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Distortion of effects caused by indirect confounding

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  • Nanny Wermuth
  • D. R. Cox
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    Abstract

    Undetected confounding may severely distort the effect of an explanatory variable on a response variable, as defined by a stepwise data-generating process. The best known type of distortion, which we call direct confounding, arises from an unobserved explanatory variable common to a response and its main explanatory variable of interest. It is relevant mainly for observational studies, since it is avoided by successful randomization. By contrast, indirect confounding, which we identify in this paper, is an issue also for intervention studies. For general stepwise-generating processes, we provide matrix and graphical criteria to decide which types of distortion may be present, when they are absent and how they are avoided. We then turn to linear systems without other types of distortion, but with indirect confounding. For such systems, the magnitude of distortion in a least-squares regression coefficient is derived and shown to be estimable, so that it becomes possible to recover the effect of the generating process from the distorted coefficient. Copyright 2008, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 95 (2008)
    Issue (Month): 1 ()
    Pages: 17-33

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    Handle: RePEc:oup:biomet:v:95:y:2008:i:1:p:17-33

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    Cited by:
    1. Sanjay Chaudhuri, 2014. "Qualitative inequalities for squared partial correlations of a Gaussian random vector," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(2), pages 345-367, April.
    2. Elena Stanghellini & Eduwin Pakpahan, 2013. "Identification of casual effects in linear models: beyond Instrumental Variables," Quaderni del Dipartimento di Economia, Finanza e Statistica 117/2013, Università di Perugia, Dipartimento Economia, Finanza e Statistica.

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