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SUMMARY:Penalized optimal design for dose finding - Pronzato\, L (CNRS)
DTSTART:20110816T090000Z
DTEND:20110816T093000Z
UID:TALK32380@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider optimal design under a cost constraint\, where a s
 calar coefficient L sets the compromise between information and cost. For 
 suitable cost functions\, one can force the support points of an optimal d
 esign measure to concentrate around points of minimum cost by increasing t
 he value of L\, which can be considered as a tuning parameter that specifi
 es the importance given to the cost constraint. \n\nAn example of adaptive
  design in a dose-finding problem with a bivariate binary model will be pr
 esented. As usual in nonlinear situations\, the optimal design for any arb
 itrary choice of L depends on the unknown value of the model parameters. T
 he construction of this optimal design can be made adaptive\, by using a s
 teepest-ascent algorithm where the current estimated value of the paramete
 rs (by Maximum Likelihood) is substituted for their unknown value. Then\, 
 taking benefit of the fact that the design space (the set of available dos
 es) is finite\, one can prove the strong consistency and asymptotic normal
 ity of the ML estimator when L is kept constant. Since the cost is reduced
  when L is increased\, it is tempting to let L increase with the number of
  observations (patients enroled in the trial). The strong consistency of t
 he ML estimator is then preserved when L increases slowly enough.\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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