Package 'MBNMAdose'

Description

Adds arm indices (arms, narms) to a dataset and adds numeric identifiers for agent and class (if included in the data).

Usage

add_index(data.ab, agents = NULL, treatments = NULL)

Arguments

Value

A data frame similar to data.ab but with additional columns:

• arm Arm identifiers coded for each study

• narm The total number of arms in each study

If agent or class are non-numeric or non-sequential (i.e. with missing numeric codes), agents/classes in the returned data frame will be numbered and recoded to enforce sequential numbering (a warning will be shown stating this).

Description

A dataset from a systematic review of Randomised-Controlled Trials (RCTs) comparing different doses of alogliptin with placebo (Langford et al. 2016). The systematic review was simply performed and was intended to provide data to illustrate a statistical methodology rather than for clinical inference. Alogliptin is a treatment aimed at reducing blood glucose concentration in type II diabetes. The outcome is continuous, and aggregate data responses correspond to the mean change in HbA1c from baseline to follow-up in studies of at least 12 weeks follow-up. The dataset includes 14 Randomised-Controlled Trials (RCTs), comparing 5 different doses of alogliptin with placebo, leading to 6 different treatments (combination of dose and agent) within the network.

Usage

alog_pcfb

Format

A data frame in long format (one row per arm and study), with 46 rows and 6 variables:

• studyID Study identifiers

• agent Character data indicating the agent to which participants were randomised

• dose Numeric data indicating the standardised dose received

• y Numeric data indicating the mean change from baseline in blood glucose concentration (mg/dL) in a study arm

• se Numeric data indicating the standard error for the mean change from baseline in blood glucose concentration (mg/dL) in a study arm

• n Numeric data indicating the number of participants randomised

Details

alog_pcfb is a data frame in long format (one row per arm and study), with the variables studyID, agent, dose, y, se, and N.

References

Langford O, Aronson JK, van Valkenhoef G, Stevens RJ (2016). “Methods for meta-analysis of pharmacodynamic dose-response data with application to multi-arm studies of alogliptin.” Stat Methods Med Res. ISSN 1477-0334 (Electronic) 0962-2802 (Linking), doi:10.1177/0962280216637093.

Description

Calculates values for EDx from an Emax model, the dose at which x% of the maximal response (Emax) is reached

Usage

calc.edx(mbnma, x = 50)

Arguments

Value

A data frame of posterior EDx summary values for each agent

Description

Update model fit statistics depending on calculation for pD

Usage

changepd(model, jagsdata = NULL, pd = "pv", likelihood = NULL, type = "dose")

Arguments

Value

A list containing pd (effective number of parameters calculated using the method specified in arguments), deviance (the posterior median of the total residual deviance) and dic (the model DIC)

Description

Check if all nodes in the network are connected (identical to function in MBNMAtime)

Usage

check.network(g, reference = 1)

Arguments

Description

Plot cumulative ranking curves from MBNMA models

Usage

cumrank(x, params = NULL, sucra = TRUE, ...)

Arguments

Value

Line plots showing the cumulative ranking probabilities for each agent/class and dose-response parameter in x. The object returned is a list which contains the plot (an object of ⁠class(c("gg", "ggplot")⁠) and a data frame of SUCRA values if sucra = TRUE.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Estimate rankings  from an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")
ranks <- rank(emax)

# Plot cumulative rankings for both dose-response parameters simultaneously
# Note that SUCRA values are also returned
cumrank(ranks)

Description

This function creates JAGS code snippets for default MBNMA model priors.

Usage

default.priors(
  fun = dloglin(),
  UME = FALSE,
  regress.mat = NULL,
  regress.effect = "common",
  om = list(rel = 5, abs = 10)
)

Arguments

Value

A list, each element of which is a named JAGS snippet corresponding to a prior in the MBNMA JAGS code.

Examples

default.priors(fun=demax())

Description

Emax dose-response function

Usage

demax(emax = "rel", ed50 = "rel", hill = NULL, p.expon = FALSE)

Arguments

Details

Emax represents the maximum response. exp(ED50) represents the dose at which 50% of the maximum response is achieved. exp(Hill) is the Hill parameter, which allows for a sigmoidal function.

Without Hill parameter:

$\frac{E_{max}\times{x}}{ET_{50}+x}$

With Hill parameter:

$\frac{E_{max}\times{x^{hill}}}{ET_{50}\times{hill}}+x^{hill}$

Value

An object of class("dosefun")

Dose-response parameters

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

# Model without a Hill parameter
demax(emax="rel", ed50="common")

# Model including a Hill parameter and defaults for Emax and ED50 parameters
demax(hill="common")

Description

Plots the deviances of two model types for comparison. Often used to assess consistency by comparing consistency (NMA or MBNMA) and unrelated mean effects (UME) models (see Pedder et al. (2021)). Models must be run on the same set of data or the deviance comparisons will not be valid.

Usage

devdev(mod1, mod2, dev.type = "resdev", n.iter = 2000, n.thin = 1, ...)

Arguments

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an poorly fitting linear dose-response
lin <- mbnma.run(network, fun=dpoly(degree=1))

# Run a better fitting Emax dose-response
emax <- mbnma.run(network, fun=demax())

# Run a standard NMA with unrelated mean effects (UME)
ume <- nma.run(network, UME=TRUE)

# Compare residual deviance contributions from linear and Emax
devdev(lin, emax) # Suggests model fit is very different

# Compare deviance contributions from Emax and UME
devdev(emax, ume) # Suggests model fit is similar

Description

Plot deviance contributions from an MBNMA model

Usage

devplot(
  mbnma,
  plot.type = "box",
  facet = TRUE,
  dev.type = "resdev",
  n.iter = mbnma$BUGSoutput$n.iter/2,
  n.thin = mbnma$BUGSoutput$n.thin,
  ...
)

Arguments

Details

Deviances should only be plotted for models that have converged successfully. If deviance contributions have not been monitored in mbnma$parameters.to.save then additional iterations will have to be run to get results for these.

For MBNMAtime, deviance contributions cannot be calculated for models with a multivariate likelihood (i.e. those that account for correlation between observations) because the covariance matrix in these models is treated as unknown (if rho = "estimate") and deviance contributions will be correlated.

Value

Generates a plot of deviance contributions and returns a list containing the plot (as an object of class(c("gg", "ggplot"))), and a data.frame of posterior mean deviance/residual deviance contributions for each observation.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an Emax dose-response MBNMA and predict responses
emax <- mbnma.run(network, fun=demax(), method="random")

# Plot deviances
devplot(emax)

# Plot deviances using boxplots
devplot(emax, plot.type="box")

# Plot deviances on a single scatter plot (not facetted by agent)
devplot(emax, facet=FALSE, plot.type="scatter")

# A data frame of deviance contributions can be obtained from the object
#returned by `devplot`
devs <- devplot(emax)
head(devs$dev.data)

# Other deviance contributions not currently implemented but in future
#it will be possible to plot them like so
#devplot(emax, dev.type="dev")

Description

Similar parameterisation to the Emax model but with non-asymptotic maximal effect (Emax). Can fit a 1-parameter (Emax only) or 2-parameter model (includes onset parameter that controls the curvature of the dose-response relationship)

Usage

dexp(emax = "rel", onset = NULL, p.expon = FALSE)

Arguments

Details

1-parameter model: $emax\times{(1-exp(-x))}$

2-parameter model: $emax\times{(1-exp(onset*-x))}$

where emax is the maximum efficacy of an agent and rate is the speed

Dose-response parameter arguments:

Value

An object of class("dosefun")

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

# Single parameter exponential function is default
dexp()

# Two parameter exponential function
dexp(onset="rel")

Description

Fractional polynomial dose-response function

Usage

dfpoly(degree = 1, beta.1 = "rel", beta.2 = "rel", power.1 = 0, power.2 = 0)

Arguments

Details

• $\beta_1$ represents the 1st coefficient.

• $\beta_2$ represents the 2nd coefficient.

