Title:	Dose-Response Network Meta-Analysis in a Frequentist Way
Version:	0.6-0
Date:	2025-04-14
Depends:	R (≥ 4.4.0), netmeta (≥ 3.1.1)
Imports:	MASS, Hmisc, meta, ggplot2, gridExtra, grid, Matrix
Maintainer:	Maria Petropoulou <maria.petropoulou@uniklinik-freiburg.de>
URL:	https://github.com/petropouloumaria/netdose
Description:	A set of functions providing the implementation of the network meta-analysis model with dose-response relationships, predicted values of the fitted model and dose-response plots in a frequentist way.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	no
LazyData:	true
Packaged:	2025-04-14 13:35:22 UTC; petropou_admin
Author:	Maria Petropoulou [aut, cre], Guido Schwarzer [aut]
Repository:	CRAN
Date/Publication:	2025-04-17 07:10:05 UTC

netdose: Brief overview of measures and methodologies for detection of outlying and influential studies in network meta-analysis.

Description

R package netdose provides methods and graphical tools to conduct the network meta-analysis with dose-response relationships in a frequentist way.

Details

R package netdose is a tool to conduct dose-response network meta-analysis a frequentist way (Petropoulou et al, 2025). The package can implement the dose-response network meta-analysis model (function (netdose)); calculate the predicted values of the dose-response network meta-analysis model (function (predict)); provide dose-response plots (function (plot.netdose)) (Petropoulou et al., 2025).

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

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

To report problems and bugs, please send an email to Dr. Maria Petropoulou <maria.petropoulou@uniklinik-freiburg.de>.

The development version of netdose is available on GitHub https://github.com/petropouloumaria/netdose.

Author(s)

Petropoulou Maria <maria.petropoulou@.uniklinik-freiburg.de>, Guido Schwarzer <guido.schwarzer@uniklinik-freiburg.de>

References

Petropoulou et al. (2025): Network meta-analysis with dose-response relationships.

See Also

Useful links:

• https://github.com/petropouloumaria/netdose

Anesthesia Dataset for Dose-Response Network Meta-Analysis

Description

This dataset is a synthesis of randomized controlled studies investigating the effects of different agents for preventing vomiting within 24 h postoperatively in adults after general anaesthesia. Multicomponent interventions have been excluded from this subset to focus on single-agent interventions and their dose-response relationships.

Usage

anesthesia

Format

A data frame with the following columns:

Details

The dataset includes data on several agents for preventing vomiting and their observed effects across multiple clinical randomized controlled trials. The outcome is the occurrence of vomiting within 24 hours after surgery. By excluding multicomponent interventions, this subset allows for a more precise evaluation of single-agent dose-response relationships.

The dataset is structured in a contrast-based format and includes the following variables:

• agent1, agent2, agent3, agent4, agent5: Names of the agents used in each study arm.

• event1, event2, event3, event4, event5: Number of participants who experienced vomiting within 24 hours postoperatively in each study arm.

• n1, n2, n3, n4, n5: Total number of participants in each study arm.

• dose1, dose2, dose3, dose4, dose5: Dose levels of the agents in each study arm.

• studyid: Unique identifier for the study.

This dataset is intended for use in dose-response network meta-analysis to explore the effects of single agents across various doses.

Source

The dataset is a subset of data derived from: Weibel S, Rücker G, Eberhart LHJ, et al. Drugs for preventing postoperative nausea and vomiting in adults after general anaesthesia: a network meta-analysis. Cochrane Database of Systematic Reviews. 2020;10(10):CD012859. Weibel S, Schaefer MS, Raj D, et al. Drugs for preventing postoperative nausea and vomiting in adults after general anaesthesia: an abridged Cochrane network meta-analysis. Anaesthesia. 2021;76:962-973.

