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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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  4:15 p.m., Tuesday, February 7, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Tyler VanderWeele} \\
Department of Biostatistics\\
Harvard School of Public Health\\
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  \textbf{Directed Acyclic Graphs and Monotonic Effects}
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\noindent

The directed acyclic graph causal framework has been used with increasing 
frequency to address concerns of confounding in a variety of research 
settings. The directed acyclic graph framework allows for the representation 
of causal and counterfactual relations amongst variables; the estimation of 
causal effects through the g-formula; the detection of independencies through 
the d-separation criteria; and the implementation of algorithms to determine 
whether conditioning on a particular set of variables, or none at all, is 
sufficient to control for confounding as well as algorithms which identity 
such a set of variables. By incorporating notions of monotonic effects, the 
directed acyclic graph casual framework can be extended so as to allow for the 
graphical representation of monotonic effects on causal directed acyclic 
graphs through signed edges; the use of monotonic effects to determine the 
sign of the causal effect of an intervention in the presence of intermediate 
variables; the use of monotonic effects to develop rules governing montonicity 
and covariance; and finally the use of monotonicity to determine the sign of 
the bias when control for confounding is inadequate.




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