• $\gamma_1$ represents the 1st fractional polynomial power

• $\gamma_2$ represents the 2nd fractional polynomial power

For a polynomial of degree=1:

${\beta_1}x^{\gamma_1}$

For a polynomial of degree=2:

${\beta_1}x^{\gamma_1}+{\beta_2}x^{\gamma_2}$

$x^{\gamma}$ is a regular power except where $\gamma=0$, where $x^{(0)}=ln(x)$. If a fractional polynomial power $\gamma$ repeats within the function it is multiplied by another $ln(x)$.

Value

An object of class("dosefun")

Dose-response parameters

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

Royston P, Altman D (1994). “Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling.” Journal of the Royal Statistical Society: Series C, 43(3), 429-467.

Examples

# 1st order fractional polynomial a value of 0.5 for the power
dfpoly(beta.1="rel", power.1=0.5)

# 2nd order fractional polynomial with relative effects for coefficients
# and a value of -0.5 and 2 for the 1st and 2nd powers respectively
dfpoly(degree=2, beta.1="rel", beta.2="rel",
  power.1=-0.5, power.2=2)

Description

Similar parameterisation to the Emax model but with non-asymptotic maximal effect (Emax). Proposed by proposed by Fu and Manner (2010)

Usage

ditp(emax = "rel", rate = "rel", p.expon = FALSE)

Arguments

Details

Emax represents the maximum response. Rate represents the rate at which a change in the dose of the drug leads to a change in the effect

${E_{max}}\times\frac{(1-exp(-{rate}\times{x}))}{(1-exp(-{rate}\times{max(x)}))}$

Value

An object of class("dosefun")

Dose-response parameters

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

Fu H, Manner D (2010). “Bayesian adaptive dose-finding studies with delayed responses.” J Biopharm Stat, 20(5), 1055-1070. doi:10.1080/10543400903315740.

Examples

# Model a common effect on rate
ditp(emax="rel", rate="common")

Description

Modelled assuming relative effects ("rel")

Usage

dloglin()

Details

$rate\times{log(x + 1)}$

Dose-response parameter arguments:

Value

An object of class("dosefun")

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

dloglin()

Description

Function combines different dose-response functions together to create an object containing parameters for multiple dose-response functions.

Usage

dmulti(funs = list())

Arguments

Value

An object of class("dosefun")

Examples

funs <- c(rep(list(demax()),3),
          rep(list(dloglin()),2),
          rep(list(demax(ed50="common")),3),
          rep(list(dexp()),2))

dmulti(funs)

Description

Used to fit monotonically increasing non-parametric dose-response relationship following the method of Owen et al. (2015))

Usage

dnonparam(direction = "increasing")

Arguments

Value

An object of class("dosefun")

References

Owen RK, Tincello DG, Keith RA (2015). “Network meta-analysis: development of a three-level hierarchical modeling approach incorporating dose-related constraints.” Value Health, 18(1), 116-26. ISSN 1524-4733 (Electronic) 1098-3015 (Linking), doi:10.1016/j.jval.2014.10.006, https://pubmed.ncbi.nlm.nih.gov/25595242/.

Examples

# Monotonically increasing dose-response
dnonparam(direction="increasing")

# Monotonically decreasing dose-response
dnonparam(direction="decreasing")

Description

Polynomial dose-response function

Usage

dpoly(
  degree = 1,
  beta.1 = "rel",
  beta.2 = "rel",
  beta.3 = "rel",
  beta.4 = "rel"
)

Arguments

Details

• $\beta_1$ represents the 1st coefficient.

• $\beta_2$ represents the 2nd coefficient.

• $\beta_3$ represents the 3rd coefficient.

• $\beta_4$ represents the 4th coefficient.

Linear model:

$\beta_1{x}$

Quadratic model:

$\beta_1{x} + \beta_2{x^2}$

Cubic model:

$\beta_1{x} + \beta_2{x^2} + \beta_3{x^3}$

Quartic model:

$\beta_1{x} + \beta_2{x^2} + \beta_3{x^3} + \beta_4{x^4}$

Value

An object of class("dosefun")

Dose-response parameters

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

# Linear model with random effects
dpoly(beta.1="rel")

# Quadratic model dose-response function
# with an exchangeable (random) absolute parameter estimated for the 2nd coefficient
dpoly(beta.1="rel", beta.2="random")

Description

Function adds additional rows to a data.frame of comparisons in a network that account for the relationship between placebo and other agents via the dose-response relationship.

Usage

DR.comparisons(data.ab, level = "treatment", doselink = NULL)

Arguments

Description

Drops arms in a way which preserves connectivity and equally removes data from each treatment in a nodesplit comparison (so as to maximise precision)

Usage

drop.comp(ind.df, drops, comp, start = 1)

Arguments

Description

Drop studies that are not connected to the network reference treatment

Usage

drop.disconnected(network, connect.dose = FALSE)

Arguments

Value

A list containing a single row per arm data frame containing only studies that are connected to the network reference treatment, and a character vector of treatment labels

Examples

# Using the triptans headache dataset
network <- mbnma.network(triptans)
drops <- drop.disconnected(network)

# No studies have been dropped since network is fully connected
length(unique(network$data.ab$studyID))==length(unique(drops$data.ab$studyID))


# Make data with no placebo
noplac.df <- network$data.ab[network$data.ab$narm>2 & network$data.ab$agent!=1,]
net.noplac <- mbnma.network(noplac.df)

# Studies are dropped as some only connect via the dose-response function
drops <- drop.disconnected(net.noplac, connect.dose=FALSE)
length(unique(net.noplac$data.ab$studyID))==length(unique(drops$data.ab$studyID))

# Studies are not dropped if they connect via the dose-response function
drops <- drop.disconnected(net.noplac, connect.dose=TRUE)
length(unique(net.noplac$data.ab$studyID))==length(unique(drops$data.ab$studyID))

Description

Used to fit B-splines, natural cubic splines, and piecewise linear splines(Perperoglu et al. 2019).

Usage

dspline(
  type = "bs",
  knots = 1,
  degree = 1,
  beta.1 = "rel",
  beta.2 = "rel",
  beta.3 = "rel",
  beta.4 = "rel"
)

Arguments

Value

An object of class("dosefun")

Dose-response parameters

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

Perperoglu A, Sauerbrei W, Abrahamowicz M, Schmid M (2019). “A review of spline function procedures in R.” BMC Medical Research Methodology, 19(46), 1-16. doi:10.1186/s12874-019-0666-3.

Examples

# Second order B spline with 2 knots and random effects on the 2nd coefficient
dspline(type="bs", knots=2, degree=2,
  beta.1="rel", beta.2="rel")

# Piecewise linear spline with knots at 0.1 and 0.5 quantiles
# Single parameter independent of treatment estimated for 1st coefficient
#with random effects
dspline(type="ls", knots=c(0.1,0.5),
  beta.1="random", beta.2="rel")

Description

User-defined dose-response function

Usage

duser(fun, beta.1 = "rel", beta.2 = "rel", beta.3 = "rel", beta.4 = "rel")

Arguments

Value

An object of class("dosefun")

Dose-response parameters

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

dr <- ~ beta.1 * (1/(dose+1)) + beta.2 * dose^2
duser(fun=dr,
  beta.1="common", beta.2="rel")

Description

Plot fitted values from MBNMA model

Usage

fitplot(
  mbnma,
  disp.obs = TRUE,
  n.iter = mbnma$BUGSoutput$n.iter,
  n.thin = mbnma$BUGSoutput$n.thin,
  ...
)

Arguments

Details

Fitted values should only be plotted for models that have converged successfully. If fitted values (theta) have not been monitored in mbnma$parameters.to.save then additional iterations will have to be run to get results for these.

Value

Generates a plot of fitted values from the MBNMA model and returns a list containing the plot (as an object of class(c("gg", "ggplot"))), and a data.frame of posterior mean fitted values for each observation.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an Emax dose-response MBNMA and predict responses
emax <- mbnma.run(network, fun=demax(), method="random")

# Plot fitted values and observed values
fitplot(emax)

# Plot fitted values only
fitplot(emax, disp.obs=FALSE)

# A data frame of fitted values can be obtained from the object
#returned by `fitplot`
fits <- fitplot(emax)
head(fits$fv)

Description

Automatically generate parameters to save for a dose-response MBNMA model

Usage

gen.parameters.to.save(fun, model, regress.mat = NULL)

Arguments

Description

Generates spline basis matrices for fitting to dose-response function

Usage

genspline(
  x,
  spline = "bs",
  knots = 1,
  degree = 1,
  max.dose = max(x),
  boundaries = NULL
)

Arguments

Value

A spline basis matrix with number of rows equal to length(x) and the number of columns equal to the number of coefficients in the spline.

