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BMC Med Res Methodol. 2016 Aug 2;16:91. doi: 10.1186/s12874-016-0189-0.

Dose-response meta-analysis of differences in means.

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Department of Public Health Sciences, Karolinska Institutet, Stockholm, Sweden.
Department of Public Health Sciences, Karolinska Institutet, Stockholm, Sweden.



Meta-analytical methods are frequently used to combine dose-response findings expressed in terms of relative risks. However, no methodology has been established when results are summarized in terms of differences in means of quantitative outcomes.


We proposed a two-stage approach. A flexible dose-response model is estimated within each study (first stage) taking into account the covariance of the data points (mean differences, standardized mean differences). Parameters describing the study-specific curves are then combined using a multivariate random-effects model (second stage) to address heterogeneity across studies.


The method is fairly general and can accommodate a variety of parametric functions. Compared to traditional non-linear models (e.g. E max, logistic), spline models do not assume any pre-specified dose-response curve. Spline models allow inclusion of studies with a small number of dose levels, and almost any shape, even non monotonic ones, can be estimated using only two parameters. We illustrated the method using dose-response data arising from five clinical trials on an antipsychotic drug, aripiprazole, and improvement in symptoms in shizoaffective patients. Using the Positive and Negative Syndrome Scale (PANSS), pooled results indicated a non-linear association with the maximum change in mean PANSS score equal to 10.40 (95 % confidence interval 7.48, 13.30) observed for 19.32 mg/day of aripiprazole. No substantial change in PANSS score was observed above this value. An estimated dose of 10.43 mg/day was found to produce 80 % of the maximum predicted response.


The described approach should be adopted to combine correlated differences in means of quantitative outcomes arising from multiple studies. Sensitivity analysis can be a useful tool to assess the robustness of the overall dose-response curve to different modelling strategies. A user-friendly R package has been developed to facilitate applications by practitioners.


Dose-response; Mean differences; Meta-analysis; Random-effects

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