Meta-Analysis: Single-Arm Proportion

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Pools a single proportion or mean across studies that have no comparison group (single-arm meta-analysis).

Combines one-group estimates — an event rate, prevalence, or mean — across studies, common for prevalence / incidence or uncontrolled outcomes.

Worked example

What is the pooled prevalence of a condition across studies?

22 prevalence studies were pooled with a random-effects single-arm meta-analysis (logit-transformed proportions).

Result

Pooled prevalence was 15% (95% CI [13%, 17%]) with substantial heterogeneity (I² = 76%).

How you'd report it (APA)

The pooled prevalence was 15%, 95% CI [13%, 17%] (I² = 76%).

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Uncontrolled outcomes across studies
    Each study reports one group with no comparator. e.g. pooling prevalence of a condition, or a complication rate across case series.
  • Prevalence or incidence synthesis
    The question is 'how common is it', not 'does A beat B'.
  • Pooling a mean with no control
    e.g. an average biomarker level across single-arm studies.

When NOT to — use instead

  • Studies have a comparison group
    If each study contrasts two arms, pool the contrast — you keep within-study randomisation and lose far less to confounding. → Random-effects meta-analysis
  • You want to compare interventions
    Single-arm pooling across studies is confounded by between-study differences; a comparative or network model is needed. → Random-effects meta-analysis

Hypotheses

Single-arm meta-analysis is an estimation, not a null-test, task: there is no comparison group and so no default H₀ of 'no effect'. A heterogeneity test still applies — H₀: all studies share the same underlying proportion/mean.
The reported result is the pooled one-group parameter with its CI (and, in a random-effects fit, a prediction interval), not a p-value against zero.

Parameter tested: the pooled single-group estimate — a proportion (usually logit-transformed then back-transformed), incidence rate, or mean — with between-study heterogeneity (Q, I², τ²)

Assumptions (and what to do if they fail)

Studies define the outcome the same wayhigh

Check: The event or measurement is operationalised consistently across studies.

If violated: The pooled proportion mixes different things; heterogeneity balloons and the estimate is not interpretable.

Appropriate transform for proportionsmedium

Check: Proportions are pooled on a transformed scale (logit or Freeman-Tukey) to stabilise variance near 0 and 1, then back-transformed.

If violated: Pooling raw proportions mis-weights studies with rates near 0% or 100%.

Heterogeneity is expected and reportedmedium

Check: Single-arm syntheses are typically highly heterogeneous (no randomisation to cancel confounders); report I² and a prediction interval.

If violated: A tight CI around a pooled prevalence with I² = 80% is misleading — the prediction interval tells the real story.

No comparative claim is drawnmedium

Check: Results describe one group; any implicit comparison to another study's arm is confounded.

If violated: Cross-study comparisons of single arms invite exactly the bias controlled trials exist to avoid.

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