 1.5,
  thickness = "se.common",
  iterate = TRUE, plastic = TRUE)
netgraph(net1, points = TRUE, cex.points = 3, cex = 1.5,
  thickness = "se.common",
  iterate = TRUE, plastic = TRUE, start = "eigen")

Description

Draw a ‘comparison-adjusted’ funnel plot to assess funnel plot asymmetry in network meta-analysis.

Usage

## S3 method for class 'netmeta'
funnel(
  x,
  order,
  pooled = ifelse(x$random, "random", "common"),
  xlab = NULL,
  level = x$level,
  pch,
  col = "black",
  legend = TRUE,
  pos.legend = "topright",
  pos.tests = "topleft",
  lump.comparator = FALSE,
  text.comparator = "comparator",
  method.bias,
  text.linreg = "(Egger)",
  text.rank = "(Begg-Mazumdar)",
  text.mm = "(Thompson-Sharp)",
  sep.trts = x$sep.trts,
  nchar.trts = x$nchar.trts,
  backtransf = x$backtransf,
  digits.pval = gs("digits.pval"),
  warn.deprecated = gs("warn.deprecated"),
  linreg = FALSE,
  rank = FALSE,
  mm = FALSE,
  ...
)

Arguments

Details

A ‘comparison-adjusted’ funnel plot (Chaimani & Salanti, 2012) is drawn in the active graphics window.

Argument order is mandatory to determine the order of treatments (Chaimani et al., 2013):

“Before using this plot, investigators should order the treatments in a meaningful way and make assumptions about how small studies differ from large ones. For example, if they anticipate that newer treatments are favored in small trials, then they could name the treatments from oldest to newest so that all comparisons refer to ‘old versus new intervention’. Other possibilities include defining the comparisons so that all refer to an active treatment versus placebo or sponsored versus non-sponsored intervention.”

Alternatively, it is possible to only provide a single or few treatment name(s) in argument order to define the comparator(s). In this case only comparisons with this / these treatment(s) will be considered. If argument lump.comparator is TRUE, all comparators will be lumped into a single group. The text for this group can be specified with argument text.comparator.

In the funnel plot, if yaxis is "se", the standard error of the treatment estimates is plotted on the y-axis which is likely to be the best choice (Sterne & Egger, 2001). Other possible choices for yaxis are "invvar" (inverse of the variance), "invse" (inverse of the standard error), and "size" (study size).

Value

A data frame with the following columns:

Author(s)

Guido Schwarzer [email protected]

References

Chaimani A & Salanti G (2012): Using network meta-analysis to evaluate the existence of small-study effects in a network of interventions. Research Synthesis Methods, 3, 161–76

Chaimani A, Higgins JP, Mavridis D, Spyridonos P, Salanti G (2013): Graphical tools for network meta-analysis in STATA. PLOS ONE, 8, e76654

Sterne JAC & Egger M (2001): Funnel plots for detecting bias in meta-analysis: Guidelines on choice of axis. Journal of Clinical Epidemiology, 54, 1046–55

See Also

netmeta, funnel.meta, metabias

Examples

## Not run: 
data(Senn2013)

net1 <- netmeta(TE, seTE, treat1, treat2, studlab,
  data = Senn2013, sm = "MD")

# 'Comparison-adjusted' funnel plot not created as argument 'order'
# is missing
#
try(funnel(net1))

# Only show comparisons with placebo
#
funnel(net1, order = "pl")

# Add result for Egger test of funnel plot asymmetry
#
funnel(net1, order = "pl", method.bias = "Egger",
  digits.pval = 2)

# (Nonsensical) alphabetic order of treatments with placebo as
# last treatment
#
ord <- c("a", "b", "me", "mi", "pi", "r", "si", "su", "v", "pl")
funnel(net1, order = ord)

# Add results for tests of funnel plot asymmetry and use different
# plotting symbols and colours
#
funnel(net1, order = ord,
  pch = rep(c(15:18, 1), 3), col = 1:3,
  method.bias = c("Egger", "Begg", "Thompson"), digits.pval = 2)

