Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-18T03:18:22.041Z Has data issue: false hasContentIssue false
  • English
  • Français

A MODEL FOR LOCKING IN GAINS WITH AN APPLICATION TO CLINICAL TRIALS

Published online by Cambridge University Press:  14 July 2009

Sheldon M. Ross ,
Henk Tijms  and
Shinyi Wu
Sheldon M. Ross
Affiliation:
Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA E-mail: smross@usc.edu
Henk Tijms
Affiliation:
Department of Operations Research, Vrije University, De Boelelaan 1105, Amsterdam, HV1081, The Netherlands, E-mail: tijms@feweb.vu.nl
Shinyi Wu
Affiliation:
Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA E-mail: shinyiwu@usc.edu
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 4 , October 2009 , pp. 637 - 647
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Centers for Disease Control and Prevention. (2007). National Diabetes Fact Sheet, 2007.Google Scholar
2.Clancy, D.E., Dismuke, C.E., Magruder, K.M., Simpson, K.N., & Bradford, D. (2008). Do diabetes group visits lead to lower medical care charges? American Journal of Managed Care 14(1): 39–44.Google ScholarPubMed
3.Clancy, D.E., Huang, P., Okonofua, E., Yeager, D., & Magruder, K.M. (2007). Group visits: Promoting adherence to diabetes guidelines. Journal of General Internal Medicine 22(5): 620–624.CrossRefGoogle ScholarPubMed
4.Clancy, D.E., Yeager, D.E., Huang, P., & Magruder, K.M. (2007). Further evaluating the acceptability of group visits in an uninsured or inadequately insured patient population with uncontrolled type 2 diabetes. Diabetes Education 33(2): 309–314.CrossRefGoogle ScholarPubMed
5.Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
6.Ross, S.M. (1996). Stochastic processes. New York: Wiley.Google Scholar
7.Trento, M., Passera, P., Tomalino, M., Bajardi, M., Pomero, F., Allione, A., Vaccari, P., Molinatti, G.M., & Porta, M. (2001). Group visits improve metabolic control in type 2 diabetes: a 2-year follow-up. Diabetes Care 24(6): 995–1000.CrossRefGoogle ScholarPubMed
8.Trento, M., Passera, P., Bajadi, M., Tomalino, M., Grassi, G., Borgo, E., Donnola, C., Cavallo, F., Bondonio, P., & Porta, M. (2002). Lifestyle intervention by group care prevents deterioration of Type II diabetes: A 4-year randomized controlled clinical trial. Diabetologia 45(9): 1231–1239.CrossRefGoogle ScholarPubMed
9.Watkinson, M. (2004). Group visits improved concordance with American Diabetes Association practice guidelines in type 2 diabetes. Evidence-Based Nursing 7(2): 57.CrossRefGoogle ScholarPubMed