netcomb: Additive network meta-analysis for combinations of treatments

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.

Usage

netcomb(
  x,
  inactive = NULL,
  sep.comps = gs("sep.comps"),
  C.matrix,
  common = x$common,
  random = x$random | !is.null(tau.preset),
  tau.preset = NULL,
  details.chkident = FALSE,
  nchar.comps = x$nchar.trts,
  sep.ia = gs("sep.ia"),
  func.inverse = invmat,
  overall.hetstat = x$overall.hetstat,
  backtransf = x$backtransf,
  na.unident = gs("na.unident"),
  warn.deprecated = gs("warn.deprecated"),
  ...
)

Value

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

studlab: Study labels.
treat1: Label/Number for first treatment.
treat2: Label/Number for second treatment.
TE: Estimate of treatment effect, i.e. difference between first and second treatment.
seTE: Standard error of treatment estimate.
seTE.adj.common, seTE.adj.random: Standard error of treatment estimate, adjusted for multi-arm studies.
design: Design of study providing pairwise comparison.
event1: Number of events in first treatment group.
event2: Number of events in second treatment group.
n1: Number of observations in first treatment group.
n2: Number of observations in second treatment group.
k: Total number of studies.
m: Total number of pairwise comparisons.
n: Total number of treatments.
d: Total number of designs (corresponding to the unique set of treatments compared within studies).
c: Total number of components.
trts: Treatments included in network meta-analysis.
k.trts: Number of studies evaluating a treatment.
n.trts: Number of observations receiving a treatment (if arguments n1 and n2 are provided).
events.trts: Number of events observed for a treatment (if arguments event1 and event2 are provided).
studies: Study labels coerced into a factor with its levels sorted alphabetically.
narms: Number of arms for each study.
designs: Unique list of designs present in the network. A design corresponds to the set of treatments compared within a study.
comps: Unique list of components present in the network.
TE.nma.common, TE.nma.random: A vector of length m of consistent treatment effects estimated by network meta-analysis (nma) (common and random effects model).
seTE.nma.common, seTE.nma.random: A vector of length m of effective standard errors estimated by network meta-analysis (common and random effects model).
lower.nma.common, lower.nma.random: A vector of length m of lower confidence interval limits for consistent treatment effects estimated by network meta-analysis (common and random effects model).
upper.nma.common, upper.nma.random: A vector of length m of upper confidence interval limits for the consistent treatment effects estimated by network meta-analysis (common and random effects model).
statistic.nma.common, statistic.nma.random: A vector of length m of z-values for test of treatment effect for individual comparisons (common and random effects model).
pval.nma.common, pval.nma.random: A vector of length m of p-values for test of treatment effect for individual comparisons (common and random effects model).
TE.cnma.common, TE.cnma.random: A vector of length m of consistent treatment effects estimated by the additive (common and random effects) model.
seTE.cnma.common, seTE.cnma.random: A vector of length m with standard errors estimated by the additive (common and random effects) model.
lower.cnma.common, lower.cnma.random: A vector of length m of lower confidence interval limits for consistent treatment effects estimated by the additive (common and random effects) model.
upper.cnma.common, upper.cnma.random: A vector of length m of upper confidence interval limits for consistent treatment effects estimated by the additive (common and random effects) model.
statistic.cnma.common, statistic.cnma.random: A vector of length m of z-values for the test of an overall effect estimated by the additive (common and random effects) model.
pval.cnma.common, pval.cnma.random: A vector of length m of p-values for the test of an overall effect estimated by the additive (common and random effects) model.
TE.common, TE.random: nxn matrix with overall treatment effects estimated by the additive (common and random effects) model.
seTE.common, seTE.random: nxn matrix with standard errors estimated by the additive (common and random effects) model.
lower.common, upper.common, lower.random, upper.random: nxn matrices with lower and upper confidence interval limits estimated by the additive (common and random effects) model.
statistic.common, pval.common, statistic.random, pval.random: nxn matrices with z-values and p-values for test of overall effect estimated by the additive (common and random effects) model.
Comp.common, Comp.random: A vector of component effects (common and random effects model).
seComp.common, seComp.random: A vector with corresponding standard errors (common and random effects model).
lower.Comp.common, lower.Comp.random: A vector with lower confidence limits for components (common and random effects model).
upper.Comp.common, upper.Comp.random: A vector with upper confidence limits for components (common and random effects model).
statistic.Comp.common, statistic.Comp.random: A vector with z-values for the overall effect of components (common and random effects model).
pval.Comp.common, pval.Comp.random: A vector with p-values for the overall effect of components (common and random effects model).
Comb.common, Comb.random: A vector of combination effects (common and random effects model).
seComb.common, seComb.random: A vector with corresponding standard errors (common and random effects model).
lower.Comb.common, lower.Comb.random: A vector with lower confidence limits for combinations (common and random effects model).
upper.Comb.common, upper.Comb.random: A vector with upper confidence limits for combinations (common and random effects model).
statistic.Comb.common, statistic.Comb.random: A vector with z-values for the overall effect of combinations (common and random effects model).
pval.Comb.common, pval.Comb.random: A vector with p-values for the overall effect of combinations (common and random effects model).
Q.additive: Overall heterogeneity / inconsistency statistic (additive model).
df.Q.additive: Degrees of freedom for test of heterogeneity / inconsistency (additive model).
pval.Q.additive: P-value for test of heterogeneity / inconsistency (additive model).
tau: Square-root of between-study variance (additive model).
I2, lower.I2, upper.I2: I-squared, lower and upper confidence limits.
Q.standard: Overall heterogeneity / inconsistency statistic (standard model).
df.Q.standard: Degrees of freedom for test of heterogeneity / inconsistency (standard model).
pval.Q.standard: P-value for test of heterogeneity / inconsistency (standard model).
Q.diff: Test statistic for difference in goodness of fit between standard and additive model.
df.Q.diff: Degrees of freedom for difference in goodness of fit between standard and additive model.
pval.Q.diff: P-value for difference in goodness of fit between standard and additive model.
A.matrix: Adjacency matrix (nxn).
B.matrix: Edge-vertex incidence matrix (mxn).
C.matrix: As defined above.
sm: Summary measure.
level.ma: Level for confidence intervals.
common, random, tau.preset: As defined above.
sep.trts: A character used in comparison names as separator between treatment labels.
nchar.comps: A numeric defining the minimum number of characters used to create unique component names.
inactive, sep.comps, sep.ia: As defined above.
backtransf: A logical indicating whether results should be back transformed in printouts and forest plots.
title: Title of meta-analysis / systematic review.
x: As defined above.
call: Function call.
version: Version of R package netmeta used to create object.