# Same results for tests of funnel plot asymmetry using reversed
# order of treatments
#
funnel(net1, order = rev(ord),
  pch = rep(c(15:18, 1), 3), col = 1:3,
  method.bias = c("Egger", "Begg", "Thompson"), digits.pval = 2)

# Calculate tests for funnel plot asymmetry
#
f1 <- funnel(net1, order = ord)
#
metabias(metagen(TE.adj, seTE, data = f1))
metabias(metagen(TE.adj, seTE, data = f1), method = "Begg")
metabias(metagen(TE.adj, seTE, data = f1), method = "Thompson")

## End(Not run)

Description

Network meta-analysis comparing the effects of a number of interventions for decreasing blood loss and blood transfusion requirements during liver transplantation.

Format

A data frame with the following columns:

Source

Gurusamy KS, Pissanou T, Pikhart H, Vaughan J, Burroughs AK, Davidson BR (2011): Methods to decrease blood loss and transfusion requirements for liver transplantation. Cochrane Database of Systematic Reviews, CD009052

See Also

pairwise, metabin, netmetabin

Examples

data(Gurusamy2011)

# Only consider three studies (to reduce runtime of example)
#
studies <- c("Findlay 2001", "Garcia-Huete 1997", "Dalmau 2000")
three <- subset(Gurusamy2011, study %in% studies)

# Transform data from long arm-based format to contrast-based
# format. Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, death, n, studlab = study,
  data = three, sm = "OR")

# Conduct Mantel-Haenszel network meta-analysis
#
netmetabin(p1, ref = "cont")

## Not run: 
p2 <- pairwise(treatment, death, n, studlab = study,
  data = Gurusamy2011, sm = "OR")

# Conduct Mantel-Haenszel network meta-analysis
netmetabin(p2, ref = "cont")

## End(Not run)

Description

This function generates a Hasse diagram for a partial order of treatment ranks in a network meta-analysis.

Usage

hasse(x, pooled = ifelse(x$random, "random", "common"), newpage = TRUE)

Arguments

Details

Generate a Hasse diagram (Carlsen & Bruggemann, 2014) for a partial order of treatment ranks in a network meta-analysis (Rücker & Schwarzer, 2017).

This R function is a wrapper function for R function hasse in R package hasseDiagram (Krzysztof Ciomek, https://github.com/kciomek/hasseDiagram), i.e., function hasse can only be used if R package hasseDiagram is installed.

Author(s)

Gerta Rücker [email protected], Guido Schwarzer [email protected]

References

Carlsen L, Bruggemann R (2014): Partial order methodology: a valuable tool in chemometrics. Journal of Chemometrics, 28, 226–34

Rücker G, Schwarzer G (2017): Resolve conflicting rankings of outcomes in network meta-analysis: Partial ordering of treatments. Research Synthesis Methods, 8, 526–36

See Also

netmeta, netposet, netrank, plot.netrank

Examples

## Not run: 
# Use depression dataset
#
data(Linde2015)

# Define order of treatments
#
trts <- c("TCA", "SSRI", "SNRI", "NRI",
  "Low-dose SARI", "NaSSa", "rMAO-A", "Hypericum", "Placebo")

# Outcome labels
#
outcomes <- c("Early response", "Early remission")

# (1) Early response
#
p1 <- pairwise(treat = list(treatment1, treatment2, treatment3),
  event = list(resp1, resp2, resp3),
  n = list(n1, n2, n3),
  studlab = id, data = Linde2015, sm = "OR")
#
net1 <- netmeta(p1, common = FALSE,
  seq = trts, ref = "Placebo", small.values = "undesirable")

# (2) Early remission
#
p2 <- pairwise(treat = list(treatment1, treatment2, treatment3),
  event = list(remi1, remi2, remi3),
  n = list(n1, n2, n3),
  studlab = id, data = Linde2015, sm = "OR")
#
net2 <- netmeta(p2, common = FALSE,
  seq = trts, ref = "Placebo", small.values = "undesirable")

