Single-arm meta-analysis
Pooling a proportion or a mean, with no comparison group
Use this module when there is no comparison: you want the pooled prevalence of a condition, the complication rate of a procedure, or the average value of a measure in a population. Follow the three-step flow, with a much shorter step 2, because without a control group several fields stop making sense.
Step 1, the data
Two submodules, chosen on the previous page.
Single proportions
| Column | What it is |
|---|---|
study |
the study label |
event |
number of participants with the outcome |
n |
sample size of the arm |
Single means
| Column | What it is |
|---|---|
study |
the study label |
n |
sample size |
mean |
mean value of the outcome |
sd |
standard deviation of the outcome |
A study reporting a median is accepted too
| Column | What it is |
|---|---|
study, n |
as above |
median, q1, q3 |
median and quartiles of the outcome |
min and max are optional. They can stand in for the quartiles when a paper reports only a range, and the conversion is then less precise.
A median with sd and nothing else is refused, and on purpose. A median cannot be turned into a mean without the quartiles or the range, and meta does not complain about it: it drops the study from the pooling with no message. Better to hear it here than to publish a review missing studies you never knew were excluded.
The two can be mixed in one file
Fill the columns each study reports and leave the rest empty. The example dataset does exactly that: eight studies with mean and SD, four with median and quartiles. MetaVidence converts the median studies before pooling, using the method of Luo and colleagues for the mean and that of Shi and colleagues for the standard deviation, which are the current defaults of the meta package.
The Data check reports how many studies were converted, so the number is in front of you before anything runs and can go straight into the methods section.
Mean and SD are the values the study measured directly. The conversion estimates them from the median and quartiles, so that a study reporting a median can join the analysis.
Extra columns stay available for subgroup analysis and meta-regression, as in the other modules. The Data check verifies the required ones, counts the studies and flags problems, including event larger than n.
Step 2, the parameters
The outcome direction field and the group name fields do not exist here: with no comparison, there is no “favors experimental” or “favors control” to label.
Single proportions
Outcome name goes into titles and file names, as always.
Summary measure (sm) (default PLOGIT) chooses the scale on which the proportions are pooled. Proportions near 0% or 100% have a very small variance on the raw scale, which is what the transformations address:
PLOGIT, logit. The default.PFT, Freeman-Tukey double arcsine. Stabilizes the variance at proportions close to the extremes. The back-transformation to the percentage scale depends on the study sample sizes.PAS, plain arcsine.PLN, log of the proportion.PRAW, raw proportion, untransformed.
Results always return to the percentage scale in plots and tables, so the transformation is a choice of method, not of presentation.
Method (default Inverse) chooses between Inverse, inverse variance, and GLMM, a random-intercept logistic model.
Inverse applies inverse-variance weighting to the transformed proportions. With studies that have zero events, or proportions very close to 0% or 100%, it adds 0.5 to each cell as a continuity correction. GLMM models the counts directly and applies no such correction. GLMM is normally paired with Tau method at ML, and Inverse with REML.
A GLMM fit produces no per-study weight, so the forest plot comes out without the Weight column and with every square the same size. This is not a defect of the plot: the weight simply does not exist in that model. The Inverse method does produce per-study weights, so the column is present there.
If you switch sm to PFT, PAS, PLN or PRAW and leave the method at GLMM, the analysis stops with an error message. When you change sm, set the method back to Inverse.
Analysis model and Tau method work as in the binary module.
This submodule has no Prediction interval, no Random CI method and no Prediction method.
Single means
Summary measure (sm) (default MRAW) has two options. MRAW pools the mean in the original measurement unit. MLN pools the mean on the log scale, which requires strictly positive values.
Analysis model, Tau method (default REML) and Prediction interval (default Yes) work as in the binary module. There is no Method field, no Random CI method and no Prediction method.
Step 3, export and results
Both submodules carry the same cards as the paired modules: Forest plot, Leave-one-out analysis, Funnel plot, Small-study effects with Egger’s test, Subgroup analysis, Meta-regression and the two summary tables as XLSX.