Arguments

x: An object of class netmeta.
inactive: A character string defining the inactive treatment component (see Details).
sep.comps: A single character to define separator between treatment components.
C.matrix: C matrix (see Details).
common: A logical indicating whether a common effects network meta-analysis should be conducted.
random: A logical indicating whether a random effects network meta-analysis should be conducted.
tau.preset: An optional value for the square-root of the between-study variance $\tau^2$.
details.chkident: A logical indicating whether details on unidentifiable components should be printed.
nchar.comps: A numeric defining the minimum number of characters used to create unique names for components (see Details).
sep.ia: A single character to define separator for interactions.
func.inverse: R function used to calculate the pseudoinverse of the Laplacian matrix L (see netmeta).
overall.hetstat: A logical indicating whether to print heterogeneity measures.
backtransf: A logical indicating whether results should be back transformed in printouts and forest plots.
na.unident: A logical indicating whether unidentifiable components and combinations should be set to missing values.
warn.deprecated: A logical indicating whether warnings should be printed if deprecated arguments are used.
...: Additional arguments (to catch deprecated arguments).

Author

Gerta Rücker gerta.ruecker@uniklinik-freiburg.de, Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de

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.

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.

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

Examples

Run this code

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)
net1

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

# Print results with two digits and test statistics with three digits
print(nc1, digits = 2, digits.stat = 3)

# Print detailed results
print(summary(nc1), digits = 2, digits.stat = 3)

# All available combinations in CNMA
combinations(nc1) # only "Face-to-face PST + SSRI"

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

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

# \donttest{
forest(net1, xlim = c(0.2, 50))
forest(nc1, xlim = c(0.2, 50))

# 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
forest(net2, xlim = c(0.2, 50))

# Additive model for treatment components (with placebo as inactive
# treatment)
#
nc2 <- netcomb(net2, inactive = "placebo")
nc2
forest(nc2, xlim = c(0.2, 50))
# }

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