One-stage dose-response meta-analysis for aggregated data

Stat Methods Med Res. 2019 May;28(5):1579-1596. doi: 10.1177/0962280218773122. Epub 2018 May 9.


The standard two-stage approach for estimating non-linear dose-response curves based on aggregated data typically excludes those studies with less than three exposure groups. We develop the one-stage method as a linear mixed model and present the main aspects of the methodology, including model specification, estimation, testing, prediction, goodness-of-fit, model comparison, and quantification of between-studies heterogeneity. Using both fictitious and real data from a published meta-analysis, we illustrated the main features of the proposed methodology and compared it to a traditional two-stage analysis. In a one-stage approach, the pooled curve and estimates of the between-studies heterogeneity are based on the whole set of studies without any exclusion. Thus, even complex curves (splines, spike at zero exposure) defined by several parameters can be estimated. We showed how the one-stage method may facilitate several applications, in particular quantification of heterogeneity over the exposure range, prediction of marginal and conditional curves, and comparison of alternative models. The one-stage method for meta-analysis of non-linear curves is implemented in the dosresmeta R package. It is particularly suited for dose-response meta-analyses of aggregated where the complexity of the research question is better addressed by including all the studies.

Keywords: Meta-analysis; dose–response; flexible model; mixed model; random-effects.

MeSH terms

  • Cause of Death
  • Coffee*
  • Computer Simulation
  • Humans
  • Linear Models*
  • Meta-Analysis as Topic*
  • Research Design


  • Coffee