Toolkit · 03 of 13

Single-arm: binary outcomes

Pooled proportions, such as complication rates, without a comparison group.

What it is

When the studies have no comparison group (case series, single-arm cohorts), the question is not which treatment is better but how often something happens: the complication rate, the success rate of a procedure. Each study contributes its number of events and its number of patients.

Proportions close to 0% or 100% have skewed, bounded distributions, so they are not pooled as they are. They are pooled on a transformed scale, most often the logit, and transformed back, or modeled directly on the binomial counts with a GLMM.

The result is a pooled proportion with its 95% confidence interval. Heterogeneity is usually high in single-arm meta-analyses, because populations, definitions and follow-up differ from series to series.

Worked exampleOne series, then six

	Events	Patients	Proportion
One series	6	20	30%

logit = ln(0.30 ÷ 0.70) = −0.85the scale on which the series are combinedSix series pooled: 15% (7%-30%)transformed back to a proportion

Postoperative ileus after the Deloyers procedure, from one of my reviews.

When to use it

Use it when

The studies are case series or single-arm cohorts, with no comparison group.
The outcome is an event: complication, recurrence, conversion, success of the procedure.
The question is how often it happens, to counsel patients or to set a benchmark for a new technique.

Choose another tool when

Some studies compare two interventions: use pairwise binary outcomes with those studies.
You want to compare two techniques using separate case series: pooled rates from different series are confounded by everything else that differs between them.
The outcome is a measurement: use single-arm continuous outcomes.

The template, parameter by parameter

Click a highlighted argument to see what it does and which values to use. Picking a value updates the code.

p <- metaprop(event = events, n = total,
              studlab = study, data = dat,
               = "PLOGIT",
               = "GLMM",
               = FALSE,  = TRUE)

# forest plot: see section 4

The forest plot, parameter by parameter

These arguments change only how the result is shown, not the result itself. Click one to see the options.

png("forest.png", width = 5500, height = 1100 + 170 * p$k, res = 500)
forest(p,
        = studlab,
        = 1,
        = c(0, 1),
        = "navyblue",
        = "black",
        = 2,
       xlab = "Proportion")
dev.off()

In my work

Figures from my published single-arm review, next to the metaprop() call behind them. Click a figure to enlarge it.

Postoperative ileusPooled proportion, 6 case series. From Colorectal Dis, 2025 ↗

p <- metaprop(
  event = e, n = n,       # events and total, one arm
  data = dat,             # one row per study
  studlab = Study,        # study names
  sm = "PLOGIT",          # logit transformation
  method = "Inverse"      # inverse variance
)

Anastomotic leakagePooled proportion, 11 case series, most with zero events. From Colorectal Dis, 2025 ↗

p <- metaprop(
  event = e, n = n,       # events and total, one arm
  data = dat,             # one row per study
  studlab = Study,        # study names
  sm = "PFT",             # Freeman-Tukey: many zeros
  method = "Inverse"      # inverse variance
)

References

Higgins JPT, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane; 2024. Chapter 10 (analysing data).
Barker TH, Migliavaca CB, Stein C, et al. Conducting proportional meta-analysis in different types of systematic reviews: a guide for synthesisers of evidence. BMC Med Res Methodol. 2021;21:189.
Stijnen T, Hamza TH, Özdemir P. Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Stat Med. 2010;29:3046-3067.
Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rücker G. Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions. Res Synth Methods. 2019;10:476-483.
Lin L, Chu H. Meta-analysis of proportions using generalized linear mixed models. Epidemiology. 2020;31:713-717.
Balduzzi S, Rücker G, Schwarzer G. How to perform a meta-analysis with R: a practical tutorial. Evid Based Ment Health. 2019;22:153-160.