A model for locking in gains with an application to clinical trials

  • Authors:

  • Sheldon m. Ross;Henk Tijms;Shinyi Wu

  • Affiliations:

  • Epstein department of industrial and systems engineering, university of southern california, los angeles, ca e-mail: smross@usc.edu;Department of operations research, vrije university, de boelelaan 1105, amsterdam, hv1081, the netherlands, e-mail: tijms@feweb.vu.nl;Epstein department of industrial and systems engineering, university of southern california, los angeles, ca e-mail: shinyiwu@usc.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2009

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Abstract

We consider a model in which each round consists of a sequence of games, with each game resulting in either a positive or a zero score. If a zero score occurs, then the current round is ended with no points being accumulated during that round. If a game ends with a positive score, then the player can either end that round or play another game in the round. If she elects to end the round, then the sum of all scores earned in games played during that round are added to her cumulative score and a new round begins. Under the assumption that successive game scores are independent and identically distributed random variables whose conditional distribution, given that it is positive, is exponential, we consider this problem under such objectives as minimizing the expected number of rounds until a cumulative score exceeds a given goal g and maximizing the probability that a cumulative score of at least g is obtained by the end of round n. We present the model in the hypothetical context of a clinical trial of a treatment for reducing glycated hemoglobin in diabetic patients.