\magnification=1200
\baselineskip=20pt
\nopagenumbers
\font\big=cmr12 scaled \magstep2

\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
\bigskip

\baselineskip=12pt
\centerline{4:15 p.m., Tuesday, January 23, 2001}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

\bigskip
\baselineskip=15pt
\centerline{\sl Susan A. Murphy}
\centerline{\sl Dept. of Statistics}
\centerline{\sl Quantitative Methodology Program}
\centerline{\sl University of Michigan}
\bigskip
\centerline{\bf Optimal Dynamic Treatment Regimes}
\bigskip

Dynamic treatment regimes are individually tailored treatments that provide
treatment  to  individuals only when and if they need the treatment and
adjust the level of treatment to the individual's need.   In a dynamic
regime, rules for how the treatment level and type should vary with time
are specified  prior to the beginning of treatment; these rules are based
on time varying measurements of subject-specific need for treatment. Thus
the assigned treatment level depends on past individual information.  These
regimes hold the promise of maximizing treatment efficacy by avoiding ill
effects due to over-treatment and by providing increased treatment levels
to those who can benefit.

If all relevant probability distributions (e.g. specifying the multivariate
distribution of the response and the time-varying subject-specific need for
the variety of different time varying treatment levels) are known then
backwards induction or dynamic programming arguments can be used to find
the optimal regime.  However if  this multivariate distribution must be
estimated, direct use of the backwards induction arguments can lead to
parametrization inconsistencies and subsequent biasing of the estimator of
the  optimal regime.  These issues along with a solution will be discussed.
 The solution will be valid when the treatment levels in the available data
are sequentially randomized.

\bye