The use of piecewise linear spline function on dose-response meta-analysis

Does-response meta-analysis is widely used in observational-based meta-analysis since proposed by Greenland et al. (1-4). The method works well in most of the situation, especially for the nonlinear trend approximating. Our argument is the linear slope insert within the function: by setting the parameters of quadratic and cubic term as zero. Linear relationship usually acts as main analysis when non-linear trend is non-significant or as additional analysis when non-linear trend is significant. Actually, only part of the linear slopes fit well (5). For J-shaped, U-shaped, S-shaped, and V-shaped curves, the linear slope fit bad since these slopes differ across pieces. We introduce a piecewise linear spline function that may be a solution for this issue (5,6). We assume log relative risks (LogRR) as dependent variable and exposure (X) as independent variable. Then a piecewise linear regression can be established as X against LogRR, with K indicates the cut points (knots) of the slopes.