Flexible piecewise linear model for investigating dose-response relationship in meta-analysis: Methodology, examples, and comparison.

Objectives: Dose-response meta-analysis (DRMA) is widely employed in establishing the potential dose-response relationship between continuous exposures and disease outcomes. However, there is no valid DRMA method readily for discrete exposures, especially when the possible dose-response trend not likely to be linear. We proposed a piecewise linear DRMA model as a solution to this issue.

Methods: We illustrated the methodology of piecewise linear model in both one-stage DRMA approach and two-stage DRMA approach. The method by testing the equality of slopes of each piecewise was employed to judge if there is "piecewise effect" against a simple linear trend. We then used sleep (continuous exposure) and parity (discrete exposure) data as examples to illustrate how to apply the model in DRMA using the Stata code attached. We also empirically compared the slopes of piecewise linear model with simple linear as well as restricted cubic spline model.

Results: Both one-stage and two-stage piecewise linear DRMA model fitted well in our examples, and the results were similar. Obvious "piecewise effects" were detected in both the two samples by the method we used. In our example, the new model showed a better fitting effect and practical, reliable results compared to the simple linear model, while similar results for to restricted cubic spline model.

Conclusion: Piecewise linear function is a valid and straightforward method for DRMA and can be used for discrete exposures, especially when the simple linear function is under fitted. It represents a superior model to linear model in DRMA and may be an alternative model to the nonlinear model.