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Response to The Query Posted by Eyal Shahar on 12 September, 2008

Posted by plosmedicine on 31 Mar 2009 at 00:30 GMT

Author: Nuala Sheenan
Position: Reader in Statistical Genetics
Institution: University of Leicester
Additional Authors: Vanessa Didelez, Paul Burton and Martin Tobin
Submitted Date: September 24, 2008
Published Date: September 26, 2008
This comment was originally posted as a “Reader Response” on the publication date indicated above. All Reader Responses are now available as comments.

The back-door criterion is irrelevant in this context as we are not interested in the causal effect of gene1 on disease: we want the causal effect of exposure on disease. Gene1 can be used as an instrument if it satisfies core conditions 1-3. In particular, it is conditionally independent of disease given exposure and confounders (all paths between gene1 and disease are blocked by confounding factors and exposure in Figures 3 and 4) and it is marginally independent of the confounding factors (all paths between gene1 and confounding factors are blocked by the empty set in Figures 3 and 4). It can be shown mathematically that under these conditions (and linearity) the ratio of the gene1-disease association (not necessarily causal) and the gene1-exposure association (not necessarily causal) is the desired causal effect of exposure on disease (see for instance Didelez and Sheehan, 2007). Note that by “confounders” here we are explicitly referring to the variable(s) U in our figures.

No competing interests declared.