The following paradox was brought to our attention by Pablo Lardelli from Granada (Spain).<\/p>\n
Pablo writes:<\/p>\n
1. Imagine that you design a cohort study to assess the causal effect of X on Y, E[Y|do(X=x)]. Prior knowledge informs you that variable M is a possible confounder of the process X—>Y, which leads you to assume X<---M--->Y.<\/p>\n
To adjust for the effect of this confounder, you decide to design a matched cohort study, matching on M non exposed to exposed. You know that matching breaks down the association between X and M in the sample. The following paradox was brought to our attention by Pablo Lardelli from Granada (Spain). Pablo writes: 1. Imagine that you design a cohort study to assess the causal effect of X on Y, E[Y|do(X=x)]. Prior knowledge informs you that variable M is a possible confounder of the process X—>Y, which leads you to assume XY. […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,24,34],"tags":[],"class_list":["post-363","post","type-post","status-publish","format-standard","hentry","category-discussion","category-matching","category-selection-bias"],"_links":{"self":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=363"}],"version-history":[{"count":0,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/363\/revisions"}],"wp:attachment":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n[……]
\nThe problem arises when you draw the DAG […] and realize that S is a collider on the path X—>S<---M and, since we are conditioning on S (because the study sample is restricted to S=1) we are in fact opening a non causal path between X and Y (through M) in the sample.\n\nBut this stands in contradiction to everything we are told by our textbooks.\n\nClick here for full discussion of matching in DAGs, persistent-unfiathfulness and unit-to-unit interactions.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"