Concept Architecture
Concept
Theoretically, One-Stage Meta-Analysis is a statistical approach that analyses all available study data simultaneously within a single unified statistical model. It is most commonly applied in individual patient data (IPD) meta-analysis, where participant-level observations from all studies are modelled together while accounting for clustering by study. The method exists to improve estimation efficiency, enable consistent adjustment for covariates and investigate treatment-effect heterogeneity at the patient level.
Mathematically, one-stage meta-analysis is implemented using hierarchical mixed-effects regression models that simultaneously estimate treatment effects and between-study variability. Fixed effects describe the overall treatment effect and covariate relationships, while random effects account for study-level clustering and heterogeneity. Depending on the outcome, linear, logistic or Cox proportional hazards mixed-effects models may be used.
In practice, one-stage meta-analysis is conducted after harmonising individual participant datasets obtained from multiple studies. It is widely used in health technology assessment, comparative effectiveness research and clinical guideline development when patient-level subgroup analyses, interaction testing or time-to-event analyses are required. The resulting treatment-effect estimates frequently provide inputs for health economic decision models.
Purpose
Used to estimate pooled treatment effects by analysing all participant-level data simultaneously within a single hierarchical model while accounting for between-study variability and patient-level covariates.
Mathematical Formulae
Primary Formula
One-stage mixed-effects model:
Y?? = ?? + ??X?? + u? + �??
where:
- Y?? = outcome for patient i in study j
- X?? = treatment indicator or covariate
- ?? = overall intercept
- ?? = pooled treatment effect
- u? = random study effect
- �?? = individual-level residual error
Supporting Formulae
Random study effects:
u? ~ N(0, ��)
Residual error:
�?? ~ N(0, ��)
Total model:
Y?? = X? + Zu + �
Related Mathematical Methods
- Individual Patient Data Meta-Analysis
- Mixed-Effects Regression
- Hierarchical Linear Models
- Random-Effects Meta-Analysis
- Logistic Mixed Models
- Cox Proportional Hazards Models
- Meta-Regression
Example
Individual patient datasets from 14 randomised controlled trials evaluating a heart failure treatment are combined into a single database containing 10,850 participants. A one-stage mixed-effects Cox regression estimates a pooled hazard ratio of 0.82 (95% confidence interval 0.75 to 0.90) while identifying greater treatment benefit among patients with reduced ejection fraction. These estimates are subsequently incorporated into a health economic model.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| FILTER | =FILTER(A2:J15000,J2:J15000="Included") | Select eligible participant records |
| SORT | =SORT(A2:J15000,1,TRUE) | Organise pooled participant-level data |
| AVERAGEIFS | =AVERAGEIFS(C:C,B:B,"Treatment") | Summarise participant characteristics |
| COUNTIFS | =COUNTIFS(B:B,"Treatment",D:D,"Event") | Summarise treatment outcomes |
| PivotTable | Participant-level summary | Explore pooled study and patient characteristics before modelling |
VBA (Optional)
Automate validation, harmonisation and preparation of pooled participant-level datasets before export for one-stage mixed-effects regression analysis.
Sources
- Riley RD, Lambert PC, Abo-Zaid G. Meta-Analysis of Individual Participant Data: Rationale, Conduct and Reporting. BMJ. 2010.
- Stewart LA, Tierney JF. To IPD or Not to IPD? Advantages and Disadvantages of Systematic Reviews Using Individual Patient Data. Evaluation & the Health Professions. 2002.
- Higgins JPT, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions.
- NICE. Health Technology Evaluation Manual.
- ISPOR Good Practice Reports.
Related Concepts (2)
Library
Publications
1
Introduction to Meta-Analysis — Borenstein, Hedges, Higgins & Rothstein, 2nd Edition ed., 2021 (John Wiley & Sons)
A clear, applied introduction to meta-analysis — computing effect sizes, fixed- and random-effects models, heterogeneity, subgroup analysis, meta-regression, and publication bias — written for readers across disciplines.
BookView source →
Frequently Asked Questions (6)
What is one-stage meta-analysis?
An individual patient data meta-analysis analysing combined patient-level data from all studies within a single unified statistical model.
Source: Stewart & Parmar 1993
How does one-stage meta-analysis handle patient-level data?
One-stage meta-analysis takes the individual patient records from all the studies and analyses them together within a single statistical model, rather than first summarising each study and then pooling those summaries. Handling the raw data in one model, while accounting for which study each patient came from, can make fuller use of the information and cope better with sparse data or complex relationships. The trade-off is a more demanding analysis that requires careful specification. Modelling all patients at once is its defining feature. Riley and colleagues (2010) describe this approach.
Source: Riley et al. 2010
How does one-stage meta-analysis work?
One-stage meta-analysis works by combining the patient-level data from all the studies into a single dataset and fitting one statistical model to it, including terms that account for the studies, such as study-specific effects or clustering, so that the analysis respects the structure of the data. The model estimates the overall effect and can incorporate patient-level covariates and interactions. So one-stage meta-analysis works by modelling all the patient-level data together in a single step, with appropriate handling of the studies, producing the combined estimate directly from the unified model rather than from separately analysed study results.
Source: Stewart & Parmar 1993
How does one-stage differ from two-stage meta-analysis?
One-stage meta-analysis analyses the combined patient-level data from all studies in a single model, while two-stage meta-analysis first analyses each study separately to obtain summary estimates and then combines those estimates in a second step, as in conventional meta-analysis. The one-stage approach can offer flexibility, for example in modelling patient-level interactions, and may be more efficient in some settings, while the two-stage approach is simpler and often gives similar results. So the two differ in whether the patient-level data are modelled jointly in one step or summarised per study and then pooled, both being approaches to individual patient data meta-analysis.
Source: Stewart & Parmar 1993
What are the advantages of one-stage meta-analysis?
The advantages of one-stage meta-analysis include the ability to model patient-level relationships and interactions directly within a single framework, which can be more flexible for examining how effects vary with patient characteristics; potential efficiency gains in some settings; and coherent handling of the full data. So one-stage meta-analysis is advantageous where detailed modelling of patient-level effects and interactions is wanted, using all the data jointly, though it requires more complex modelling and care in specifying the model, particularly in how the studies are accounted for, which can affect the results if done inappropriately.
Source: Stewart & Parmar 1993
What are the considerations in one-stage meta-analysis?
Considerations in one-stage meta-analysis include how to account for the studies in the model, since ignoring the clustering of patients within studies can bias the results, so study effects must be handled appropriately, for example as fixed or random effects; the greater complexity of the modelling and the need for expertise; and ensuring the model is specified consistently with the questions of interest. So one-stage meta-analysis requires careful model specification, particularly regarding the studies, and the choices made can affect the estimates, which is why the approach is applied with attention to correctly modelling the structure of the pooled patient-level data.
Source: Stewart & Parmar 1993
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 3 Dec 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-ESM-043
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