Title:	Ranking using Probabilistic Models and Treatment Choice Criteria
Version:	0.2-0
Date:	2025-06-03
Depends:	R (≥ 4.0.0), meta (≥ 8.1-0), netmeta (≥ 3.2-0)
Imports:	PlackettLuce, dplyr, magrittr, ggplot2
Suggests:	rmarkdown, knitr
Maintainer:	Theodoros Evrenoglou <theodoros.evrenoglou@uniklinik-freiburg.de>
URL:	https://github.com/TEvrenoglou/mtrank
Description:	Estimation of treatment hierarchies in network meta-analysis using a novel frequentist approach based on treatment choice criteria (TCC) and probabilistic ranking models, as described by Evrenoglou et al. (2024) <doi:10.48550/arXiv.2406.10612>. The TCC are defined using a rule based on the smallest worthwhile difference (SWD). Using the defined TCC, the NMA estimates (i.e., treatment effects and standard errors) are first transformed into treatment preferences, indicating either a treatment preference (e.g., treatment A > treatment B) or a tie (treatment A = treatment B). These treatment preferences are then synthesized using a probabilistic ranking model, which estimates the latent ability parameter of each treatment and produces the final treatment hierarchy. This parameter represents each treatments ability to outperform all the other competing treatments in the network. Here the terms ability to outperform indicates the propensity of each treatment to yield clinically important and beneficial effects when compared to all the other treatments in the network. Consequently, larger ability estimates indicate higher positions in the ranking list.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
RoxygenNote:	7.3.2
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2025-06-03 10:38:03 UTC; sc
Author:	Theodoros Evrenoglou [aut, cre], Guido Schwarzer [aut]
Repository:	CRAN
Date/Publication:	2025-06-04 08:00:09 UTC

mtrank: Brief overview

Description

R package mtrank enables the estimation of treatment hierarchies in network meta-analysis using a novel frequentist approach based on treatment choice criteria (TCC) and probabilistic ranking models, as described by Evrenoglou et al. (2024). The TCC are defined using a rule based on the smallest worthwhile difference (SWD). Using the defined TCC, the NMA estimates (i.e., treatment effects and standard errors) are first transformed into treatment preferences, indicating either a treatment preference (e.g., treatment A > treatment B) or a tie (treatment A = treatment B). These treatment preferences are then synthesized using a probabilistic ranking model, which estimates the latent ability parameter of each treatment and produces the final treatment hierarchy. This parameter represents each treatments ability to outperform all the other competing treatments in the network. Here the terms "ability to outperform" indicates the propensity of each treatment to yield clinically important and beneficial effects when compared to all the other treatments in the network. Consequently, larger ability estimates indicate higher positions in the ranking list.

Details

The R package mtrank provides the following functions:

• Function tcc defines the TCC and produces a treatment preference format based on network meta-analysis estimates.

• Function mtrank synthesizes the output of the tcc function and estimates the final treatment ability.

• Forest plots are created either for the results of the TCC (forest.tcc) or the final ability estimates (forest.mtrank).

• Function fitted.mtrank uses the ability estimates obtained from mtrank to calculate pairwise probabilities that any treatment 'A' can be better, equal, or worse than any other treatment 'B' in the network.

• The function linegraph visualizes the output of mtrank across different SWD values. It serves as a sensitivity analysis to the initial choice of SWD.

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

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

To report problems and bugs, please send an email to Theodoros Evrenoglou <theodoros.evrenoglou@uniklinik-freiburg.de>.

The development version of mtrank is available on GitHub https://github.com/TEvrenoglou/mtrank.

Author(s)

Theodoros Evrenoglou <theodoros.evrenoglou@uniklinik-freiburg.de>, Guido Schwarzer <guido.schwarzer@uniklinik-freiburg.de>

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Rücker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

See Also

Useful links:

• https://github.com/TEvrenoglou/mtrank

Network meta-analysis for major depressive disorder

Description

Network meta-analysis comparing antidepressants in patients with major depressive disorder.

