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Abstract:
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Children exposed to toxic agents such as lead are at high risk to experience significant friction in their growth and development of sexual maturation. This paper is primarily motived by a study that aims to assess environmental taxicants-modified effects of risk factors related to the hazards of early or late onset of menarche among girls living in Mexico City. To address the scientific hypothesis of potential nonlinear modification on covariate effects, we propose a new Cox regression model with multiple functional covariate-environment interactions, which allows covariate effects to be altered nonlinearly by mixtures of exposed toxicants. This new class of models is rather flexible and includes many existing semi-parametric Cox models as special cases. To achieve estimation efficiency, we develop the global partial likelihood method for estimation and inference, in which we establish key large-sample results. The proposed methodology is examined by simulation studies, and applied to the analysis of the motivating data, where mother's prenatal and postnatal exposures to lead are found as important risk modifiers of timing of menarche.
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