Exploring the data"
In MBNMAtime: Run Time-Course Model-Based Network Meta-Analysis (MBNMA) Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5,
  warning = FALSE,
  eval=rmarkdown::pandoc_available("1.12.3")
)

library(MBNMAtime)
library(rmarkdown)
library(knitr)
library(dplyr)
#load(system.file("extdata", "vignettedata.rda", package="MBNMAtime", mustWork = TRUE))

Inspecting the data

Before embarking on an analysis, the first step is to have a look at the raw data. Two features (network connectivity and time-course relationship) are particularly important for MBNMA. To investigate these we must first get our dataset into the right format for the package. We can do this using mb.network(). This requires specifying the desired treatment to use for the network reference treatment, though one will automatically be specified if not given.

# Using the pain dataset
network.pain <- mb.network(osteopain, reference = "Pl_0")
print(network.pain)

This takes a dataset with the columns:

studyID Study identifiers
time Numeric data indicating continuous follow-up times (e.g. days, weeks, months)
y Numeric data indicating the mean response for a given observation
se Numeric data indicating the standard error for a given observation
treatment Treatment identifiers (can be numeric, factor or character)
class An optional column indicating a particular class that may be shared by several treatments.
N An optional column indicating the number of participants used to calculate the response at a given observation.

Additional columns can be included in the dataset. These will simply be added to the mb.network object, though will not affect the classification of the data.

mb.network then performs the following checks on the data:

The dataset has the required column names
There are no missing values
All standard errors (SE) are positive
Observations are made at the same time points in all arms of a study (i.e. the data are balanced)
Class labels are consistent within each treatment
Studies have at least two arms

Unless otherwise specified, mb.network() will automatically determine whether each study in the dataset is reported as change from baseline or absolute - studies that include a measurement at time=0 are assumed to report absolute values, whilst those with no measurement at time=0 are assumed to be change from baseline. This can also be explicitly specified by the user by including a logical vector for the argument cfb in mb.network() - TRUE indicates a study reports change from baseline, and FALSE indicates that it reports absolute values.

Finally, mb.network() converts the data into an object of class("mb.network"), which contains indices for study arms and follow-up measurements, and generates numeric values for treatments and classes. By convention, treatments are numbered alphabetically, though if the original data for treatments is provided as a factor then the factor codes will be used. This then contains all the necessary information for subsequent MBNMAtime functions.

Network connectivity

Looking at how the evidence in the network is connected and identifying which studies compare which treatments helps to understand which treatment effects can be estimated and what information will be helping to inform those estimates. A network plot can be generated which shows which treatments have been compared in head-to-head trials. Typically the thickness of connecting lines ("edges") is proportional to the number of studies that make a particular comparison and the size of treatment nodes ("vertices") is proportional to the total number of patients in the network who were randomised to a given treatment (provided N is included as a variable in the original dataset for mb.network()).

In MBNMAtime these plots are generated using igraph, and can be plotted by calling plot(). The generated plots are objects of class("igraph") meaning that, in addition to the options specified in plot(), various igraph functions can be used to make more detailed edits to them.

# Prepare data using the alogliptin dataset
network.alog <- mb.network(alog_pcfb, reference = "placebo")

# Plot network
plot(network.alog)

Within these network plots, treatments are automatically aligned in a circle (as the default) and can be tidied by shifting the label distance away from the nodes.