Format

A data frame with the following columns:

Source

Cipriani A, Furukawa T, Salanti G, Chaimani A, et al. (2018): Comparative efficacy and acceptability of 21 antidepressant drugs for the acute treatment of adults with major depressive disorder: a systematic review and network meta-analysis Lancet, 391, 1357–66

See Also

mtrank, tcc

Examples

data(antidepressants)
head(antidepressants)
#
# Examples:
# example(tcc)
# example(mtrank)
# example(fitted.mtrank)

Network meta-analysis studying the incidence of diabetes

Description

Network meta-analysis comparing six antihypertensive drugs against the incidence of diabetes.

Format

A data frame with the following columns:

Source

Elliott WJ, Meyer PM (2007): Incident diabetes in clinical trials of antihypertensive drugs: A network meta-analysis Lancet, 369, 201–7, doi:10.1016/S0140-6736(07)60108-1

See Also

mtrank, tcc

Examples

data(diabetes)
head(diabetes)
#

pw <- pairwise(studlab = study, treat = t,
  n = n, event = r, data = diabetes, sm = "OR")
#
net <- netmeta(pw, reference.group = "PLA")
#
ranks <- tcc(net, swd = 1.20, small.values = "desirable")
#
forest(ranks)
forest(ranks, reference.group = "ARB", baseline.reference = FALSE)

Calculate pairwise fitted probabilities for mtrank object.

Description

This function uses the estimates of ability and tie prevalence parameters from a mtrank object and calculates fitted pairwise probabilities about the preference or the tie between two treatments based on equations (7) and (8) in Evrenoglou et al. (2024).

Usage

## S3 method for class 'mtrank'
fitted(object, treat1, treat2, type, ...)

## S3 method for class 'fitted.mtrank'
print(x, type = attr(x, "type"), digits = 4, ...)

Arguments

Details

Pairwise fitted probabilities between any two treatments in the network can be calculated using the ability estimates obtained from mtrank and equations (7) and (8) in Evrenoglou et al. (2024). The fitted probabilities are calculated in the direction treat1 vs treat2. The available probability types are

• "better": probability that treat1 is better than treat2,

• "tie": probability that treat1 is equal to treat2,

• "worse": probability that treat1 is worse than treat2,

• "all": all three probabilities.

Please note that all the arguments of this function are mandatory.

Value

The probability (or probabilities) of interest for the comparison treat1 vs treat2 based on the argument type.

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Rücker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

Examples

data(antidepressants)
#
pw1 <- pairwise(studlab = studyid, treat = drug_name,
  n = ntotal, event = responders,
  data = antidepressants, sm = "OR")
# Use subset to reduce runtime
pw0 <- subset(pw1, studyid < 60)
#
net0 <- netmeta(pw0, reference.group = "tra")
#
ranks0 <- tcc(net0, swd = 1.20, small.values = "undesirable")
#
fit0 <- mtrank(ranks0)
#
fitted(fit0, type = c("better", "worse"),
  treat1 = "bupropion", treat2 = "escitalopram")
#
fitted(fit0, type = c("better", "worse"),
  treat1 = "escitalopram", treat2 = "bupropion")
#
fitted(fit0, type = "all",
  treat1 = c("bupropion", "escitalopram"),
  treat2 = c("escitalopram", "bupropion"))

## Not run: 
# Run analysis with full data set
net1 <- netmeta(pw1, reference.group = "tra")
#
ranks1 <- tcc(net1, swd = 1.20, small.values = "undesirable")
#
fit1 <- mtrank(ranks1)
#
fitted(fit1, type = c("better", "worse"),
  treat1 = "bupropion", treat2 = "escitalopram")
#
fitted(fit1, type = c("better", "worse"),
  treat1 = "escitalopram", treat2 = "bupropion")
#
fitted(fit1, type = "all",
  treat1 = c("bupropion", "escitalopram"),
  treat2 = c("escitalopram", "bupropion"))

## End(Not run)

Forest plot of ability estimates produced with mtrank

Description

This function produces a forest plot that visualizes the ability estimates calculated with mtrank.

