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Copula regression spline models for binary outcomes

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Abstract

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.

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Acknowledgments

We would like to thank two anonymous reviewers and the Associate Editor for many suggestions which helped to clarify the contribution of the paper and improved considerably the presentation of the article.

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Authors and Affiliations

  1. Department of Economics, Mathematics and Statistics, Birkbeck, Malet Street, London, WC1E 7HX, UK

    Rosalba Radice

  2. Department of Statistical Science, University College London, Gower Street, London, WC1E 6BT, UK

    Giampiero Marra

  3. Centre for Mathematical Sciences, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UK

    Małgorzata Wojtyś

  4. Faculty of Mathematics and Information Science, Warsaw University of Technology, UL. Koszykowa 75, 00-662, Warszawa, Poland

    Małgorzata Wojtyś

Authors
  1. Rosalba Radice
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  2. Giampiero Marra
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  3. Małgorzata Wojtyś
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Correspondence to Rosalba Radice.

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Radice, R., Marra, G. & Wojtyś, M. Copula regression spline models for binary outcomes. Stat Comput 26, 981–995 (2016). https://doi.org/10.1007/s11222-015-9581-6

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