Examples

data(anesthesia)
# Summarize the dataset
summary(anesthesia)

Antidepressants Dataset for Dose-Response Network Meta-Analysis

Description

This dataset is a synthesis of randomized controlled studies investigating the effects of antidepressant interventions for unipolar major depressive disorder.

Usage

antidepressants

Format

A data frame with the following columns:

Details

The dataset includes data on several antidepressant agents and their observed effects across multiple clinical randomized controlled trials. The primary outcome is the response rate, defined as the proportion of patients achieving at least a 50

The dataset is structured in an arm-level format and includes the following variables:

• drug: Name of the antidepressant agent.

• r: Number of participants who responded to treatment.

• n: Total number of participants in the study arm.

• dose: Dose level of the antidepressant agent.

• studyid: Unique study identifier.

This dataset is intended for use in dose-response network meta-analysis to explore the effects of the several agents across various doses.

Source

The dataset is a subset of data derived from: Cipriani A et al. 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. The Lancet. 2018;391:1357–1366.

Examples

data(antidepressants)
# Summarize the dataset
summary(antidepressants)

Network meta-analysis with dose-response relationships

Description

The 'netdose' function performs a dose-response network meta-analysis in a frequentist way. It accepts a dataset with study-level data, constructs a design matrix for the dose-response model, and computes treatment effects under common and/or random effects models. The function supports multiple dose-response relationship modeling approaches, including linear, exponential, quadratic, restricted cubic splines (rcs), and fractional polynomial methods (fp1).

Usage

netdose(
  TE,
  seTE,
  agent1,
  dose1,
  agent2,
  dose2,
  studlab,
  data = NULL,
  subset = NULL,
  n1 = NULL,
  n2 = NULL,
  event1 = NULL,
  event2 = NULL,
  sm,
  common = gs("common"),
  random = gs("random") | !is.null(tau.preset),
  tau.preset = NULL,
  method = "linear",
  param = NULL,
  reference.group,
  common.dose = NULL,
  level = gs("level.comb"),
  backtransf = gs("backtransf"),
  tol.multiarm = 0.001,
  tol.multiarm.se = NULL,
  details.chkmultiarm = FALSE,
  func.inverse = invmat,
  keepdata = gs("keepdata"),
  warn = TRUE,
  ...
)

Arguments

Details

The dose-response network meta-analysis (DR-NMA) has been implemented by modelling different dose-response functions, as described by Mandema et al. 2005 and Mawdsley et al. 2016 and by using restricted cubic splines (Hamza et al. 2020) in Bayesian framework.

The function netdose conducts a dose-response network meta-analysis with a variety of dose-response functions (such as the linear, exponential, fractional polynomials and restricted cubic splines) in a frequentist way as described in Petropoulou et al. (2025).

The following dose-response functions are available:

• Linear dose-response relationship (method = "linear")

• Exponential dose-response relationship (method = "exponential")

• Quadratic polynomial dose-response relationship (method = "quadratic")

• Restricted cubic splines (method = "rcs")

• Fractional polynomial (order 1) (method = "fp1")

• Fractional polynomial (order 2) (method = "fp2")

By default, a linear dose-response relationship is assumed.

The parameters for the selected dose-response function can be specified using argument param: a numeric vector specifying the percentiles to set the knots for the restricted cubic splines (default: knots at the 10th, 50th, and 90th percentile), a single numeric specifying the power of the fractional polynomial with order 1 (default: -0.5), or a numeric vector of length 2 specifying the first and second power of a fractional polynomial with order 2 (default: -0.5 and -0.5). The input for argument param is ignored for a linear, exponential or quadratic polynomial dose-response relationship.