Examples

x <- 0:100

genspline(x)

# Generate a quadratic B-spline with 1 equally spaced internal knot
genspline(x, spline="bs", knots=2, degree=2)

# Generate a natural cubic spline with 3 knots at selected quantiles
genspline(x, spline="ns", knots=c(0.1, 0.5, 0.7))

# Generate a piecewise linear spline with 3 equally spaced knots
genspline(x, spline="ls", knots=3)

Description

Identical to get.prior() in MBNMAtime package. This function takes JAGS model presented as a string and identifies what prior values have been used for calculation.

Usage

get.prior(model)

Arguments

Details

Even if an MBNMA model that has not initialised successfully and results have not been calculated, the JAGS model for it is saved in mbnma$model.arg$jagscode and therefore priors can still be obtained. This allows for priors to be changed even in failing models, which may help solve issues with compiling or updating.

Value

A character vector, each element of which is a line of JAGS code corresponding to a prior in the JAGS code.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an Emax dose-response MBNMA
result <- mbnma.run(network, fun=demax(), method="random")

# Obtain model prior values
print(result$model.arg$priors)

# Priors when using mbnma.run with an exponential function
result <- mbnma.run(network, fun=dexp(), method="random")
print(result$model.arg$priors)

Description

Calculates league table of effects between treatments in MBNMA and/or NMA models

Usage

get.relative(
  lower.diag,
  upper.diag = lower.diag,
  treatments = list(),
  lower.direction = "colvrow",
  upper.direction = "rowvcol",
  regress.vals = NULL,
  eform = FALSE,
  lim = "cred"
)

Arguments

Value

An array of ⁠length(treatments) x length(treatments) x nsims⁠, where nsims is the number of iterations monitored in lower.diag. The array contains the individual MCMC values for each relative effect calculated between all treatments on the link scale specified in the lower.diag and upper.diag models.

Examples

# Using the osteoarthritis data
network <- mbnma.network(osteopain)

# Run an MBNMA model
expon <- mbnma.run(network, fun=dexp(), method="random")

# Calculate relative effects for MBNMA between:
# Celebrex 100mg/d, Celebrex 200mg/d, Tramadol 100mg/d
rel.eff <- get.relative(lower.diag=expon,
  treatments=list("Celebrex"=c(100,200), "Tramadol"=100))

# Run an NMA model
nma <- nma.run(network, method="random")

# Compare results between MBNMA and NMA models
rel.eff <- get.relative(lower.diag=expon, upper.diag=nma,
  treatments=list("Celebrex"=c(100,200), "Tramadol"=100),
  upper.direction="colvrow")

Description

Converts MBNMA data frame to a list for use in JAGS model

Usage

getjagsdata(
  data.ab,
  class = FALSE,
  sdscale = FALSE,
  regress = NULL,
  regress.effect = "common",
  likelihood = check.likelink(data.ab)$likelihood,
  link = check.likelink(data.ab)$link,
  level = "agent",
  fun = NULL,
  nodesplit = NULL
)

Arguments

Value

A named list of numbers, vector, matrices and arrays to be sent to JAGS. List elements are:

• If likelihood="normal":

  • y An array of mean responses for each arm within each study

  • se An array of standard errors for each arm within each study

• If likelihood="binomial":

  • r An array of the number of responses/count for each each arm within each study

  • n An array of the number of participants for each arm within each study

• If likelihood="poisson":

  • r An array of the number of responses/count for each each arm within each study

  • E An array of the total exposure time for each arm within each study

• dose A matrix of doses for each arm within each study (if level="agent")

• narm A numeric vector with the number of arms per study

• NS The total number of studies in the dataset

• Nagent The total number of agents in the dataset (if level="agent")

• agent A matrix of agent codes within each study (if level="agent")

• NT The total number of treatment in the dataset (if level="treatment")

• treatment A matrix of treatment codes within each study (if level="treatment")

• Nclass Optional. The total number of classes in the dataset

• class Optional. A matrix of class codes within each study

• classkey Optional. A vector of class codes that correspond to agent codes. Same length as the number of agent codes.

• split.ind Optional. A matrix indicating whether a specific arm contributes evidence to a nodesplit comparison.

Examples

# Using the triptans headache dataset
network <- mbnma.network(triptans)
jagsdat <- getjagsdata(network$data.ab, likelihood="binomial", link="logit")


# Get JAGS data with class
netclass <- mbnma.network(osteopain)
jagsdat <- getjagsdata(netclass$data.ab, class=TRUE)


# Get JAGS data at the treatment level for split Network Meta-Analysis
network <- mbnma.network(triptans)
jagsdat <- getjagsdata(network$data.ab, level="treatment")

Description

A dataset from a systematic review of interventions for lowering Serum Uric Acid (SUA) concentration in patients with gout (not published previously). The outcome is continuous, and aggregate data responses correspond to the mean change from baseline in SUA in mg/dL at 2 weeks follow-up. The dataset includes 10 Randomised-Controlled Trials (RCTs), comparing 5 different agents, and placebo. Data for one agent (RDEA) arises from an RCT that is not placebo-controlled, and so is not connected to the network directly. In total there were 19 different treatments (combination of dose and agent).

Usage

gout

Format

A data frame in long format (one row per arm and study), with 27 rows and 5 variables:

• studyID Study identifiers

• y Numeric data indicating the mean change from baseline in SUA in a study arm

• se Numeric data indicating the standard error for the mean change from baseline in SUA in a study arm

• agent Character data indicating the agent to which participants were randomised

• dose Numeric data indicating the standardised dose received

Source

Pfizer Ltd.

Description

Identify comparisons informed by both direct and indirect evidence from independent sources, which therefore fulfill the criteria for testing for inconsistency via node-splitting.

Usage

inconsistency.loops(df, checkindirect = TRUE, incldr = FALSE)

Arguments

Details

Similar to gemtc::mtc.nodesplit.comparisons() but uses a fixed reference treatment and therefore identifies fewer loops in which to test for inconsistency. Heterogeneity can also be parameterised as inconsistency and so testing for inconsistency in additional loops whilst changing the reference treatment would also be identifying heterogeneity. Depends on igraph.

Value

A data frame of comparisons that are informed by direct and indirect evidence from independent sources. Each row of the data frame is a different treatment comparison. Numerical codes in t1 and t2 correspond to treatment codes. path indicates the treatment codes that connect the shortest path of indirect evidence.

If incldr=TRUE then path may indicate doseresp for some comparisons. These are comparisons for which indirect evidence is only available via the dose-response relationship. The two numbers given after (e.g. ⁠3 2⁠) indicate the number of doses available in the indirect evidence with which to estimate the dose-response function for the treatments in t1 and t2 respectively/

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

# Identify comparisons informed by direct and indirect evidence
#in triptans dataset
network <- mbnma.network(triptans)
inconsistency.loops(network$data.ab)

# Include indirect evidence via dose-response relationship
inconsistency.loops(network$data.ab, incldr=TRUE)



# Do not perform additional connectivity check on data
data <- data.frame(studyID=c(1,1,2,2,3,3,4,4,5,5,5),
            treatment=c(1,2,1,3,2,3,3,4,1,2,4)
            )
inconsistency.loops(data, checkindirect=FALSE)

Description

Identify unique contrasts within a network that make up all the head-to-head comparisons. Repetitions of the same treatment comparison are grouped together.

Usage

mbnma.comparisons(df)

Arguments

Value

A data frame of unique comparisons in which each row represents a different comparison. t1 and t2 indicate the treatment codes that make up the comparison. nr indicates the number of times the given comparison is made within the network.

If there is only a single follow-up observation for each study within the dataset (i.e. as for standard network meta-analysis) nr will represent the number of studies that compare treatments t1 and t2.