# Partial order of treatment rankings
#
po <- netposet(netrank(net1), netrank(net2), outcomes = outcomes)

# Hasse diagram
#
hasse(po)

## End(Not run)

Description

Auxiliary function to derive hat matrix from network meta-analysis

Usage

hatmatrix(
  x,
  method = "Ruecker",
  type,
  common = x$common,
  random = x$random,
  nchar.trts = x$nchar.trts,
  nchar.studlab = x$nchar.studlab
)

## S3 method for class 'hatmatrix'
print(
  x,
  common = x$x$common,
  random = x$x$random,
  nchar.trts = x$x$nchar.trts,
  nchar.studlab = x$x$nchar.studlab,
  digits = gs("digits"),
  legend = gs("legend"),
  legend.studlab = TRUE,
  ...
)

Arguments

Details

This auxiliary function can be used to derive various hat matrices from a network meta-analysis object.

Hat matrix by Rücker (2012)

This hat matrix is estimated if method = "Ruecker".

Let n be the number of different treatments (nodes, vertices) in a network and let m be the number of existing comparisons (edges) between the treatments. If there are only two-arm studies, m is equal to the number of studies, k. Let seTE.adj.common and seTE.adj.random be the vectors of adjusted standard errors under the common and random effects model (see netmeta). Let W be the m x m diagonal matrix that contains the inverse variance 1 / seTE.adj.common$^2$ or 1 / seTE.adj.random$^2$.

The given comparisons define the network structure. Therefrom an m x n design matrix X (edge-vertex incidence matrix) is formed; for more precise information, see Rücker (2012). Moreover, the n x n Laplacian matrix L and its Moore-Penrose pseudoinverse L$^+$ are calculated (both matrices play an important role in graph theory and electrical network theory). Using these matrices, the variances based on both direct and indirect comparisons can be estimated. The hat matrix H is estimated by H = XL$^+$X$^T$W = X(X$^T$W X)$^+$X$^T$W.

Hat matrices by Krahn et al. (2013)

One of the following hat matrices is estimated if method = "Krahn".

Use of type = "design" (default) results in a hat matrix of dimension n(n-1)/2 x s, where s is the sum of the number of independent comparisons from each design.

Use of type = "studies" results in a hat matrix of dimension n(n-1)/2 x l, where l is the number of independent pairwise comparisons, i.e., a three-arm study contributes two pairwise comparisons.

Hat matrices by Davies et al. (2022)

One of three hat matrices is estimated if method = "Davies".

Here, we focus on the hat matrix of the aggregate (two-step) version of the graph theoretical NMA model. In the first step, a pairwise meta-analysis is performed across each edge using the adjusted weights (these account for correlations due to multi-arm trials). From this we obtain direct treatment effect estimates (and corresponding aggregate weights) associated with each edge. In step two, we combine these direct estimates in a network meta analysis to obtain the network estimates. This is done using weighted least squares regression. The hat matrix associated with this second step is called the aggregate hat matrix.

All three versions of the aggregate hat matrix contain the same information: the second two can be derived directly from the first. They differ in their dimensionality.

Each row of the hat matrix that represents a treatment comparison (ij) describes the flow of evidence through each edge for that comparison. This defines a directed acyclic 'flow graph' from node i to node j.

(1) Use of type = "short" (default) results in a hat matrix of dimension e x e, where e is the number of (unique) edges (direct comparisons) in the network. This is the aggregate hat matrix described in Davies et al. (2022). Each row and column represents a pair of treatments for which there is at least one direct comparison.

(2) Use of type = "long" results in a hat matrix of dimension n(n-1)/2 x e. There is a row for every possible pair of treatments in the network - regardless of whether there is direct evidence for this comparison. Each column represents a pair of treatments for which there is at least one direct comparison. The extra rows can be calculated from the short hat matrix using consistency equations.

(3) Use of type = "full" results in a hat matrix of dimension n(n-1)/2 x n(n-1)/2. In comparison to the long hat matrix, columns of zeroes are added for comparisons that do not have any direct evidence. Therefore, there is a row and column for every pair of treatments in the network. This hat matrix is used to calculate the transition matrices for the random walk in netcontrib.

Value

A list with two hat matrices: common (common effects model) and random (random effects model).