Value

An object of class netdose; a list containing the following components:

#' **Common/Random effects model results:**

**Heterogeneity and goodness-of-fit statistics:**

Author(s)

Maria Petropoulou <maria.petropoulou@uniklinik-freiburg.de>, Guido Schwarzer <guido.schwarzer@uniklinik-freiburg.de>

References

Mandema JW, Cox EJ (2005): Therapeutic benefit of eletriptan compared to sumatriptan for the acute relief of migraine pain–results of a model-based meta-analysis that accounts for encapsulation. Cephalalgia, 25, 715-725

Mawdsley D, Bennetts M, Dias S, Boucher M, Welton N (2016): Model-Based Network Meta-Analysis: A Framework for Evidence Synthesis of Clinical Trial Data. PT Pharmacometrics & Systems Pharmacology, 5, 393-401

Hamza T, Furukawa TA, Orsin N, Cipriani A, Iglesias C, Salanti G (2022): A dose-effect network meta-analysis model: an application in antidepressants. Statistical Methods in Medical Research

Petropoulou et al. (2025): Network meta-analysis with dose-response relationships.

Examples

# Load anesthesia data
data(anesthesia)

# Use a subset of 5 studies
anesthesia_subset <- subset(anesthesia, study %in% unique(anesthesia$study)[1:5])

# Prepare data for DR-NMA
dat <- meta::pairwise(
  agent = list(agent1, agent2, agent3),
  event = list(event1, event2, event3),
  n = list(n1, n2, n3),
  dose = list(dose1, dose2, dose3),
  data = anesthesia_subset,
  studlab = study,
  append = FALSE,
  sm = "RR"
)

# Perform DR-NMA with a linear dose-response function
dr1 <- netdose(
  TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat
)


# DR-NMA with FP1 dose-response function with p = -0.5
FP1 <- netdose(TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat,
  method = "fp1"
)

# DR-NMA with FP1 dose-response function with p = 0.5
FP1_p0.5 <- netdose(TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat,
  method = "fp1", param = 0.5
)


# DR-NMA with RCS dose-response function with knots at 10th, 50th and 90th percentiles
dr_rcs <- netdose(TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat,
  method = "rcs"
)

# DR-NMA with RCS dose-response function with knots at 25th, 50th and 100th percentiles
dr_rcs2 <- netdose(TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat,
  method = "rcs", p = c(0.25, 0.50, 1),
)

Dose-response curve plot

Description

Generates a dose-response plot based on the results of a dose-response network meta-analysis (DR-NMA). The plot visualizes predicted dose-response curves alongside observed responses for easy interpretation of model outputs.

Usage

## S3 method for class 'netdose'
plot(
  x,
  pooled = if (x$random) "random" else "common",
  only.direct = TRUE,
  col.direct = if (only.direct) "black" else "green",
  col.indirect = "red",
  agents = NULL,
  same.ylim = TRUE,
  ylim = NULL,
  benchmark.threshold = 0.01,
  plateau.threshold = 1e-04,
  ...
)

Arguments

Details

The function plots the dose-response curve alongside the observed responses: - The vertical axis represents the dose range, which is defined from 0 to the maximum observed dose, with 100 evenly spaced points generated within this range. - The horizontal axis represents the predicted response values, calculated using the predict.netdose function.

The plot includes shaded confidence intervals for the predicted dose-response curve. Observed responses are overlaid for comparison, differentiated into direct and indirect comparisons with customizable colors.

The function also optionally displays the Benchmark Dose (BMD) and the Benchmark Dose Lower Confidence Limit (BMDL), based on a user-defined benchmark response threshold (e.g., 0.01 for 10 percent increase).

If the model indicates that the predicted response stabilizes beyond a certain dose level, the function estimates and plots the Maximum Effective Dose (MED) — the smallest dose beyond which the predicted response increases less than a given threshold (controlled via plateau.threshold). MED is shown only if it occurs after the BMDL, ensuring biological and statistical coherence.

Value

No return value, called for side effects (generates a plot).

