A program for sequential allocation of Bernoulli populations

A program for optimizing and analyzing sequential allocation problems involving three Bernoulli populations and a general objective function is described. Previous researchers had considered this problem computationally intractable, and there appears to be no prior exact optimizations for such problems, even for very small sample sizes. This paper contains a description of the program, along with the techniques used to scale it to large sample sizes. The program currently handles problems of size 200 or more by using a modest parallel computer, and problems of size 100 on a workstation. As an illustration, the program is used to create an adaptive sampling procedure that is the optimal solution to a 3-arm bandit problem. The bandit procedure is then compared to two other allocation procedures along various Bayesian and frequentist metrics. Extensions enabling the program to solve a variety of related problems are discussed. c 1999 Published by Elsevier Science B.V. All rights reserved.

[1]  Mikhail J. Atallah,et al.  Algorithms and Theory of Computation Handbook , 2009, Chapman & Hall/CRC Applied Algorithms and Data Structures series.

[2]  H. Büringer,et al.  Nonparametric Sequential Selection Procedures , 1980 .

[3]  Rebecca A. Betensky,et al.  An O'Brien-Fleming sequential trial for comparing three treatments , 1996 .

[4]  P. W. Jones,et al.  Bandit Problems, Sequential Allocation of Experiments , 1987 .

[5]  Quentin F. Stout,et al.  A Parallel Program for 3-Arm Bandits , 1997 .

[6]  D. Coad,et al.  Sequential allocation rules for multi-armed clinical trials , 1995 .

[7]  ScienceDirect.  Computational statistics & data analysis , 1983 .

[8]  Christian M. Ernst,et al.  Multi-armed Bandit Allocation Indices , 1989 .

[9]  V. G. Kulkarni,et al.  Optimal Bayes procedures for selecting the better of two Bernoulli populations , 1986 .

[10]  R A Betensky,et al.  Sequential analysis of censored survival data from three treatment groups. , 1997, Biometrics.

[11]  Quentin F. Stout,et al.  Using Path Induction to Evaluate Sequential Allocation Procedures , 1999, SIAM J. Sci. Comput..

[12]  You-Gan Wang.  Sequential allocation in clinical trials , 1991 .

[13]  Quentin F. Stout,et al.  Path induction for evaluating sequential allocation procedures , 1999 .

[14]  J. Bather,et al.  Multi‐Armed Bandit Allocation Indices , 1990 .

[15]  D. Siegmund,et al.  A sequential clinical trial for comparing three treatments , 1993 .

[16]  John Bather,et al.  Sequential procedures for comparing several medical treatments , 1992 .

[17]  P. Armitage.  The search for optimality in clinical trials , 1985 .

[18]  D. Berry,et al.  Adaptive assignment versus balanced randomization in clinical trials: a decision analysis. , 1995, Statistics in medicine.

[19]  Anthony Skjellum,et al.  Using MPI - portable parallel programming with the message-parsing interface , 1994 .

[20]  R. Simon,et al.  Adaptive treatment assignment methods and clinical trials. , 1977, Biometrics.

[21]  Quentin F. Stout,et al.  Scalable parallel implementation of high-dimensional dynamic programming , 1999 .

[22]  Quentin F. Stout,et al.  Adaptive Allocation in the Presence of Missing Outcomes , 1998 .

[23]  Quentin F. Stout,et al.  Exact computational analyses for adaptive designs , 1995 .

[24]  Shanti S. Gupta,et al.  Selecting the best binomial population: parametric empirical Bayes approach , 1989 .