Abstract:
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Motivated by a study evaluating complex time-varying prenatal environmental exposures’ influence on fetal growth, we propose a novel dynamic functional single-index model to study the accumulative effects of multiple functional exposures on a scalar outcome. Through a nonparametric bivariate link function, our proposed model can capture the dynamic nature in the predictor-response relationship. The effects of multiple functional exposures are aggregated by a single index combination. Employing B-spline tensor product to approximate the unknown bivariate function, we develop a numerically stable and computationally efficient estimation procedure using profile least square method, followed with asymptotic properties for the single-index coefficient estimates including consistency and asymptotic normality. In addition, we propose a wild bootstrap test statistics to test whether the exposure-outcome relationship is truly dynamic. The performance of our method is evaluated under extensive simulation scenarios and applied to a real study to evaluate the relationship between air pollutants and birth weight.
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