Toolkit · 01 of 13

Pairwise: binary outcomes

Risk and odds ratios for events such as complications or mortality.

What it is

Every patient in every trial answers the same yes-or-no question: did the event happen? Inside one trial, that gives a simple 2×2 table, with events and non-events in each arm.

Each table is turned into one number that compares the arms, most often the risk ratio: the risk with the intervention divided by the risk with the control. The meta-analysis then combines these numbers across trials, giving more weight to larger and more informative trials.

The result is one pooled effect with its 95% confidence interval, and a measure of how much the trials disagree with each other (heterogeneity).

Worked exampleOne trial, step by step

	Event	No event	Risk
Intervention	12	88	12%
Control	20	80	20%

RR = 12% ÷ 20% = 0.6040% lower risk with the interventionRD = 12% − 20% = −8 pointsabout 1 event avoided per 13 patients treated

Repeat for every trial, then pool: that is the meta-analysis.

When to use it

Use it when

The outcome is an event that either happens or does not: complication, transfusion, recurrence, mortality, conversion to open surgery.
You are comparing two groups, such as a new technique against the standard one.
Each study reports how many patients had the event, and how many patients there were, in each group.

Choose another tool when

The outcome is a measurement (minutes, days, a score): use continuous outcomes.
Follow-up time differs a lot between patients and timing matters, as in survival: use time-to-event methods.
There is no comparison group, only case series: use single-arm binary 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.

m <- metabin(event.e = ev_int, n.e = n_int,
             event.c = ev_ctl, n.c = n_ctl,
             studlab = study, data = dat,
              = "RR",
              = "MH",
              = "REML",
              = 0.5,  = "only0",
              = FALSE,
              = FALSE,  = TRUE,
              = FALSE,
             label.e = "Intervention", label.c = "Control")

m <- update(m,
             = if (m$tau2 > 0) "HK" else "classic")

# 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.

("forest.png", width = 5500, height = 1100 + 170 * m$k,  = 500)
forest(m,
        = "RevMan5",
        = studlab,
        = c(0.1, 10),
        = "navyblue",
        = "black",
        = TRUE,
        = 2,
       label.left = "Favors intervention",
       label.right = "Favors control",
       colgap.forest.left = "7mm")
()

In my work

Figures from my published reviews, next to the metabin() call behind them. These analyses used the Wald confidence interval: when they were done, Cochrane had not yet recommended switching to Hartung-Knapp when tau² > 0. Click a figure to enlarge it.

Need for red blood cell transfusionRisk ratio, 14 trials. From JAMA Surg, 2026 ↗

m <- metabin(
  e.e, n.e, e.c, n.c,           # events/totals per arm
  data = dat,                   # one row per study
  studlab = Study,              # study names
  sm = "RR",                    # risk ratio
  method = "MH",                # Mantel-Haenszel
  method.tau = "DL",            # DerSimonian-Laird tau²
  method.random.ci = "classic"  # Wald CI
)

ReoperationOdds ratio, 5 studies. From Tech Coloproctol, 2026 ↗

m <- metabin(
  e.e, n.e, e.c, n.c,           # events/totals per arm
  data = dat,                   # one row per study
  studlab = Study,              # study names
  sm = "OR",                    # odds ratio
  method = "MH",                # Mantel-Haenszel
  method.tau = "REML",          # tau², REML
  method.random.ci = "classic"  # Wald CI
)

References

Higgins JPT, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane; 2024. Chapter 6 (effect measures) and Chapter 10 (analysing data).
Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst. 1959;22:719-748.
Veroniki AA, Jackson D, Viechtbauer W, et al. Methods to estimate the between-study variance and its uncertainty in meta-analysis. Res Synth Methods. 2016;7:55-79.
IntHout J, Ioannidis JPA, Borm GF. The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method. BMC Med Res Methodol. 2014;14:25.
Riley RD, Higgins JPT, Deeks JJ. Interpretation of random effects meta-analyses. BMJ. 2011;342:d549.
Sweeting MJ, Sutton AJ, Lambert PC. What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. Stat Med. 2004;23:1351-1375.
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.