STATISTICAL METHOD
Meta-Analysis Methodology
Statistical Consulting for Pooling Study Results
We apply meta-analysis methodology to the studies you have identified, choosing the effect measure and the common-effect or random-effects model by the inferential goal, and reporting the pooled estimate with its 95% confidence interval, heterogeneity and a prediction interval.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is a Meta-Analysis?
A meta-analysis combines effect estimates from several studies of the same question into one summary estimate, weighting each study by its precision, and describes how much the studies differ. It needs one effect measure on a common scale, such as a risk ratio or mean difference, with a standard error from each study. A common-effect (fixed-effect) model assumes one true effect shared by all studies, while a random-effects model assumes the true effects vary and estimates their mean and spread. Pooling is justified only when the studies are comparable enough to answer one question. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides meta-analysis methodology support within your review design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is a Meta-Analysis Appropriate?
A meta-analysis fits a set of comparable studies of one question, and these are the research situations in which researchers most often ask us to plan, run or confirm one.
Comparable Trials on One Question Randomized trials found through a Systematic Review compare one intervention with one comparator, and a pooled effect with its uncertainty is needed.
Pooling Observational Estimates Cohort or case-control studies report adjusted associations, and the synthesis must combine them without presenting the result as randomized evidence.
Deciding Whether Pooling Is Sound Results disagree across studies, and the question is whether populations and outcomes are comparable enough to pool, or whether the right decision is not to pool.
Reviewing a Completed Meta-Analysis A forest plot exists and a reviewer has questioned the model or the extracted data. Independent Statistical Review re-examines the pooling and its inputs.
ANALYTICAL APPROACH
How We Apply Meta-Analysis Methodology
Within the family of Evidence Synthesis & Meta-Research, pooling is chosen only after comparability, effect measures and the purpose of the model have been examined.
Comparability and Extraction We check that populations, interventions and outcomes are comparable enough to pool and verify units, since a standard error entered as a standard deviation fakes heterogeneity.
Effect Measure and Model The effect measure suits the outcome and the model matches the goal, common-effect for one shared effect or random-effects for varying ones. A heterogeneity p-value does not decide.
Heterogeneity and Uncertainty Tau-squared and a prediction interval describe the spread of true effects, while I-squared is only a proportion. Few studies call for the Hartung-Knapp adjustment of intervals.
Bias and Sensitivity Analyses Funnel plots and Egger-type tests need about ten studies, and asymmetry has causes beyond publication bias. Leave-one-out and risk-of-bias analyses show what drives the result.
DELIVERABLES
What You Receive
As part of our Meta-Analysis & Evidence Synthesis service, the pooled analysis is delivered with the estimates, checks and files needed to report and defend it.
Data & Variable Review Extracted values are checked against units and scales, and multi-arm trials, overlapping samples and zero-event cells are resolved before any model is fitted.
Method-Specific Checks Heterogeneity, small-study effects and the influence of single studies are examined, with leave-one-out, risk-of-bias and common-effect sensitivity analyses.
Statistical Results The pooled effect with its 95% confidence interval and prediction interval, tau-squared with I-squared, study weights and prespecified subgroup comparisons.
Publication-Ready Tables & Figures Forest plot analysis of study and pooled estimates, funnel plots and summary tables, in line with PRISMA 2020, MOOSE for observational studies or the journal's requirements.
Interpretation The pooled result is written as an estimate with its uncertainty and the certainty of the evidence in the GRADE framework, without claiming more than the studies support.
Reproducible Analysis Files R scripts, Stata do-files or SPSS syntax are provided with the extraction sheet, so every pooled value can be traced and rerun when studies are added.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
We choose the method by the question and by what the studies report. Pooling is not always the right step, and these methods fit other structures of evidence.
01
Meta-Regression
When the question is why effects differ, study-level moderators can be examined, within the limits of how few studies are usually available per covariate.
02
Network Meta-Analysis (NMA)
When three or more treatments were compared in different trials, a network combines direct and indirect evidence, which a pairwise meta-analysis cannot do.
03
Individual Participant Data (IPD) Meta-Analysis
When trials define outcomes or follow-up differently, or report them selectively, participant-level data allow one reanalysis under common definitions and time points.
04
SWiM (Synthesis Without Meta-Analysis)
When studies differ too much in design, outcome or reporting to pool, a structured synthesis that groups them by a set rule is more defensible than a forced average.
CASE EXAMPLE
How We Work in Practice
An illustration of how a pooled analysis moves from a written plan to a reportable, defensible summary estimate.
ILLUSTRATIVE EXAMPLE · HEALTH TECHNOLOGY ASSESSMENT · UNITED STATES
A health technology assessment team needed to pool randomized trials of a blood pressure self-monitoring program for an assessment report, with a plan its committee could defend.
The protocol, written before any results were extracted, specified a random-effects model with the Hartung-Knapp adjustment and the mean difference in systolic pressure. Duplicate extraction showed that two trials had entered standard errors where standard deviations belonged, which would have manufactured heterogeneity, and that one trial had two intervention arms sharing a control group. We corrected the units and combined the arms so control participants were counted once. Tau-squared and a prediction interval were reported beside the confidence interval, with leave-one-out analyses and a cautiously read funnel plot.
Outcome: The team received the pooled mean difference with its 95% confidence interval and prediction interval, tau-squared, forest and funnel plots, the sensitivity analyses and the analysis scripts.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Pooling Studies
Meta-analysis statistical methods are run in R, Stata, IBM SPSS and Python, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Meta-Analysis Across Research Fields
Meta-analysis is used wherever trials or cohorts have estimated the same effect, and each field has its own preferred effect measures and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a health technology assessment analyst who needed the comparability of studies and the handling of heterogeneity checked.
“I had already started the Meta-Analysis, but I was not confident about whether the studies were comparable enough to pool and how heterogeneity should be handled. The team checked the setup against our study design, explained the decisions in plain language, and returned results we could actually use. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your meta-analysis, and the review, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your meta-analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The review question, eligibility criteria and conclusions remain with you, and our statistical interpretation stays within what the pooled estimates and the included studies support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Meta-Analysis
Short answers to what researchers ask before pooling studies, from model choice and publication bias to confidentiality and the assessment process.
Should I use a fixed-effect or a random-effects model?
The model should match the inferential goal, not the heterogeneity test. A fixed effect meta-analysis assumes one true effect shared by all studies, while a random effects meta-analysis estimates the mean of effects that vary across settings, usually the more realistic assumption. A heterogeneity p-value has little power with few studies, so choosing from it is unreliable. We state the choice in the protocol and show the alternative as a sensitivity analysis.
How many studies do I need to assess publication bias?
Tests for funnel plot asymmetry, such as Egger’s regression, are generally advised only with about ten or more studies, because their power is low and they can mislead with fewer. Asymmetry also has causes other than publication bias, including true heterogeneity and differences in study quality, so we describe it as small-study effects and add sensitivity analyses.
Can I pool studies that report different effect measures?
Only after converting them to one measure that suits the question, such as standardized mean differences when scales differ, with the conversion assumptions stated. Risk ratios and mean differences cannot simply be mixed. If the conversion needs assumptions the studies cannot support, a structured synthesis without pooling is the more defensible choice.
Can you review an analysis that has already been completed?
Yes, we can review a completed meta-analysis before submission or a response to reviewers. We check the extracted data and units, the effect measure and model, the handling of multi-arm trials and overlapping samples, and the reporting of heterogeneity and bias, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your extraction sheets, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With a
Meta-Analysis?
Share your review question, the extracted study data and your protocol. We assess whether the studies can be pooled and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014