Publication Date


UMMS Affiliation

Graduate School of Nursing

Document Type



Clinical Epidemiology | Epidemiology


OBJECTIVE: Methods for meta-analysis of studies with individual participant data and continuous exposure variables are well described in the statistical literature but are not widely used in clinical and epidemiological research. The purpose of this case study is to make the methods more accessible.

STUDY DESIGN AND SETTING: A two-stage process is demonstrated. Response curves are estimated separately for each study using fractional polynomials. The study-specific curves are then averaged pointwise over all studies at each value of the exposure. The averaging can be implemented using fixed effects or random effects methods.

RESULTS: The methodology is illustrated using samples of real data with continuous outcome and exposure data and several covariates. The sample data set, segments of Stata and R code, and outputs are provided to enable replication of the results.

CONCLUSION: These methods and tools can be adapted to other situations, including for time-to-event or categorical outcomes, different ways of modelling exposure-outcome curves, and different strategies for covariate adjustment.


Continuous variables, Fractional polynomials, Individual participant data, Meta-analysis

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© 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (

DOI of Published Version



Darssan D, Mishra GD, Greenwood DC, Sandin S, Brunner EJ, Crawford SL, El Khoudary SR, Brooks MM, Gold EB, Simonsen MK, Chung HF, Weiderpass E, Dobson AJ. Meta-analysis for individual participant data with a continuous exposure: A case study. J Clin Epidemiol. 2021 Dec;140:79-92. doi: 10.1016/j.jclinepi.2021.08.033. Epub 2021 Sep 4. PMID: 34487835. Link to article on publisher's site

Journal/Book/Conference Title

Journal of clinical epidemiology

Related Resources

Link to Article in PubMed

PubMed ID


Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.