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Copula regression spline models for binary outcomes

机译：Copula回归样条模型用于二元结果

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摘要

We introduce a framework for estimating the effect that a binary treatment has on a binary outcome in the presence of unobserved confounding. The methodology is applied to a case study which uses data from the Medical Expenditure Panel Survey and whose aim is to estimate the effect of private health insurance on health care utilization. Unobserved confounding arises when variables which are associated with both treatment and outcome are not available (in economics this issue is known as endogeneity). Also, treatment and outcome may exhibit a dependence which cannot be modeled using a linear measure of association, and observed confounders may have a non-linear impact on the treatment and outcome variables. The problem of unobserved confounding is addressed using a two-equation structural latent variable framework, where one equation essentially describes a binary outcome as a function of a binary treatment whereas the other equation determines whether the treatment is received. Non-linear dependence between treatment and outcome is dealt using copula functions, whereas covariate-response relationships are flexibly modeled using a spline approach. Related model fitting and inferential procedures are developed, and asymptotic arguments presented.
机译：我们引入了一个框架，用于估计在存在未观察到的混杂因素的情况下二元治疗对二元结果的影响。该方法适用于案例研究，该案例使用医疗支出小组调查的数据，其目的是估计私人医疗保险对医疗保健利用的影响。当无法获得与治疗和结果相关的变量时，就会出现无法观察到的混淆（在经济学上，这个问题称为内生性）。而且，治疗和结果可能显示出依赖关系，而这种依赖关系无法使用线性关联度进行建模，并且观察到的混杂因素可能对治疗和结果变量具有非线性影响。使用两方程式结构潜变量框架解决了无法观察到的混杂问题，其中一个方程式实质上描述了作为二进制处理函数的二进制结果，而另一个方程式确定是否接受了处理。使用copula函数处理治疗和结果之间的非线性相关性，而使用样条方法灵活地建模协变量-响应关系。开发了相关的模型拟合和推论过程，并提出了渐近论证。

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