Measurement error modelling with an approximate instrumental variable
AbstractConsider using regression modelling to relate an exposure (predictor) variable to a disease outcome (response) variable. If the exposure variable is measured with error, but this error is ignored in the analysis, then misleading inferences can result. This problem is well known and has spawned a large literature on methods which adjust for measurement error in predictor variables. One theme is that the requisite assumptions about the nature of the measurement error can be stronger than what is actually known in many practical situations. In particular, the assumptions that are required to yield a model which is formally identified from the observable data can be quite strong. The paper deals with one particular strategy for measurement error modelling, namely that of seeking an "instrumental variable", i.e. a covariate "S" which is associated with exposure and conditionally independent of the outcome given exposure. If these two conditions hold exactly, then we call "S" an "exact instrumental variable", and an identified model results. However, the second is not checkable empirically, since the actual exposure is unobserved. In practice then, investigators typically seek a covariate which is plausibly thought to satisfy it. We study inferences which acknowledge the approximate nature of this assumption. In particular, we consider Bayesian inference with a prior distribution that posits that "S" is "probably close to" conditionally independent of outcome given exposure. We refer to this as an "approximate instrumental variable" assumption. Although the approximate instrumental variable assumption is more realistic for most applications, concern arises that a non-identified model may result. Thus the paper contrasts inferences arising from the approximate instrumental variable assumption with their exact instrumental variable counterparts, with particular emphasis on the benefit of basing inferences on a more realistic model "versus" the cost of basing inferences on a non-identified model. Copyright 2007 Royal Statistical Society.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Volume (Year): 69 (2007)
Issue (Month): 5 ()
Contact details of provider:
Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom
Web page: http://www.blackwellpublishing.com/journal.asp?ref=1369-7412
More information through EDIRC
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statistics
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.