Direct evidence plot

Network measures plot

NMA

For each comparison, the proportion of direct evidence, the mean length of the paths that contribute, and the minimal parallelism.

NMASpecialized

Direct evidence proportion, mean path length, and minimal parallelism for the random-effects network estimates against placebo in the diabetes network. Data: netmeta::Senn2013.

Family

Network geometry and evidence flow

Purpose

Summarize how direct, indirect, and robust each network estimate is.

Inputs

A fitted network meta-analysis.

Software

R netmeta::netmeasures() with ggplot2; older netmeta::direct.evidence.plot()

What it shows

König, Krahn, and Binder proposed three measures per network estimate. The direct evidence proportion is the share of the estimate’s information that comes from head-to-head trials. The mean path length is the average length of the paths through which evidence flows; long paths mean the estimate relies on long indirect chains. Minimal parallelism is the smallest amount of evidence along parallel paths, a measure of how robust the estimate is to the failure of a single path.

How to read it

Rows: network estimates (here against placebo).
Direct evidence proportion: 1 means entirely direct, 0 entirely indirect.
Mean path length: 1 for purely direct estimates; larger is more indirect.
Minimal parallelism: larger values indicate more independent support.

Interpretation

Four comparisons (sitagliptin, vildagliptin, miglitol, benfluorex) are informed only by direct evidence, with a mean path length of 1 and little parallelism. Pioglitazone relies mostly on indirect evidence, and sulfonylurea versus placebo is entirely indirect with the longest mean path. Those are the estimates most exposed to intransitivity.

Pitfalls

A high direct proportion is not a guarantee of validity; direct trials can be biased too.
The measures depend on the model’s weights and heterogeneity.

Code

library(netmeta)
library(ggplot2)

data(Senn2013)

net <- netmeta(
  TE, seTE, treat1.long, treat2.long, studlab,
  data = Senn2013, sm = "MD",
  common = FALSE, reference.group = "Placebo"
)

# Network measures per comparison: proportion of direct evidence,
# mean path length, and minimal parallelism
nm <- netmeasures(net, random = TRUE)
d <- data.frame(comparison = names(nm$proportion),
                `Direct evidence proportion` = nm$proportion,
                `Mean path length` = nm$meanpath,
                `Minimal parallelism` = nm$minpar,
                check.names = FALSE)
d <- d[grepl("Placebo", d$comparison), ]
d$comparison <- factor(d$comparison, levels = d$comparison[order(d$`Direct evidence proportion`)])
long <- tidyr::pivot_longer(d, -comparison, names_to = "measure")

ggplot(long, aes(value, comparison)) +
  geom_col(fill = "#9fb3c8", colour = "#1d4e89", width = 0.7) +
  facet_wrap(~ measure, scales = "free_x") +
  labs(x = NULL, y = NULL, title = "Direct evidence plot",
       subtitle = "Comparisons with placebo in the diabetes network") +
  theme(panel.grid.major.y = element_blank())

References

König J, Krahn U, Binder H. Visualizing the flow of evidence in network meta-analysis and characterizing mixed treatment comparisons. Stat Med. 2013;32:5414-5429. doi:10.1002/sim.6001