If there are multiple observations for each study within the dataset (as in time-course MBNMA) nr will represent the number of time points in the dataset in which treatments t1 and t2 are compared.

Examples

df <- data.frame(studyID=c(1,1,2,2,3,3,4,4,5,5,5),
  treatment=c(1,2,1,3,2,3,3,4,1,2,4)
  )

# Identify unique comparisons within the data
mbnma.comparisons(df)


# Using the triptans headache dataset
network <- mbnma.network(triptans) # Adds treatment identifiers
mbnma.comparisons(network$data.ab)

Description

Splits contributions for a given set of treatment comparisons into direct and indirect evidence. A discrepancy between the two suggests that the consistency assumption required for NMA and MBNMA may violated.

Usage

mbnma.nodesplit(
  network,
  fun = dpoly(degree = 1),
  method = "common",
  comparisons = NULL,
  incldr = TRUE,
  ...
)

## S3 method for class 'nodesplit'
plot(x, plot.type = "forest", ...)

Arguments

Details

The S3 method plot() on an nodesplit object generates either forest plots of posterior medians and 95\% credible intervals, or density plots of posterior densities for direct and indirect evidence.

Value

Plots the desired graph if plot.type="forest" and plots and returns an object of class(c("gg", "ggplot")) if plot.type="density".

Functions

• plot(nodesplit): Plot outputs from treatment-level nodesplit MBNMA models

Examples

# Using the triptans data
network <- mbnma.network(triptans)

split <- mbnma.nodesplit(network, fun=demax(), likelihood = "binomial", link="logit",
  method="common")


#### To perform nodesplit on selected comparisons ####

# Check for closed loops of treatments with independent evidence sources
# Including indirect evidence via the dose-response relationship
loops <- inconsistency.loops(network$data.ab, incldr=TRUE)

# This...
single.split <- mbnma.nodesplit(network, fun=dexp(), likelihood = "binomial", link="logit",
             method="random", comparisons=rbind(c("sumatriptan_1", "almotriptan_1")))

#...is the same as...
single.split <- mbnma.nodesplit(network, fun=dexp(), likelihood = "binomial", link="logit",
             method="random", comparisons=rbind(c(6, 12)))


# Plot results
plot(split, plot.type="density") # Plot density plots of posterior densities
plot(split, txt_gp=forestplot::fpTxtGp(cex=0.5)) # Plot forest plots (with smaller label size)

# Print and summarise results
print(split)
summary(split) # Generate a data frame of summary results

Description

Fits a Bayesian dose-response for model-based network meta-analysis (MBNMA) that can account for multiple doses of different agents by applying a desired dose-response function. Follows the methods of Mawdsley et al. (2016).

Usage

mbnma.run(
  network,
  fun = dpoly(degree = 1),
  method = "common",
  regress = NULL,
  regress.effect = "common",
  class.effect = list(),
  UME = FALSE,
  sdscale = FALSE,
  cor = FALSE,
  omega = NULL,
  parameters.to.save = NULL,
  pd = "pd.kl",
  likelihood = NULL,
  link = NULL,
  priors = NULL,
  n.iter = 20000,
  n.chains = 3,
  n.burnin = floor(n.iter/2),
  n.thin = max(1, floor((n.iter - n.burnin)/1000)),
  autojags = FALSE,
  Rhat = 1.05,
  n.update = 10,
  model.file = NULL,
  jagsdata = NULL,
  ...
)

Arguments

Details

When relative effects are modelled on more than one dose-response parameter and cor = TRUE, correlation between the dose-response parameters is automatically estimated using a vague Wishart prior. This prior can be made slightly more informative by specifying the relative scale of variances between the dose-response parameters using omega. cor will automatically be set to FALSE if class effects are modelled.

Value

An object of S3 class(c("mbnma", "rjags")) containing parameter results from the model. Can be summarized by print() and can check traceplots using R2jags::traceplot() or various functions from the package mcmcplots.

Nodes that are automatically monitored (if present in the model) have the following interpretation:

If there are errors in the JAGS model code then the object will be a list consisting of two elements - an error message from JAGS that can help with debugging and model.arg, a list of arguments provided to mbnma.run() which includes jagscode, the JAGS code for the model that can help users identify the source of the error.

Dose-response parameter arguments

Dose-response function

Several general dose-response functions are provided, but a user-defined dose-response relationship can instead be used.

As of version 0.4.0 dose-response functions are specified as an object of class("dosefun"). See help details for each of the functions below for the interpretation of specific dose-response parameters.

Built-in dose-response functions are:

• dpoly(): polynomial (e.g. for a linear model - dpoly(degree=1))

• dloglin(): log-linear

• dexp(): exponential

• demax(): (emax with/without a Hill parameter)

• dspline(): splines (can fit B-splines (type="bs"), restricted cubic splines (type="rcs"), natural splines (type="ns"), or piecewise linear splines (type="ls"))

• dfpoly(): fractional polynomials

• dnonparam(): Non-parametric monotonic function (direction can be either "increasing" or "decreasing") following the method of Owen et al. (2015)

• duser(): user-defined function

• dmulti(): allows agent-specific dose-response functions to be fitted. A separate function must be provided for each agent in the network.

References

Gelman A, Rubin DB (1992). “Inference from iterative simulation using multiple sequences.” Statistical Science, 7(4), 457-511. https://projecteuclid.org/journals/statistical-science/volume-7/issue-4/Inference-from-Iterative-Simulation-Using-Multiple-Sequences/10.1214/ss/1177011136.full.

Mawdsley D, Bennetts M, Dias S, Boucher M, Welton NJ (2016). “Model-Based Network Meta-Analysis: A Framework for Evidence Synthesis of Clinical Trial Data.” CPT Pharmacometrics Syst Pharmacol, 5(8), 393-401. ISSN 2163-8306 (Electronic) 2163-8306 (Linking), doi:10.1002/psp4.12091, https://pubmed.ncbi.nlm.nih.gov/27479782/.

Owen RK, Tincello DG, Keith RA (2015). “Network meta-analysis: development of a three-level hierarchical modeling approach incorporating dose-related constraints.” Value Health, 18(1), 116-26. ISSN 1524-4733 (Electronic) 1098-3015 (Linking), doi:10.1016/j.jval.2014.10.006, https://pubmed.ncbi.nlm.nih.gov/25595242/.

Plummer M (2008). “Penalized loss functions for Bayesian model comparison.” Biostatistics, 9(3), 523-39. ISSN 1468-4357 (Electronic) 1465-4644 (Linking), https://pubmed.ncbi.nlm.nih.gov/18209015/.

Plummer M (2017). JAGS user manual. https://people.stat.sc.edu/hansont/stat740/jags_user_manual.pdf.

Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002). “Bayesian measures of model complexity and fit.” J R Statistic Soc B, 64(4), 583-639.

Examples

# Using the triptans data
network <- mbnma.network(triptans)


######## Dose-response functions ########

# Fit a dose-response MBNMA with a linear function
# with common treatment effects
result <- mbnma.run(network, fun=dpoly(degree=1), method="common")

# Fit a dose-response MBNMA with a log-linear function
# with random treatment effects
result <- mbnma.run(network, fun=dloglin(), method="random")

# Fit a dose-response MBNMA with a fractional polynomial function
# with random treatment effects
# with a probit link function
result <- mbnma.run(network, fun=dfpoly(), method="random", link="probit")

# Fit a user-defined function (quadratic)
fun.def <- ~ (beta.1 * dose) + (beta.2 * (dose^2))
result <- mbnma.run(network, fun=duser(fun=fun.def), method="common")

# Fit an Emax function
# with a single random (exchangeable) parameter for ED50
# with common treatment effects
result <- mbnma.run(network, fun=demax(emax="rel", ed50="random"),
              method="common")

# Fit an Emax function with a Hill parameter
# with a fixed value of 5 for the Hill parameter
# with random relative effects
result <- mbnma.run(network, fun=demax(hill=5), method="random")

# Fit a model with natural cubic splines
# with 3 knots at 10% 30% and 60% quartiles of dose ranges
depnet <- mbnma.network(ssri) # Using the sSRI depression dataset
result <- mbnma.run(depnet, fun=dspline(type="ns", knots=c(0.1,0.3,0.6)))