Author(s)

Guido Schwarzer [email protected]

References

Davies AL, Papakonstantinou T, Nikolakopoulou A, Rücker G, Galla T (2022): Network meta-analysis and random walks. Statistics in Medicine, 41, 2091–2114

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

Rücker G (2012): Network meta-analysis, electrical networks and graph theory. Research Synthesis Methods, 3, 312–24

See Also

netmeta, netcontrib, netheat

Examples

data(Dong2013)
# Only consider first ten studies for concise output
first10 <- subset(Dong2013, id <= 10)
p1 <- pairwise(treatment, death, randomized, studlab = id,
  data = first10, sm = "OR")
net1 <- netmeta(p1, common = FALSE)

hatmatrix(net1)
hatmatrix(net1, method = "k")
hatmatrix(net1, method = "k", type = "studies")
hatmatrix(net1, method = "d")
hatmatrix(net1, method = "d", type = "long")
hatmatrix(net1, method = "d", type = "full")

Description

Generic function for heat plots

Usage

heatplot(x, ...)

Arguments

Details

For more details, look at the following function to generate heat plots:

• heatplot.netmeta

• heatplot.crossnma (if installed)

Author(s)

Guido Schwarzer [email protected]

Examples

data(Senn2013)

# Only consider first five studies (to reduce runtime of example)
#
studies <- unique(Senn2013$studlab)
Senn2013.5 <- subset(Senn2013, studlab %in% studies[1:5])

# Conduct random effects network meta-analysis with
# placebo as reference treatment
#
net1 <- netmeta(TE, seTE, treat1.long, treat2.long, studlab,
  data = Senn2013.5, sm = "MD", common = FALSE, reference = "plac")
      
# Generate a heat plot (with abbreviated treatment labels)
#
heatplot(net1, nchar.trts = 4)

Description

Produces a heat plot containing treatment estimates with confidence intervals for all possible pairwise comparisons.

Usage

## S3 method for class 'netmeta'
heatplot(
  x,
  pooled = ifelse(x$random, "random", "common"),
  seq = x$seq,
  nchar.trts = x$nchar.trts,
  low.colour = "red",
  mid.colour = "white",
  high.colour = "springgreen4",
  size = 6,
  size.trt = 16,
  size.axis = 12,
  digits = gs("digits.forest"),
  backtransf = x$backtransf,
  ...
)

Arguments

Value

League heat plot, where a color scale is used to represent the values of relative treatment effects.

Examples

data(Senn2013)

# Only consider first five studies (to reduce runtime of example)
#
studies <- unique(Senn2013$studlab)
Senn2013.5 <- subset(Senn2013, studlab %in% studies[1:5])

# Conduct random effects network meta-analysis with
# placebo as reference treatment
#
net1 <- netmeta(TE, seTE, treat1.long, treat2.long, studlab,
  data = Senn2013.5, sm = "MD", common = FALSE, reference = "plac")
      
# Generate a heat plot (with abbreviated treatment labels)
#
heatplot(net1, nchar.trts = 4)

Description

Calculates the Moore-Penrose pseudoinverse of a square matrix X.

Usage

invmat(X)

Arguments

Details

This function is used by default in R package netmeta to calculate the Moore-Penrose pseudoinverse L$^+$ of the Laplacian matrix L (Rücker, 2012):

L$^+$ = (X - J / n)$^{-1}$ + J / n with identity matrix J of dimension nxn.

Value

The Moore-Penrose pseudoinverse for matrix X.

Author(s)

Gerta Rücker [email protected], Guido Schwarzer [email protected]

References

Rücker G (2012): Network meta-analysis, electrical networks and graph theory. Research Synthesis Methods, 3, 312–24

See Also

netmeta, solve

Examples

data(smokingcessation)

p1 <- pairwise(list(treat1, treat2, treat3),
  event = list(event1, event2, event3), n = list(n1, n2, n3),
  data = smokingcessation, sm = "OR")
net1 <- netmeta(p1)

invmat(net1$L.matrix.common)

## Not run: 
data(Senn2013)

net2 <- netmeta(TE, seTE, treat1.long, treat2.long, studlab,
  data = Senn2013)
L1 <- net2$L.matrix.common
L2 <- invmat(net2$Lplus.matrix.common)
all.equal(round(L1, 10), round(L2, 10))

## End(Not run)

Description

Network meta-analysis of nine classes of antidepressants including placebo for the primary care setting; partly shown in Linde et al. (2015), supplementary Table 2.