Usage

## S3 method for class 'mtrank'
forest(
  x,
  sorting = "ability",
  backtransf = FALSE,
  xlab = "",
  leftcols = "studlab",
  leftlabs = "Treatment",
  rightcols = c("effect", "ci"),
  rightlabs = c(paste0(if (!backtransf) "log-", "Abilities"), NA),
  label.left = "Favors average treatment",
  label.right = "Favors treatment",
  header.line = TRUE,
  ...
)

Arguments

Details

The function produces a forest plot and visualizes the ability estimates obtained from mtrank. The order of the estimates in the forest plot (argument sorting) can be one of the following:

• "ability": sort by descending ability estimates (default),

• "se": sort by descending precision, i.e., increasing standard errors,

• "none": use order from data set.

Value

A forest plot is plotted in the active graphics device.

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Rücker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

Examples

# Examples: example(mtrank)

Forest plot showing the treatment preference format of the NMA estimates according to treatment choice criterion.

Description

This function produces a forest plot and visualizes the treatment preference format of the NMA estimates as defined from the treatment choice criterion in tcc.

Usage

## S3 method for class 'tcc'
forest(
  x,
  reference.group = x$reference.group,
  baseline.reference = x$baseline.reference,
  backtransf = FALSE,
  leftcols = "studlab",
  leftlabs,
  rightcols = c("effect", "ci"),
  col.winner = "red",
  col.tie = "black",
  lty.equi = gs("lty.cid"),
  col.equi = gs("col.cid"),
  fill.equi = "lightblue",
  fill.swd.below.null = "transparent",
  fill.swd.above.null = "transparent",
  smlab,
  header.line = TRUE,
  ...
)

Arguments

Details

This function produces forest plots for the NMA treatment effect estimates. The color indicates whether treatment effects show a preference (red color) or tie (black color). Additionally, the respective range of equivalence defined at the function tcc is visualized for the forest plot.

The argument reference.group is optional. By default, the graph plots the NMA estimates of all treatments versus the common reference treatment used in the netmeta object.

Value

A forest plot is plotted in the active graphics device.

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Rücker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

Examples

data("antidepressants")
#
pw1 <- pairwise(studlab = studyid, treat = drug_name,
  n = ntotal, event = responders,
  data = antidepressants, sm = "OR")
# Use subset to reduce runtime
pw0 <- subset(pw1, studyid < 60)
#
net0 <- netmeta(pw0, reference.group = "tra")

ranks0 <- tcc(net0, swd = 1.20, small.values = "undesirable")

# Comparison other drugs vs trazodone
forest(ranks0,
  label.left = "Favours trazodone",
  label.right = "Favours other drug")

# Comparison escitalopram vs other drugs
forest(ranks0, reference.group = "esc", baseline = FALSE,
  label.left = "Favours other drug",
  label.right = "Favours escitalopram")

## Not run: 
# Store a PDF file in the current working directory showing all results
# (this is the default, i.e., if argument 'reference.group' is missing)
forest(ranks0, baseline = FALSE, reference.group = trts,
  file = "forest_tcc_antidepressants.pdf")

# Run analysis with full data set
net1 <- netmeta(pw1, reference.group = "tra")

ranks1 <- tcc(net1, swd = 1.20, small.values = "undesirable")

# Comparison other drugs vs trazodone
forest(ranks1,
  label.left = "Favours trazodone",
  label.right = "Favours other drug")

# Comparison escitalopram vs other drugs
forest(ranks1, reference.group = "esc", baseline = FALSE,
  label.left = "Favours other drug",
  label.right = "Favours escitalopram")

## End(Not run)

Line graph showing the results of mtrank across different smallest worthwhile difference (SWD) values

Description

This function produces a line graph that visualizes the results of mtrank in terms of either abilities or probabilities across different smallest worthwhile difference (SWD) values.

Usage

linegraph(
  x,
  swd,
  swd.ref,
  small.values = x$small.values,
  type = "probability",
  k = length(x$trts),
  backtransf = FALSE,
  linewidth = 1.1,
  point.size = 2,
  ...
)

Arguments

Details

This function creates a line graph to visualize probability or ability estimates obtained from mtrank across different SWD values. The order of treatments in the graph is based on their hierarchy at the reference SWD value (swd.ref).

Value

A ggplot object.