# Fit a model with different dose-response functions for each agent
multifun <- dmulti(list(dloglin(), # for placebo (can be any function)
                       demax(), # for eletriptan
                       demax(), # for sumatriptan
                       dloglin(), # for frovatriptan
                       demax(), # for almotriptan
                       demax(), # for zolmitriptan
                       dloglin(), # for naratriptan
                       demax())) # for rizatriptan

multidose <- mbnma.run(network, fun=multifun)


########## Class effects ##########

 # Using the osteoarthritis dataset
 pain.df <- osteopain

 # Set a shared class (NSAID) only for Naproxcinod and Naproxen
 pain.df <- pain.df %>% dplyr::mutate(
                class = dplyr::case_when(agent %in% c("Naproxcinod", "Naproxen") ~ "NSAID",
                        !agent %in% c("Naproxcinod", "Naproxen") ~ agent
                        )
                )

 # Run an Emax MBNMA with a common class effect on emax
 painnet <- mbnma.network(pain.df)
 result <- mbnma.run(painnet, fun = demax(),
                class.effect = list(emax = "common"))


####### Priors #######

# Obtain priors from a fractional polynomial function
result <- mbnma.run(network, fun=dfpoly(degree=1), method="random")
print(result$model.arg$priors)

# Change the prior distribution for the power
newpriors <- list(power.1 = "dnorm(0,0.001) T(0,)")
newpriors <- list(sd = "dnorm(0,0.5) T(0,)")

result <- mbnma.run(network, fun=dfpoly(degree=1), method="random",
              priors=newpriors)


########## Sampler options ##########

# Change the number of MCMC iterations, the number of chains, and the thin
result <- mbnma.run(network, fun=dloglin(), method="random",
              n.iter=5000, n.thin=5, n.chains=4)

# Calculate effective number of parameters via plugin method
result <- mbnma.run(network, fun=dloglin(), method="random",
              pd="plugin")

# Calculate effective number of parameters using penalized expected deviance
result <- mbnma.run(network, fun=dloglin(), method="random",
              pd="popt")


####### Examine MCMC diagnostics (using mcmcplots or coda packages) #######

# Density plots
mcmcplots::denplot(result)

# Traceplots
mcmcplots::traplot(result)

# Caterpillar plots
mcmcplots::caterplot(result, "rate")

# Autocorrelation plots (using the coda package)
coda::autocorr.plot(coda::as.mcmc(result))

####### Automatically run jags until convergence is reached #########

# Rhat of 1.08 is set as the criteria for convergence
#on all monitored parameters
conv.res <- mbnma.run(network, fun=demax(),
              method="random",
              n.iter=10000, n.burnin=9000,
              autojags=TRUE, Rhat=1.08, n.update=8)


########## Output ###########

# Print R2jags output and summary
print(result)
summary(result)

# Plot forest plot of results
plot(result)

Description

Useful for obtaining deviance contributions or fitted values. Same function used in MBNMAdose and MBNMAtime packages.

Usage

mbnma.update(
  mbnma,
  param = "theta",
  armdat = TRUE,
  n.iter = mbnma$BUGSoutput$n.iter,
  n.thin = mbnma$BUGSoutput$n.thin
)

Arguments

Value

A data frame containing the posterior mean of the updates by arm and study, with arm and study identifiers.

For MBNMAdose:

• facet indicates the agent identifier in the given arm of a study

• fupdose indicates the dose in the given arm of a study

For MBNMAtime:

• facet indicates the treatment identifier in the given arm of the study

• fupdose indicates the follow-up time at the given observation in the given arm of the study

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Fit a dose-response MBNMA, monitoring "psi" and "resdev"
result <- mbnma.run(network, fun=dloglin(), method="random",
  parameters.to.save=c("psi", "resdev"))

mbnma.update(result, param="theta") # monitor theta

mbnma.update(result, param="rhat") # monitor rhat

mbnma.update(result, param="delta") # monitor delta

Description

Validates that a dataset fulfills requirements for MBNMA

Usage

mbnma.validate.data(data.ab, single.arm = FALSE)

Arguments

Details

Checks done within the validation:

• Checks data.ab has required column names

• Checks there are no NAs

• Checks that all SEs are >0 (if variables are included in dataset)

• Checks that all doses are >=0

• Checks that all r and n are positive (if variables are included in dataset)

• Checks that all y, se, r, n and E are numeric

• Checks that class codes are consistent within each agent

• Checks that agent/class names do not contain restricted characters

• Checks that studies have at least two arms (if single.arm = FALSE)

• Checks that each study includes at least two treatments

• Checks that agent names do not include underscores

• Checks that standsd values are consistent within a study

Value

An error if checks are not passed. Runs silently if checks are passed

Description

Writes JAGS code for a Bayesian time-course model for model-based network meta-analysis (MBNMA).

Usage

mbnma.write(
  fun = dpoly(degree = 1),
  method = "common",
  regress.mat = NULL,
  regress.effect = "common",
  sdscale = FALSE,
  cor = FALSE,
  cor.prior = "wishart",
  omega = NULL,
  om = list(rel = 5, abs = 10),
  class.effect = list(),
  UME = FALSE,
  likelihood = "binomial",
  link = NULL
)

Arguments

Details

When relative effects are modelled on more than one dose-response parameter and cor = TRUE, correlation between the dose-response parameters is automatically estimated using a vague Wishart prior. This prior can be made slightly more informative by specifying the relative scale of variances between the dose-response parameters using omega. cor will automatically be set to FALSE if class effects are modelled.

Value

A single long character string containing the JAGS model generated based on the arguments passed to the function.

Examples

# Write model code for a model with an exponential dose-response function,
# with random treatment effects
model <- mbnma.write(fun=dexp(),
             method="random",
             likelihood="binomial",
             link="logit"
             )
names(model) <- NULL
print(model)

# Write model code for a model with an Emax dose-response function,
# relative effects modelled on Emax with a random effects model,
# a single parameter estimated for ED50 with a common effects model
model <- mbnma.write(fun=demax(emax="rel", ed50="common"),
             likelihood="normal",
             link="identity"
             )
names(model) <- NULL
print(model)

# Write model code for a model with an Emax dose-response function,
# relative effects modelled on Emax and ED50.
# Class effects modelled on ED50 with common effects
model <- mbnma.write(fun=demax(),
             likelihood="normal",
             link="identity",
             class.effect=list("ed50"="common")
             )
names(model) <- NULL
print(model)

# Write model code for a model with an Emax dose-response function,
# relative effects modelled on Emax and ED50 with a
# random effects model that automatically models a correlation between
# both parameters.
model <- mbnma.write(fun=demax(),
             method="random",
             likelihood="normal",
             link="identity",
             )
names(model) <- NULL
print(model)

Description

Splits contributions for a given set of treatment comparisons into direct and indirect evidence. A discrepancy between the two suggests that the consistency assumption required for NMA (and subsequently MBNMA) may violated.

Usage

nma.nodesplit(
  network,
  likelihood = NULL,
  link = NULL,
  method = "common",
  comparisons = NULL,
  drop.discon = TRUE,
  ...
)

## S3 method for class 'nma.nodesplit'
plot(x, plot.type = NULL, ...)

Arguments

Details

The S3 method plot() on an nma.nodesplit object generates either forest plots of posterior medians and 95\% credible intervals, or density plots of posterior densities for direct and indirect evidence.

