Chapter 7 Conclusions

The methods presented in this thesis enrich the set of tools available for applying dose–response meta-analyses and for addressing specific questions, including how to evaluate the goodness-of-fit and how to measure the impact of the between-studies heterogeneity. Furthermore, this thesis describes alternative models for pooling results in case of heterogeneous exposure range and for estimating complex models without excluding relevant studies. The proposed methods have been illustrated using real data from published meta-analyses and implemented in user-friendly R packages available on CRAN.

More specifically we conclude the following:

• The dosresmeta R package has been widely used throughout the world and applied by practitioners in conducting dose–response meta-analyses. More recent developments are available to apply the methods presented in this thesis. Dedicated functions have been useful to avoid pitfalls frequently encountered in published meta-analyses, such as definition of the design matrix and prediction of the pooled results (Paper I).

• The proposed tools consist of descriptive measures to summarize the agreement between fitted and observed data (the deviance and the coefficient of determination), and graphical tools to visualize the fit of the model (decorrelated residuals-versus-exposure plot). These tools can be employed to identify systematic dose–response patterns and possible sources of heterogeneity, and to support the conclusions. Goodness-of-fit should be regularly evaluated in applied dose–response meta-analyses (Paper II).

• The new measure of heterogeneity, \(\hat R_b\), quantifies the proportion of the variance of the pooled estimate attributable to the between-study heterogeneity. Contrary to the available measures of heterogeneity, it does not require specification of a typical value for these quantities. Therefore, we recommend the use of the \(\hat R_b\) as a preferred measure for quantifying the impact of heterogeneity (Paper III).

• A point-wise strategy for dose–response meta-analysis does not require the specification of a unique model as in the traditional approaches, and therefore allows for more flexibility in modeling the individual curves. In addition, the extent of extrapolation is limited by predicting the study-specific relative risk based on the observe exposure range. The use of the described strategy may improve the robustness of the results, especially in case of heterogeneous exposure range (Paper IV).

• The proposed one-stage approach for dose–response meta-analysis consists of a linear mixed-effects model, offering useful tools for describing the impact of heterogeneity over the exposure range, for comparing the fit of different models, and for predicting individual dose–response associations. The main advantage is that flexible curves can be estimated regardless of the number of data-points in the individual analyses (Paper V).