Case studies / Research
Random Effects Meta-analysis of Forty-Five Published Studies
Combining heterogeneous evidence into a defensible overall estimate, with publication bias investigated rather than assumed away.
The challenge
What the organisation came with
A research organisation needed to combine evidence across multiple published studies into a single robust estimate — the quantitative foundation for a body of work that would later be peer reviewed.
The studies differed substantially in methodology, participant characteristics and outcome measures. That between-study heterogeneity is not a nuisance to be minimised; it is a property of the evidence base, and a synthesis that ignores it produces a precise-looking estimate of something that does not exist.
Publication bias also had to be investigated. If studies finding no effect are less likely to be published, the published literature is a biased sample of the research conducted, and any synthesis of it inherits that bias.
The approach
How it was analysed, and why that method
Why random effects rather than fixed effects
A random effects model was used. It assumes the true effect varies between studies and estimates both the average effect and the extent of that variation, which is the honest representation of an evidence base drawn from different populations and designs.
Fixed-effects models were rejected because the assumption of a single common underlying effect was not supported by the data. Applying one would have produced artificially narrow confidence intervals — a more confident answer to a question the evidence could not support.
Explaining heterogeneity, and testing for bias
Meta-regression was used to examine whether study-level characteristics accounted for some of the between-study variation, which turns heterogeneity from a caveat into a finding. Publication bias was assessed using funnel plots and formal testing, and sensitivity analyses established how far the pooled estimate depended on any individual study.
A pooled estimate that changes materially when one study is removed is not a robust finding. Establishing that before publication is considerably better than a reviewer establishing it afterwards.
Delivered
What the client received
The value
What changed as a result
The findings supported evidence-based decision-making and formed the quantitative basis of a peer-reviewed publication.
Because the code was delivered with the report, the synthesis can be updated as new studies appear rather than being repeated from scratch.
Written from the assigned statistician's own project notes. The client is not named and no identifying detail, data or figures are published. Scale and timeframe are approximate.
Related services
The services behind this work
Statistical consultancy
Design, analysis and reporting for charities, universities, the NHS and business.
From £950Results chapter review
A statistician checks the chapter you wrote before it is submitted.
Fixed quoteDissertation statistics help
Analysis of the data you collected, explained test by test so you can defend it.
From £95Send the data. Get a fixed quote.
Attach your dataset or just describe the project. A named statistician replies with a price and a deadline, usually within one working day.