Value

Plots the desired graph(s) and returns an object (or list of object if plot.type=NULL) of class(c("gg", "ggplot"))

Methods (by generic)

• plot(nma.nodesplit): Plot outputs from treatment-level nodesplit models

Examples

# Using the triptans data
network <- mbnma.network(triptans)

split <- nma.nodesplit(network, likelihood = "binomial", link="logit",
  method="common")



#### To perform nodesplit on selected comparisons ####

# Check for closed loops of treatments with independent evidence sources
loops <- inconsistency.loops(network$data.ab)

# This...
single.split <- nma.nodesplit(network, likelihood = "binomial", link="logit",
             method="random", comparisons=rbind(c("sumatriptan_1", "almotriptan_1")))

#...is the same as...
single.split <- nma.nodesplit(network, likelihood = "binomial", link="logit",
             method="random", comparisons=rbind(c(6, 12)))


# Plot results
plot(split, plot.type="density") # Plot density plots of posterior densities
plot(split, plot.type="forest") # Plot forest plots of direct and indirect evidence

# Print and summarise results
print(split)
summary(split) # Generate a data frame of summary results

Description

Converts mean and variance of normal distribution to the parameters for a log-normal distribution with the same mean and variance

Usage

norm2lnorm(m, v)

Arguments

Value

A vector of length two. The first element is the mean and the second element is the variance of the log-normal distribution

Examples

norm <- rnorm(1000, mean=5, sd=2)
params <- norm2lnorm(5, 2^2)
lnorm <- rlnorm(1000, meanlog=params[1], sdlog=params[2]^0.5)

# Mean and SD of lnorm is equivalent to mean and sd of norm
mean(lnorm)
sd(lnorm)

Description

A dataset from a systematic review of interventions for pain relief in osteoarthritis, used previously in Pedder et al. (2019). The outcome is continuous, and aggregate data responses correspond to the mean WOMAC pain score at 2 weeks follow-up. The dataset includes 18 Randomised-Controlled Trials (RCTs), comparing 8 different agents with placebo. In total there were 26 different treatments (combination of dose and agent). The active treatments can also be grouped into 3 different classes, within which they have similar mechanisms of action.

Usage

osteopain

Format

A data frame in long format (one row per arm and study), with 74 rows and 7 variables:

• studyID Study identifiers

• agent Character data indicating the agent to which participants were randomised

• dose Numeric data indicating the standardised dose received

• class Character data indicating the drug class to which the agent belongs to

• y Numeric data indicating the mean pain score on the WOMAC scale in a study arm

• se Numeric data indicating the standard error for the mean pain score on the WOMAC scale in a study arm

• n Numeric data indicating the number of participants randomised

Source

Pfizer Ltd.

References

Pedder H, Dias S, Bennetts M, Boucher M, Welton NJ (2019). “Modelling time-course relationships with multiple treatments: Model-Based Network Meta-Analysis for continuous summary outcomes.” Res Synth Methods, 10(2), 267-286.

Description

Uses results from MBNMA JAGS models to calculate pD via the plugin method (Spiegelhalter et al. 2002). Can only be used for models with known standard errors or covariance matrices. Currently only functions with univariate likelihoods. Function is identical in MBNMAdose and MBNMAtime packages.

Usage

pDcalc(
  obs1,
  obs2,
  fups = NULL,
  narm,
  NS,
  theta.result,
  resdev.result,
  likelihood = "normal",
  type = "time"
)

Arguments

Details

Method for calculating pD via the plugin method proposed by Spiegelhalter (Spiegelhalter et al. 2002). Standard errors / covariance matrices must be assumed to be known. To obtain values for theta.result and resdev.result these parameters must be monitored when running the MBNMA model (using parameters.to.save).

For non-linear time-course MBNMA models residual deviance contributions may be skewed, which can lead to non-sensical results when calculating pD via the plugin method. Alternative approaches are to use pV as an approximation or pD calculated by Kullback-Leibler divergence (Plummer 2008).

Value

A single numeric value for pD calculated via the plugin method.

References

Plummer M (2008). “Penalized loss functions for Bayesian model comparison.” Biostatistics, 9(3), 523-39. ISSN 1468-4357 (Electronic) 1465-4644 (Linking), https://pubmed.ncbi.nlm.nih.gov/18209015/.

Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002). “Bayesian measures of model complexity and fit.” J R Statistic Soc B, 64(4), 583-639.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Fit a dose-response MBNMA, monitoring "psi" and "resdev"
result <- mbnma.run(network, fun=dloglin(), method="random",
              parameters.to.save=c("psi", "resdev"))


#### Calculate pD for binomial data ####

# Prepare data for pD calculation
r <- result$model$data()$r
n <- result$model$data()$n
narm <- result$model$data()$narm
NS <- result$model$data()$NS

psi <- result$BUGSoutput$median$psi
resdevs <- result$BUGSoutput$median$resdev

# Calculate pD via plugin method
pD <- pDcalc(obs1=r, obs2=n, narm=narm, NS=NS,
          theta.result=psi, resdev.result=resdevs,
          likelihood="binomial", type="dose")

Description

Generates a forest plot for dose-response parameters.

Usage

## S3 method for class 'mbnma'
plot(x, params = NULL, ...)

Arguments

Value

A forest plot of class c("gg", "ggplot") that has separate panels for different dose-response parameters. Results are plotted on the link scale.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an exponential dose-response MBNMA and generate the forest plot
exponential <- mbnma.run(network, fun=dexp())
plot(exponential)

# Plot only Emax parameters from an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")
plot(emax, params=c("emax"))


#### Forest plots including class effects ####
# Generate some classes for the data
class.df <- triptans
class.df$class <- ifelse(class.df$agent=="placebo", "placebo", "active1")
class.df$class <- ifelse(class.df$agent=="eletriptan", "active2", class.df$class)
netclass <- mbnma.network(class.df)
emax <- mbnma.run(netclass, fun=demax(), method="random",
            class.effect=list("ed50"="common"))

Description

Creates an object of class("mbnma.network"). Various MBNMA functions can subsequently be applied to this object.

Usage

## S3 method for class 'mbnma.network'
plot(
  x,
  level = "treatment",
  v.color = "connect",
  doselink = NULL,
  layout = igraph::in_circle(),
  remove.loops = FALSE,
  edge.scale = 1,
  v.scale = NULL,
  label.distance = 0,
  legend = TRUE,
  legend.x = "bottomleft",
  legend.y = NULL,
  ...
)

mbnma.network(data.ab, description = "Network")

Arguments

Details

The S3 method plot() on an mbnma.network object generates a network plot that shows how different treatments are connected within the network via study comparisons. This can be used to identify how direct and indirect evidence are informing different treatment comparisons. Depends on igraph.

Agents/classes for arms that have dose = 0 will be relabelled as "Placebo". Missing values (NA) cannot be included in the dataset. Single arm studies cannot be included.

Value

plot(): An object of class("igraph") - any functions from the igraph package can be applied to this object to change its characteristics.

mbnma.network(): An object of class("mbnma.network") which is a list containing:

• description A short description of the network

• data.ab A data frame containing the arm-level network data (treatment identifiers will have been recoded to a sequential numeric code)

• studyID A character vector with the IDs of included studies

• agents A character vector indicating the agent identifiers that correspond to the new agent codes.

• treatments A character vector indicating the treatment identifiers that correspond to the new treatment codes.

• classes A character vector indicating the class identifiers (if included in the original data) that correspond to the new class codes.

Methods (by generic)

• plot(mbnma.network): Generate a network plot

Examples

# Create an mbnma.network object from the data
network <- mbnma.network(triptans)

# Generate a network plot from the data
plot(network)

# Generate a network plot at the agent level that removes loops indicating comparisons
#within a node
plot(network, level="agent", remove.loops=TRUE)

# Generate a network plot at the treatment level that colours nodes by agent
plot(network, v.color="agent", remove.loops=TRUE)

# Generate a network plot that includes connections via the dose-response function
# For a one parameter dose-response function (e.g. exponential)
plot(network, level="treatment", doselink=1, remove.loops=TRUE)

# For a two parameter dose-response function (e.g. Emax)
plot(network, level="treatment", doselink=2, remove.loops=TRUE)

# Arrange network plot in a star with the reference treatment in the centre
plot(network, layout=igraph::as_star(), label.distance=3)

#### Plot a network with no placebo data included ####
# Make data with no placebo
noplac.df <- network$data.ab[network$data.ab$narm>2 & network$data.ab$agent!=1,]
net.noplac <- mbnma.network(noplac.df)

# Plotting network automatically plots connections to Placebo via dose-response
plot(net.noplac)
# Using the triptans headache dataset
print(triptans)

# Define network
network <- mbnma.network(triptans, description="Example network")

summary(network)
plot(network)

Description

Plots predicted responses on the natural scale from a dose-response MBNMA model.