Author(s)

Maria Petropoulou <maria.petropoulou@uniklinik-freiburg.de>, Guido Schwarzer <guido.schwarzer@uniklinik-freiburg.de>

Examples

# Load anesthesia data
data(anesthesia)

# Use a subset of 5 studies
anesthesia_subset <- subset(anesthesia, study %in% unique(anesthesia$study)[1:5])

# Prepare data for DR-NMA
dat <- meta::pairwise(
  agent = list(agent1, agent2, agent3),
  event = list(event1, event2, event3),
  n = list(n1, n2, n3),
  dose = list(dose1, dose2, dose3),
  data = anesthesia_subset,
  studlab = study,
  append = FALSE,
  sm = "RR"
)


# DR-NMA with linear dose-response function
dr1 <- netdose(TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat
)

# Dose-response plot
plot(dr1)

Predicted values for dose-response network meta-analysis

Description

This function provides the predicted values based on the results of dose-response network meta-analysis.

Usage

## S3 method for class 'netdose'
predict(object, agent1 = NULL, dose1 = NULL, agent2 = NULL, dose2 = NULL, ...)

Arguments

Details

The predict.netdose function calculates predicted effects for specified doses of one or more agents, based on a dose-response network meta-analysis. It supports both linear and non-linear dose-response relationships, accommodating various modeling methods including linear, exponential, fractional polynomials, restricted cubic splines (RCS), and quadratic relationships. This function is particularly useful for exploring comparative effectiveness at specific dose levels of the agents, facilitating the interpretation of complex dose-response relationships in a network meta-analysis setting. By allowing predictions for multiple combinations of agents and doses, it offers flexibility in evaluating hypothetical scenarios or estimating effects for doses outside the directly observed range (where extrapolation is appropriate).

Value

A data frame with additional class predict.netdose containing the following variables:

Author(s)

Maria Petropoulou <maria.petropoulou@uniklinik-freiburg.de>, Guido Schwarzer <guido.schwarzer@uniklinik-freiburg.de>

References

Petropoulou et al. (2025): Network meta-analysis with dose-response relationships.

Examples

# Load anesthesia data
data(anesthesia)

# Use a subset of 5 studies
anesthesia_subset <- subset(anesthesia, study %in% unique(anesthesia$study)[1:5])

# Prepare data for DR-NMA
dat <- meta::pairwise(
  agent = list(agent1, agent2, agent3),
  event = list(event1, event2, event3),
  n = list(n1, n2, n3),
  dose = list(dose1, dose2, dose3),
  data = anesthesia_subset,
  studlab = study,
  append = FALSE,
  sm = "RR"
)


# Perform DR-NMA with a linear dose-response function
dr1 <- netdose(
  TE, seTE, agent1, dose1, agent2,
  dose2, studlab,
  data = dat
)

# Predicted values
pred1 <- predict(dr1)

Print method for objects of class netdose

Description

Displays a summary of the dose-response network meta-analysis results stored in a netdose object.

Usage

## S3 method for class 'netdose'
print(
  x,
  common = x$common,
  random = x$random,
  backtransf = x$backtransf,
  digits = gs("digits"),
  digits.stat = gs("digits.stat"),
  digits.pval = gs("digits.pval"),
  digits.pval.Q = max(gs("digits.pval.Q"), 2),
  digits.Q = gs("digits.Q"),
  digits.tau2 = gs("digits.tau2"),
  digits.tau = gs("digits.tau"),
  digits.I2 = gs("digits.I2"),
  scientific.pval = gs("scientific.pval"),
  big.mark = gs("big.mark"),
  text.tau2 = gs("text.tau2"),
  text.tau = gs("text.tau"),
  text.I2 = gs("text.I2"),
  ...
)

Arguments

Value

The input object is printed to the console. No return value.

Print method for objects of class predict

Description

Print method for objects of class predict

Usage

## S3 method for class 'predict.netdose'
print(
  x,
  backtransf = attr(x, "backtransf"),
  digits = gs("digits"),
  big.mark = gs("big.mark"),
  ...
)

Arguments

Value

The input object is printed to the console. No return value.