# Draw network plot in a star layout using the gout dataset
network.gout <- mb.network(goutSUA_CFB, reference = "Plac")
plot(network.gout, layout=igraph::as_star(), label.distance = 5)

# Draw network plot in a star layout using the gout dataset
network.gout <- mb.network(goutSUA_CFB, reference = "Plac")
plot(network.gout, layout=igraph::as_star(), label.distance = 5)

This command returns a warning stating that some treatments are not connected to the network reference treatment through any pathway of head-to-head evidence. The nodes that are coloured white represent these treatments. This means that it will not be possible to estimate relative effects for these treatments versus the network reference treatment (or any treatments connected to it). Several options exist to allow for inclusion of these treatments in an analysis which we will discuss in more detail later, but one approach is to assume a shared effect among treatments within the same class/agent. We can generate a network plot at the class level to examine this more closely, and can see that the network is connected at the class level.

plot(network.gout, level = "class", remove.loops = TRUE, label.distance = 5)

suppressWarnings(plot(network.gout, level = "class", remove.loops = TRUE, label.distance = 5))

It is also possible to plot a network at the treatment level but to colour the treatments by the class that they belong to.

plot(network.gout, level = "treatment", v.color = "class", label.distance = 5)

suppressWarnings(plot(network.gout, level = "treatment", v.color = "class", label.distance = 5))

Examining the time-course relationship

In order to consider which functional forms may be appropriate for modelling the time-course relationship, it is important to look at the responses in each arm plotted over time. This can easily be done using the timeplot() function on an object of class("mb.network")

# Prepare data using the pain dataset
network.pain <- mb.network(osteopain, reference="Pl_0")

# Draw plot of raw study responses over time
timeplot(network.pain)

As the mean response for all treatments shows a rapid reduction in pain score followed by a levelling out after 2-5 weeks, an Integrated Two-component Prediction (ITP) time-course function might be a reasonable fit for this dataset. More complex alternatives could be Emax models (with or without a Hill parameter), fractional polynomials or a spline function.

Responses can also be plotted grouped by class rather than by treatment, and the relative effects between each treatment/class can be plotted instead of the absolute treatment responses. Since the MBNMA framework models the time-course on relative effects [@pedder2019] this can in fact make interpretation of the plots easier with regards to identifying a best-fitting time-course function.

# Draw plot of within-study relative effects over time grouped by class
network.gout <- mb.network(goutSUA_CFBcomb)
timeplot(network.gout, level="class", plotby="rel")

Many of the profiles here appear to be quite different within the same class, which would suggest modelling class effects may be inappropriate for this dataset.

Another approach to investigate the time-course relationship is to perform several standard "lumped" NMAs at different time "bins", time periods within which we are assuming treatment effects are constant over time. This means that, for the purposes of this plot, rather than considering time as a continuous variable it is chunked up into segments.

We can do this within a single plot using binplot() and specifying the boundaries of multiple time bins. Separate NMAs are then performed within each time bin on data points from studies that fall within the time bin (only a single follow-up time is taken from each study to avoid double counting). "fixed" or "random" effects can be specified for the NMA. Note that the wider the time bin boundaries specified by the user, the larger the potential range of included follow-up times and this can introduce heterogeneity or inconsistency.

# Plot results for NMAs performed between 0-5, 5-10, 10-15 and 15-26 weeks
binplot(network.pain, overlay.nma=c(0,5,10,15,26))

Results are plotted versus the network reference and are plotted on the relevant scale depending on the function specified in link (in this case "identity" - i.e. mean differences versus Pl_0 are shown). Each time bin window is marked on the plot by vertical dashed lines. The NMA estimates within each time bin are plotted as a horizontal solid black line (the posterior median) with a shaded region indicating the 95% credible interval (prediction intervals can instead be plotted). The width of these shaded regions is equal to the range of study time-points included in the NMA performed within that time-bin, which may therefore be more narrow than the time bin specified in the binplot() command due to the follow-up times at which data is available in included studies. For example, for the time bin between 10-15 weeks, studies from the dataset included in this time bin have follow-ups between 12-13 weeks.

From this plot we can see that, whilst there clearly is a rapid onset of treatment efficacy within the first 5 weeks, indicated by a treatment effect \<0 for most treatments. This treatment effect then persists and remains more or less constant for some treatments within later time bins, though for others (e.g. Ce_200, Ro_25, Na_1000, Na_1500, Va_10) there appears to be a loss of efficacy for later time bins, suggesting a more complex time-course function may be required to fully capture this relationship.