Usage

## S3 method for class 'mbnma.predict'
plot(
  x,
  disp.obs = FALSE,
  overlay.split = FALSE,
  method = "common",
  agent.labs = NULL,
  scales = "free_x",
  ...
)

Arguments

Details

For the S3 method plot(), it is advisable to ensure predictions in predict are estimated using a sufficient number of doses to ensure a smooth predicted dose-response curve. If disp.obs = TRUE it is advisable to ensure predictions in predict are estimated using an even sequence of time points to avoid misrepresentation of shaded densities.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an Emax dose-response MBNMA and predict responses
emax <- mbnma.run(network, fun=demax(), method="random")
pred <- predict(emax, E0 = 0.5)
plot(pred)

# Display observed doses on the plot
plot(pred, disp.obs=TRUE)

# Display split NMA results on the plot
plot(pred, overlay.split=TRUE)

# Split NMA results estimated using random treatment effects model
plot(pred, overlay.split=TRUE, method="random")

# Add agent labels
plot(pred, agent.labs=c("Elet", "Suma", "Frov", "Almo", "Zolmi",
      "Nara", "Riza"))

# These labels will throw an error because "Placebo" is included in agent.labs when
#it will not be plotted as a separate panel
#### ERROR ####
#plot(pred, agent.labs=c("Placebo", "Elet", "Suma", "Frov", "Almo", "Zolmi",
#      "Nara", "Riza"))


# If insufficient predictions are made across dose-response function
# then the plotted responses are less smooth and can be misleading
pred <- predict(emax, E0 = 0.5, n.doses=3)
plot(pred)

Description

Plot histograms of rankings from MBNMA models

Usage

## S3 method for class 'mbnma.rank'
plot(x, params = NULL, treat.labs = NULL, ...)

Arguments

Value

A series of histograms that show rankings for each treatment/agent/prediction, with a separate panel for each parameter. The object returned is a list containing a separate element for each parameter in params which is an object of class(c("gg", "ggplot")).

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Estimate rankings  from an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")
ranks <- rank(emax)

# Plot rankings for both dose-response parameters (in two separate plots)
plot(ranks)

# Plot rankings just for ED50
plot(ranks, params="ed50")

# Plot rankings from prediction
doses <- list("eletriptan"=c(0,1,2,3), "rizatriptan"=c(0.5,1,2))
pred <- predict(emax, E0 = "rbeta(n, shape1=1, shape2=5)",
            exact.doses=doses)
rank <- rank(pred)
plot(rank)


# Trying to plot a parameter that has not been ranked will return an error
#### ERROR ####
# plot(ranks, params="not.a.parameter")

Description

Used for calculating treatment-level NMA results, either when comparing MBNMA models to models that make no assumptions regarding dose-response , or to estimate split results for overlay.split. Results can also be compared between consistency (UME=FALSE) and inconsistency (UME=TRUE) models to test the validity of the consistency assumption at the treatment-level.

Usage

## S3 method for class 'nma'
plot(x, bydose = TRUE, scales = "free_x", ...)

nma.run(
  network,
  method = "common",
  likelihood = NULL,
  link = NULL,
  priors = NULL,
  sdscale = FALSE,
  warn.rhat = TRUE,
  n.iter = 20000,
  drop.discon = TRUE,
  UME = FALSE,
  pd = "pd.kl",
  parameters.to.save = NULL,
  ...
)

Arguments

Functions

• plot(nma): Plot outputs from treatment-level NMA models

  Results can be plotted either as a single forest plot, or facetted by agent and plotted with increasing dose in order to identify potential dose-response relationships. If Placebo (or any agents with dose=0) is included in the network then this will be used as the reference treatment, but if it is not then results will be plotted versus the network reference used in the NMA object (x).

Examples

# Run random effects NMA on the alogliptin dataset
alognet <- mbnma.network(alog_pcfb)
nma <- nma.run(alognet, method="random")
print(nma)
plot(nma)

# Run common effects NMA keeping treatments that are disconnected in the NMA
goutnet <- mbnma.network(gout)
nma <- nma.run(goutnet, method="common", drop.discon=FALSE)

# Run an Unrelated Mean Effects (UME) inconsistency model on triptans dataset
tripnet <- mbnma.network(triptans)
ume <- nma.run(tripnet, method="random", UME=TRUE)

Description

Used to predict responses for different doses of agents or to predict the results of a new study. This is calculated by combining relative treatment effects with a given reference treatment response (specific to the population of interest).

Usage

## S3 method for class 'mbnma'
predict(
  object,
  n.doses = 30,
  exact.doses = NULL,
  E0 = 0.2,
  synth = "fixed",
  lim = "cred",
  regress.vals = NULL,
  ...
)

Arguments

Details

The range of doses on which to make predictions can be specified in one of two ways:

1. Use max.dose and n.doses to specify the maximum dose for each agent and the number of doses within that agent for which to predict responses. Doses will be chosen that are equally spaced from zero to the maximum dose for each agent. This is useful for generating plots of predicted responses (using ⁠[plot-mbnma.predict]⁠) as it will lead to fitting a smooth dose-response curve (provided n.doses is sufficiently high).

2. Use exact.doses to specify the exact doses for which to predict responses for each agent. This may be more useful when ranking different predicted responses using ⁠[rank-mbnma.predict]⁠

Value

An S3 object of class mbnma.predict that contains the following elements:

• predicts A named list of matrices. Each matrix contains the MCMC results of predicted responses at follow-up times specified in times for each treatment specified in treats

• likelihood The likelihood used in the MBNMA model object

• link The link function used in the MBNMA model object

• network The dataset in mbnma.network format

• E0 A numeric vector of value(s) used for E0 in the prediction, on the link scale.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Run an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")


###########################
###### Specifying E0 ######
###########################

#### Predict responses using deterministic value for E0 ####
# Data is binomial so we specify E0 on the natural scale as a probability
pred <- predict(emax, E0 = 0.2)

# Specifying non-sensical values will return an error
#pred <- predict(emax, E0 = -10)
### ERROR ###

#### Predict responses using stochastic value for E0 ####
# Data is binomial so we might want to draw from a beta distribution
pred <- predict(emax, E0 = "rbeta(n, shape1=1, shape2=5)")

# Misspecifying the RNG string will return an error
#pred <- predict(emax, E0 = "rbeta(shape1=1, shape2=5)")
### ERROR ###


#### Predict responses using meta-analysis of dose = 0 studies ####

# E0 is assigned a data frame of studies to synthesis
# Can be taken from placebo arms in triptans dataset
ref.df <- network$data.ab[network$data.ab$agent==1,]

# Synthesis can be fixed/random effects
pred <- predict(emax, E0 = ref.df, synth="random")



######################################################################
#### Specifying which doses/agents for which to predict responses ####
######################################################################

# Change the number of predictions for each agent
pred <- predict(emax, E0 = 0.2, n.doses=20)
pred <- predict(emax, E0 = 0.2, n.doses=3)

# Specify several exact combinations of doses and agents to predict
pred <- predict(emax, E0 = 0.2,
            exact.doses=list("eletriptan"=c(0:5), "sumatriptan"=c(1,3,5)))
plot(pred) # Plot predictions

# Print and summarise `mbnma.predict` object
print(pred)
summary(pred)

# Plot `mbnma.predict` object
plot(pred)

Description

Print mbnma.network information to the console

Usage

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

Arguments

Description

Print summary information from an mbnma.predict object

Usage

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

Arguments

Description

Prints summary information about an mbnma.rank object

Usage

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

Arguments

Description

Prints summary results from an nma.nodesplit object

Usage

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

Arguments

Description

Prints summary results from a nodesplit object

Usage

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

Arguments

Description

Print posterior medians (95% credible intervals) for table of relative effects/mean differences between treatments/classes

Usage

## S3 method for class 'relative.array'
print(x, digits = 2, ...)

Arguments

Description

A dataset from a systematic review of Randomised-Controlled Trials (RCTs) comparing biologics at different doses and placebo (Warren et al. 2019). The outcome is the number of patients experiencing 100% improvement on the Psoriasis Area and Severity Index (PASI) measured at 12 weeks follow-up. The dataset includes 19 Randomised-Controlled Trials (RCTs), comparing 8 different biologics at different doses with placebo.

