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

Abstract

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 doseresponse 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. K E Y W O R D S dose-response meta-analysis, discrete exposure, piecewise linear function

Resting Heart Rate and the Risk of Atrial Fibrillation

“…However, the previous study did not identify a significant RR (0.97, 95% CI: 0.92-1.02) of AF per 10 bpm increase because the simple linear function is insufficient for detecting J-shaped or U-shaped associations. 5) In order to solve this problem, we first applied a piecewise linear regression model in the meta-analysis described by Xu, et al and Gould, et al, 20,54) which demonstrated that a 10 bpm decrease or increase in the RHR was associated with a 9% or a 6% risk of AF, respectively, compared with RHRs of 70 bpm. Strengths and limitations: Our meta-analysis has several strengths.…”

“…Thus, we first used a piecewise linear regression model in the metaanalysis to establish the "average" trends between different RHRs and AF by treating the slope as two piecewise points greater than and less than 70 bpm to demonstrate the linear trends. 9,20) The reference dose was set at 70 bpm because we assumed that an RHR of approximately 70 bpm had the lowest risk of AF, according to previous studies. [5][6][7] Possible publication bias was assessed using Begg's test 21) and Egger's test.…”

Relationship Between Serum Albumin and Risk of Atrial Fibrillation: A Dose-Response Meta-Analysis

“…We calculated the study-specific slopes (linear trends) and 95% CIs from the natural logs of the reported ORs and CIs across categories of serum albumin by using the method described by Greenland and Longnecker ( 16 ). Nonlinear dose–response models were fitted by using the robust error meta-regression method ( 17 , 18 ) that required at least two quantitative serum albumin level ORs with variance estimates. We estimated the midpoint of each category by averaging the lower and upper boundaries of that category if the median or mean serum albumin was not provided and reported in ranges ( 19 ).…”

Relationship between serum growth differentiation factor 15, fibroblast growth factor-23 and risk of atrial fibrillation: A systematic review and meta-analysis

“…In the linear exposure-effect analysis, the method described by Greenland and Longnecker ( 22 ) was used to estimate study-specific slopes and 95% CIs. The robust error meta-regression method developed by Xu and Doi ( 23 , 24 ) was applied for the non-linear dose-response analysis. The levels of GDF-15 and FGF-23 and their effect size with variance estimates were required for at least two quantitative exposure categories.…”