Estimand
Single-arm meta-analysis estimates an outcome within one group. It can summarize a proportion, incidence rate, or raw mean across studies. It does not compare an intervention with a comparator and therefore does not estimate comparative effectiveness.
This distinction matters. A high pooled response rate, a low incidence rate, or a favorable pooled mean in single-arm studies does not prove that an intervention caused the outcome. Background prognosis, participant selection, follow-up duration, measurement definitions, and study design can all affect the observed value.
Proportion model
Each study supplies events x_i and denominator n_i. The observed proportion is p_i = x_i / n_i. Near 0 or 1, normal approximations on the raw proportion scale can behave poorly.
The R service uses meta::metaprop with method GLMM and summary measure PLOGIT for single-arm proportions. The logit transformation is logit(p) = log(p / (1 - p)); back-transformation uses expit(z) = exp(z) / (1 + exp(z)).
For GLMM proportion meta-analysis, Coventra forces method.tau to ML because the underlying method requires it. If another tau method is requested, the service records a warning and uses ML.
Incidence rate model
A single-arm incidence rate uses events and person-time. The raw rate is r_i = events_i / time_i. When reported on a log scale, log(rate_i) = log(events_i / time_i), with approximate SE about 1 / sqrt(events_i) when events are positive.
Coventra uses meta::metarate with method GLMM, summary measure IRLN, method.tau ML, and classic random-effects confidence intervals for the single-arm rate path.
- Person-time units must be consistent or converted before synthesis.
- First events and recurrent events should not be mixed without a clear model and interpretation.
- Follow-up definitions and event ascertainment should be comparable across studies.
- A rate is not a risk; it depends on time at risk.
Raw mean model
A single-arm raw mean synthesis uses n_i, mean_i, and sd_i. The approximate within-study variance is sd_i^2 / n_i.
Coventra uses meta::metamean with summary measure MRAW for raw means. The default tau estimator follows the selected method_tau setting, REML by default.
The interpretation depends on whether studies use the same measurement instrument, unit, timing, and population. If studies use different scales, a raw mean is usually not meaningful without transformation or standardization.
Changeable settings
- Users choose single-arm analysis before extraction.
- Binary single-arm outcomes use proportion as the effect measure.
- Continuous single-arm outcomes can use mean or rate, depending on whether extraction records mean/SD/N or events/person-time.
- Tau estimator is changeable for raw mean synthesis. Proportion and rate GLMM paths use ML where required by the underlying model.
- Common/random display, confidence level, HKSJ setting where compatible, prediction display, subgroup fields, and plot options can be changed.
- Funnel and trim-and-fill outputs are available but carry single-arm interpretation warnings.
Single-arm method-source profiles
Single-arm workflows default to Recommended settings. They explicitly send GLMM/logit proportion, GLMM/log-rate, or raw-mean REML settings and record any HK rule applied to raw means. Native meta 8.5-0 defaults remain available as an advanced reproducibility option; package-default mode omits supported package-controlled arguments and records the effective method, tau estimator, confidence-interval method, package, and version.
Manual mode is available for raw-mean tau and Hartung-Knapp selection. Manual proportion and rate controls remain unavailable until the complete compatible GLMM parameter set is exposed.
Heterogeneity and prediction intervals
Single-arm studies often have high heterogeneity because they are not protected by a common comparator. Differences in population, setting, diagnostic criteria, follow-up, and measurement can dominate the pooled estimate.
Prediction intervals can be especially useful because they describe expected dispersion of true effects across settings. However, prediction intervals require enough studies to estimate between-study variance meaningfully.
Interpretation limits
- A pooled response rate does not prove treatment effect.
- Different follow-up windows or event definitions can make a pooled proportion uninterpretable.
- Different person-time units or recurrent-event definitions can make pooled rates uninterpretable.
- Different measurement instruments, units, or timepoints can make pooled raw means uninterpretable.
- High heterogeneity is common because there is no comparator arm to absorb baseline-risk differences.
- Funnel asymmetry can reflect prevalence and denominator patterns rather than publication bias.
Reporting checklist
- Report event definition, denominator, and follow-up window.
- For rates, report event definition, person-time unit, and whether recurrent events were counted.
- For means, report scale, unit, timepoint, SD, N, and whether medians were converted.
- Report GLMM/logit transformation and back-transformed pooled proportion.
- Report transformation/back-transformation for rates and proportions where used.
- Report heterogeneity and prediction interval where used.
- Avoid causal language unless supported by separate comparative evidence.