Combining non-randomized and randomized data in clinical trials using commensurate priors

Hong Zhao, Brian P. Hobbs, Haijun Ma, Qi Jiang, Brad Carlin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Randomization eliminates selection bias, and attenuates imbalance among study arms with respect to prognostic factors, both known and unknown. Thus, information arising from randomized clinical trials (RCTs) is typically considered the gold standard for comparing therapeutic interventions in confirmatory studies. However, RCTs are limited in contexts wherein patients who are willing to accept a random treatment assignment represent only a subset of the patient population. By contrast, observational studies (OSs) often enroll patient cohorts that better reflect the broader patient population. However, OSs often suffer from selection bias, and may yield invalid treatment comparisons even after adjusting for known confounders. Therefore, combining information acquired from OSs with data from RCTs in research synthesis is often criticized due to the limitations of OSs. In this article, we combine randomized and non-randomized substudy data from FIRST, a recent HIV/AIDS drug trial. We develop hierarchical Bayesian approaches devised to combine data from all sources simultaneously while explicitly accounting for potential discrepancies in the sources’ designs. Specifically, we describe a two-step approach combining propensity score matching and Bayesian hierarchical modeling to integrate information from non-randomized studies with data from RCTs, to an extent that depends on the estimated commensurability of the data sources. We investigate our procedure’s operating characteristics via simulation. Our findings have implications for HIV/AIDS research, as well as elucidate the extent to which well-designed non-randomized studies can complement RCTs.

Original languageEnglish (US)
Pages (from-to)154-171
Number of pages18
JournalHealth Services and Outcomes Research Methodology
Issue number3
StatePublished - Sep 1 2016

Bibliographical note

Funding Information:
The work of the first and last authors was supported in part by a grant from the Amgen Research Grant Program. The work of the second and last authors was supported in part by National Cancer Institute Grant 1-R01-CA157458-01A1. Finally, the work of the second author was supported in part by National Cancer Institute M.D. Anderson Cancer Center Support Grant P30-CA016672.

Publisher Copyright:
© 2016, Springer Science+Business Media New York.


  • Bayesian analysis
  • Commensurate priors
  • Markov chain Monte Carlo (MCMC)
  • Observational studies (OSs)
  • Propensity score matching
  • Randomized clinical trials (RCTs)


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