Format

A data frame with the following columns:

Source

Linde K, Kriston L, Rücker G, et al. (2015): Efficacy and acceptability of pharmacological treatments for depressive disorders in primary care: Systematic review and network meta-analysis. Annals of Family Medicine, 13, 69–79

See Also

pairwise, metabin, netmeta, netposet

Examples

data(Linde2015)

# Transform data from arm-based format to contrast-based format
# Outcome: early response
p1 <- pairwise(list(treatment1, treatment2, treatment3),
  event = list(resp1, resp2, resp3),
  n = list(n1, n2, n3),
  studlab = id, data = Linde2015, sm = "OR")
p1

## Not run: 
# Define order of treatments
trts <- c("TCA", "SSRI", "SNRI", "NRI", "Low-dose SARI",
  "NaSSa", "rMAO-A", "Hypericum", "Placebo")

# Conduct random effects network meta-analysis
net1 <- netmeta(p1, common = FALSE, reference = "Placebo", seq = trts)
print(net1, digits = 2)

## End(Not run)

Description

Network meta-analysis of 22 treatments (including placebo and usual care) for the primary care of depression.

Format

A data frame with the following columns:

Source

Linde K, Rücker G, Schneider A et al. (2016): Questionable assumptions hampered interpretation of a network meta-analysis of primary care depression treatments. Journal of Clinical Epidemiology, 71, 86–96

See Also

netmeta, netcomb

Examples

data(Linde2016)

# Only consider studies including Face-to-face PST (to reduce
# runtime of example)
#
face <- subset(Linde2016, id %in% c(16, 24, 49, 118))

# Conduct random effects network meta-analysis
#
net1 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = face, reference.group = "placebo",
  sm = "OR", common = FALSE, nchar.trts = 6)
#
net1

## Not run: 
# Conduct random effects network meta-analysis
#
net2 <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = Linde2016, reference.group = "placebo",
  sm = "OR", common = FALSE, nchar.trts = 6)
#
net2

## End(Not run)

Description

Merge pairwise object with additional data, e.g., information on network connectivity.

Usage

## S3 method for class 'pairwise'
merge(x, y, all.x = TRUE, ...)

Arguments

Value

An object of class pairwise.

Author(s)

Guido Schwarzer [email protected]

See Also

pairwise, netconnection

Examples

data(Woods2010)

# Transform data from long arm-based format to contrast-based
# format Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, event = r, n = N,
  studlab = author, data = Woods2010, sm = "OR")
head(p1)

# Add information on network connectivity
nc1 <- netconnection(p1)
p1nc1 <- merge(p1, nc1)
head(p1nc1)

Description

Test of funnel plot asymmetry in network meta-analysis

Usage

## S3 method for class 'netmeta'
metabias(
  x,
  order,
  pooled = ifelse(x$random, "random", "common"),
  method.bias = "Egger",
  lump.comparator = gs("lump.comparator"),
  ...
)

Arguments

Details

Test of funnel plot asymmetry in network meta-analysis

Argument order is mandatory to determine the order of treatments (Chaimani et al., 2013):

“[...] investigators should order the treatments in a meaningful way and make assumptions about how small studies differ from large ones. For example, if they anticipate that newer treatments are favored in small trials, then they could name the treatments from oldest to newest so that all comparisons refer to ‘old versus new intervention’. Other possibilities include defining the comparisons so that all refer to an active treatment versus placebo or sponsored versus non-sponsored intervention.”

Alternatively, it is possible to only provide a single or few treatment name(s) in argument order to define the comparator(s). In this case only comparisons with this / these treatment(s) will be considered. If argument lump.comparator is TRUE, all comparators will be lumped into a single group.

Value

A list with class metabias containing the following components if a test for funnel plot asymmetry is conducted: