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Abstract:
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In the field of epidemiology, when modeling the relationship between placental-fetal hormone level and infant outcome, such as birth weight, researchers often consider linear regression models. If the underlying relationship is suspected to be curvilinear, regression spline, smoothing spline or penalized regression spline method is superior to linear regression. To detect the underlying shape among increasing, decreasing, convex and concave, researchers can apply the shape-restricted regression spline technique to the data. In many cases, the shapes of placental-fetal hormone level and infant outcome are different between different groups (exposure vs. non-exposure, male vs. female, etc.). In order to detect the group-level shape, a factor-by-curve interaction should be incorporated into the model. In this article, we extend the original shape-restricted regression spline by adding the interaction term and restricting the behaviors of both main and interaction effects. We conduct several simulation studies to illustrate the method.
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