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Ruecker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

Examples

data("antidepressants")
#
pw <- pairwise(studlab = studyid, treat = drug_name,
  n = ntotal, event = responders,
  data = antidepressants, sm = "OR")
# Use subset to reduce runtime
pw <- subset(pw, studyid < 60)
#
net <- netmeta(pw, reference.group = "tra")
#
ranks <- tcc(net, swd = 1.20, small.values = "undesirable")
#
fit <- mtrank(ranks)
#
# Perform a sensitivity analysis across different SWD values assuming that
# 1.20 is the reference value
swd.vec <- seq(1.10, 1.50, by = 0.10)
swd.ref <- 1.20
# plot all the treatments in the network
linegraph(fit, swd = swd.vec, swd.ref = swd.ref)

# plot only the first three treatments in the order appearing at the
# 'swd.ref' value
linegraph(fit, swd = swd.vec, swd.ref = swd.ref, k = 3)
# plot in terms of ability estimates 
linegraph(fit, swd = swd.vec, swd.ref = swd.ref, type = "ability")

  

Estimate the treatment hierarchy in network meta-analysis using a probabilistic ranking model

Description

This function fits the Davidson-Bradley-Terry ranking model and produces a treatment hierarchy based on the method described by Evrenoglou et al. (2024) for network meta-analysis.

Usage

mtrank(x, level = x$level, ...)

## S3 method for class 'mtrank'
print(
  x,
  sorting = "ability",
  backtransf = FALSE,
  digits = gs("digits"),
  digits.prop = gs("digits.prop"),
  ...
)

Arguments

Details

This function fits a Davidson-Bradley-Terry model to the treatment preferences tcc function. It estimates the ability of each treatment to outperform the other treatments in the network, along with the respective standard errors, using a maximum likelihood approach. The term 'ability to outperform' refers to a latent characteristic that indicates the propensity of each treatment in the network to yield clinically relevant and beneficial treatment effects, in the context of the defined treatment choice criterion, when compared to the rest of the treatments. Consequently, treatments with larger ability estimates are ranked more prominently in the treatment hierarchy.

To retain identifiability, the maximization of the log-likelihood takes place subject to the constrain that the ability estimates sum to 1. Then, the maximum likelihood estimates (MLEs) are calculated iteratively. Note that the final estimates of the ability parameters are not necessarily needed to sum to 1 as after the first iteration of the algorithm the ability estimates are not normalized. However, by normalizing the final ability estimates to sum up to 1 these can be interpreted as "the probability that each treatment is having the highest ability".

Finally, a parameter "v" controlling the prevalence of ties in the network is also estimated. Although the estimated values of this parameter do not have a direct interpretation they are useful for estimating the fitted pairwise probabilities (see fitted.mtrank).

Value

• A data frame containing the resulting log-ability estimates, their standard errors and their confidence intervals.

• The estimate of the tie prevalence parameter v, on the log-scale.

• The normalized ability estimates for each treatment.

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Rücker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

Examples

data("antidepressants")
#
pw <- pairwise(studlab = studyid, treat = drug_name,
  n = ntotal, event = responders,
  data = antidepressants, sm = "OR")
# Use subset to reduce runtime
pw <- subset(pw, studyid < 60)
#
net <- netmeta(pw, reference.group = "tra")

ranks <- tcc(net, swd = 1.20, small.values = "undesirable")
#
fit <- mtrank(ranks)

# Print log-ability estimates
fit
#
# Print ability estimates
print(fit, backtransf = TRUE)

# Visualize results
forest(fit)
 

Auxiliary function to transform data from paired-preference to long-arm format

Description

Auxiliary function to transform data from paired-preference to long-arm format

Usage

pp2long(x)

Arguments

Value

Data set in long-arm format that can be used as input to rankings.

Author(s)

Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de

See Also

tcc, rankings

Examples

data(diabetes)
#
pw <- pairwise(studlab = study, treat = t,
  n = n, event = r, data = diabetes, sm = "OR")
# Use subset to reduce runtime
pw1 <- subset(pw, id >= 6 & id <= 10)
net1 <- netmeta(pw1, reference.group = "PLA")
#
ranks1 <- tcc(net1, swd = 1.20, small.values = "desirable")
#
pdat1 <- ranks1$ppdata
#
ldat1 <- pp2long(pdat1)
head(ldat1)


net <- netmeta(pw, reference.group = "PLA")
#
ranks <- tcc(net, swd = 1.20, small.values = "desirable")
#
pdat <- ranks$ppdata
#
ldat <- pp2long(pdat)
head(ldat)

library("PlackettLuce")
preferences <- rankings(ldat, id = "id", item = "treat", rank = "rank")
#
fit <- PlackettLuce(preferences)
#
coef(summary(fit, ref = ranks$reference.group))[, 1]
# Results stored in mtrank()
mtrank(ranks)$estimates$log_ability

Apply a treatment-choice criterion (TCC) to get treatment preferences based on network meta-analysis estimates.

