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Multilevel regression and poststratification for estimating population quantities from large health studies: a simulation study based on US population structure
  1. Marnie Downes1,2,
  2. John Carlin1,2,3
  1. 1 Department of Paediatrics, The University of Melbourne, Parkville, Australia
  2. 2 Murdoch Children's Research Institute, Parkville, Australia
  3. 3 Melbourne School of Population and Global Health, The University of Melbourne, Parkville, Australia
  1. Correspondence to Marnie Downes, Department of Paediatrics, The University of Melbourne, Royal Children’s Hospital, 50 Flemington Road, Parkville, Victoria 3052, Australia; marnie.downes{at}


Introduction Recruiting a representative sample of participants is becoming increasingly difficult in large-scale health surveys. Multilevel regression and poststratification (MRP) has been shown to be effective in estimating population descriptive quantities in non-representative samples. We performed a simulation study, previously applied to an Australian population, this time to a US population, to assess MRP performance.

Methods Data were extracted from the 2017 Current Population Survey representing a population of US adult males aged 18–55 years. Simulated datasets of non-representative samples were generated. State-level prevalence estimates for a dichotomous outcome using MRP were compared with the use of sampling weights (with and without raking adjustment). We also investigated the impact on MRP performance of sample size, model misspecification, interactions and the addition of a geographic-level covariate.

Results MRP was found to achieve generally superior performance, with large gains in precision vastly outweighing the increased accuracy observed for sampling weights with raking adjustment. MRP estimates were generally robust to model misspecification. We found a tendency of MRP to over-pool between-state variation in the outcome, particularly for the least populous states and small sample sizes. The inclusion of a state-level covariate appeared to mitigate this and further improve MRP performance.

Discussion MRP has been shown to be effective in estimating population descriptive quantities in two different populations. This provides promising evidence for the general applicability of MRP to populations with different geographic structures. MRP appears to be a valuable analytic strategy for addressing potential participation bias from large-scale health surveys.

  • Multilevel modelling
  • biostatistics
  • study design

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  • Contributors MD extracted relevant data from public sources, planned and conducted all simulation analyses, interpreted the results, was primarily responsible for the first draft of the manuscript, and revised the manuscript following feedback from journal reviewers. JC supervised the planning and execution of all statistical analyses and assisted with manuscript drafting and review.

  • Funding The analytic work reported in this paper was funded by an Australian Government Research Training Program Scholarship to the first author.

  • Competing interests None declared.

  • Patient consent for publication Not required.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Data availability statement Data are available upon reasonable request.

  • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.