Usage

psoriasis100

Format

A data frame in long format (one row per arm and study), with 81 rows and 9 variables:

• studyID Study identifiers

• agent Character data indicating the agent to which participants were randomised

• dose_mg Numeric data indicating the dose to which participants were randomised in mg

• freq Character data indicating the frequency of the dose to which participants were randomised

• dose Numeric data indicating the dose in mg/week to which the participants were randomised

• n Numeric data indicating the number of participants randomised

• r Numeric data indicating the number of participants who achieved 100% improvement in PASI score after 12 weeks

References

Warren RB, Gooderham M, Burge R, Zhu B, Amato D, Liu KH, Shrom D, Guo J, Brnabic A, Blauvelt A (2019). “Comparison of cumulative clinical benefits of biologics for the treatment of psoriasis over 16 weeks: Results from a network meta-analysis.” J Am Acad Dermatol, 82(5), 1138-1149.

Description

A dataset from a systematic review of Randomised-Controlled Trials (RCTs) comparing biologics at different doses and placebo (Warren et al. 2019). The outcome is the number of patients experiencing >=75% improvement on the Psoriasis Area and Severity Index (PASI) measured at 12 weeks follow-up. The dataset includes 28 Randomised-Controlled Trials (RCTs), comparing 9 different biologics at different doses with placebo.

Usage

psoriasis75

Format

A data frame in long format (one row per arm and study), with 81 rows and 9 variables:

• studyID Study identifiers

• agent Character data indicating the agent to which participants were randomised

• dose_mg Numeric data indicating the dose to which participants were randomised in mg

• freq Character data indicating the frequency of the dose to which participants were randomised

• dose Numeric data indicating the dose in mg/week to which the participants were randomised

• n Numeric data indicating the number of participants randomised

• r Numeric data indicating the number of participants who achieved >=75% improvement in PASI score after 12 weeks

References

Warren RB, Gooderham M, Burge R, Zhu B, Amato D, Liu KH, Shrom D, Guo J, Brnabic A, Blauvelt A (2019). “Comparison of cumulative clinical benefits of biologics for the treatment of psoriasis over 16 weeks: Results from a network meta-analysis.” J Am Acad Dermatol, 82(5), 1138-1149.

Description

A dataset from a systematic review of Randomised-Controlled Trials (RCTs) comparing biologics at different doses and placebo (Warren et al. 2019). The outcome is the number of patients experiencing >=90% improvement on the Psoriasis Area and Severity Index (PASI) measured at 12 weeks follow-up. The dataset includes 24 Randomised-Controlled Trials (RCTs), comparing 9 different biologics at different doses with placebo.

Usage

psoriasis90

Format

A data frame in long format (one row per arm and study), with 81 rows and 9 variables:

• studyID Study identifiers

• agent Character data indicating the agent to which participants were randomised

• dose_mg Numeric data indicating the dose to which participants were randomised in mg

• freq Character data indicating the frequency of the dose to which participants were randomised

• dose Numeric data indicating the dose in mg/week to which the participants were randomised

• n Numeric data indicating the number of participants randomised

• r Numeric data indicating the number of participants who achieved >=90% improvement in PASI score after 12 weeks

References

Warren RB, Gooderham M, Burge R, Zhu B, Amato D, Liu KH, Shrom D, Guo J, Brnabic A, Blauvelt A (2019). “Comparison of cumulative clinical benefits of biologics for the treatment of psoriasis over 16 weeks: Results from a network meta-analysis.” J Am Acad Dermatol, 82(5), 1138-1149.

Description

Set rank as a method

Usage

rank(x, ...)

Arguments

Description

Only parameters that vary by agent/class can be ranked.

Usage

## S3 method for class 'mbnma'
rank(
  x,
  params = NULL,
  lower_better = TRUE,
  level = "agent",
  to.rank = NULL,
  ...
)

Arguments

Details

Ranking cannot currently be performed on non-parametric dose-response MBNMA

Value

An object of class("mbnma.rank") which is a list containing a summary data frame, a matrix of rankings for each MCMC iteration, a matrix of probabilities that each agent has a particular rank, and a matrix of cumulative ranking probabilities for each agent, for each parameter that has been ranked.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Rank selected agents from a log-linear dose-response MBNMA
loglin <- mbnma.run(network, fun=dloglin())
ranks <- rank(loglin, to.rank=c("zolmitriptan", "eletriptan", "sumatriptan"))
summary(ranks)

# Rank only ED50 parameters from an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")
ranks <- rank(emax, params="ed50")
summary(ranks)


#### Ranking by class ####
# Generate some classes for the data
class.df <- triptans
class.df$class <- ifelse(class.df$agent=="placebo", "placebo", "active1")
class.df$class <- ifelse(class.df$agent=="eletriptan", "active2", class.df$class)
netclass <- mbnma.network(class.df)
emax <- mbnma.run(netclass, fun=demax(), method="random",
            class.effect=list("ed50"="common"))

# Rank by class, with negative responses being worse
ranks <- rank(emax, level="class", lower_better=FALSE)
print(ranks)

# Print and generate summary data frame for `mbnma.rank` object
summary(ranks)
print(ranks)

# Plot `mbnma.rank` object
plot(ranks)

Description

Ranks predictions at different doses from best to worst.

Usage

## S3 method for class 'mbnma.predict'
rank(x, lower_better = TRUE, rank.doses = NULL, ...)

Arguments

Details

If predict contains multiple predictions at dose=0, then only the first of these will be included, to avoid duplicating rankings.

Value

An object of class("mbnma.rank") which is a list containing a summary data frame, a matrix of rankings for each MCMC iteration, and a matrix of probabilities that each agent has a particular rank, for each parameter that has been ranked.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Rank all predictions from a log-linear dose-response MBNMA
loglin <- mbnma.run(network, fun=dloglin())
pred <- predict(loglin, E0 = 0.5)
rank <- rank(pred)
summary(rank)

# Rank selected predictions from an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")
doses <- list("eletriptan"=c(0,1,2,3), "rizatriptan"=c(0.5,1,2))
pred <- predict(emax, E0 = "rbeta(n, shape1=1, shape2=5)",
            exact.doses=doses)
rank <- rank(pred,
            rank.doses=list("eletriptan"=c(0,2), "rizatriptan"=2))

# Print and generate summary data frame for `mbnma.rank` object
summary(rank)
print(rank)

# Plot `mbnma.rank` object
plot(rank)

Description

Ranks "relative.table" objects generated by get.relative().

Usage

## S3 method for class 'relative.array'
rank(x, lower_better = TRUE, ...)

Arguments

Value

An object of class("mbnma.rank") which is a list containing a summary data frame, a matrix of rankings for each MCMC iteration, and a matrix of probabilities that each agent has a particular rank, for each parameter that has been ranked.

Examples

# Using the triptans data
network <- mbnma.network(triptans)

# Rank selected predictions from an Emax dose-response MBNMA
emax <- mbnma.run(network, fun=demax(), method="random")
rels <- get.relative(emax)
rank <- rank(rels, lower_better=TRUE)

# Print and generate summary data frame for `mbnma.rank` object
summary(rank)
print(rank)

# Plot `mbnma.rank` object
plot(rank)

Description

Assigns agent or class variables numeric identifiers

Usage

recode.agent(data.ab, level = "agent")

Arguments

Details

Also relabels the agent for any arms in which dose = 0 to "Placebo_0"

Value

A list containing a data frame with recoded agent/class identifiers and a character vector of original agent/class names

Description

Synthesises single arm studies to estimate E0. Used in predicting responses from a dose-response MBNMA.

Usage

ref.synth(
  data.ab,
  mbnma,
  synth = "fixed",
  n.iter = mbnma$BUGSoutput$n.iter,
  n.burnin = mbnma$BUGSoutput$n.burnin,
  n.thin = mbnma$BUGSoutput$n.thin,
  n.chains = mbnma$BUGSoutput$n.chains,
  ...
)