Description

This function uses a treatment choice criterion defined by the user and transforms the network meta-analysis estimates into a preference format that indicates either a treatment preference or a tie. In this setting, a treatment preference implies that the respective NMA estimate represents a clinically important result (i.e. that fulfills the TCC) while a tie indicates that the respective NMA estimate lacks enough evidence to represent a treatment preference. The resulting preference format is then used as input to mtrank.

Usage

tcc(
  x,
  pooled = if (x$random) "random" else "common",
  swd = NULL,
  swd.below.null = NULL,
  swd.above.null = NULL,
  small.values = x$small.values,
  relax = TRUE,
  level = x$level.ma
)

## S3 method for class 'tcc'
print(x, ...)

Arguments

Details

R function mtrank expects data in a preference format, where a treatment preference or tie is indicated for each network meta-analysis (NMA) estimate. For example, for the comparison between treatments A and B the potential outcomes are:

• A > B

• A < B

• A = B

The transformation takes place based on the NMA estimates and the treatment choice criterion which has the form of a decision rule.

This function implements treatment choice criteria based on the range of equivalence (ROE) which are specified by

• argument swd. Then the limits of the ROE will be defined based on the values (i) swd, 1 / swd for ratio measures and (ii) swd and -swd for difference measures.

• arguments swd.below.null and swd.above.null. These arguments allow the users to define their own limits of the ROE, given the restriction that the lower limit will always be smaller than the upper limit.

Note that when the argument swd is specified, the arguments swd.below.null and swd.above.null are ignored. Either only the swd or both of the swd.below.null and swd.above.null must be specified for the proper definition of the ROE.

After setting the ROE, each NMA treatment effect will be categorised as a treatment preference or a tie. The argument relax controls the amount of conservatism of the treatment choice criterion. If set to FALSE, a TCC will be built requiring both clinical importance as statistical significance of the results. If set to TRUE (default), the criterion uses only the ROE bounds and therefore the NMA treatment effects need to be only clinically important to indicate a treatment preference.

Value

NMA estimates in a preference format.

References

Evrenoglou T, Nikolakopoulou A, Schwarzer G, Rücker G, Chaimani A (2024): Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria, https://arxiv.org/abs/2406.10612

Examples

data("antidepressants")
#
pw1 <- pairwise(studlab = studyid, treat = drug_name,
  n = ntotal, event = responders,
  data = antidepressants, sm = "OR")
# Use subset to reduce runtime
pw0 <- subset(pw1, studyid < 60)
#
net0 <- netmeta(pw0, reference.group = "tra")

ranks0 <- tcc(net0, swd = 1.20, small.values = "undesirable")

# Comparison other drugs vs trazodone
forest(ranks0,
  label.left = "Favours trazodone",
  label.right = "Favours other drug")

# Comparison escitalopram vs other drugs
forest(ranks0, reference.group = "esc", baseline = FALSE,
  label.left = "Favours other drug",
  label.right = "Favours escitalopram")

## Not run: 
# Store a PDF file in the current working directory showing all results
# (this is the default, i.e., if argument 'reference.group' is missing)
forest(ranks0, baseline = FALSE, reference.group = trts,
  file = "forest_tcc_antidepressants.pdf")

# Run analysis with full data set
net1 <- netmeta(pw1, reference.group = "tra")

ranks1 <- tcc(net1, swd = 1.20, small.values = "undesirable")

# Comparison other drugs vs trazodone
forest(ranks1,
  label.left = "Favours trazodone",
  label.right = "Favours other drug")

# Comparison escitalopram vs other drugs
forest(ranks1, reference.group = "esc", baseline = FALSE,
  label.left = "Favours other drug",
  label.right = "Favours escitalopram")

## End(Not run)