Adaptive Allocation in the Presence of Missing Observations

Janis Hardwick     Robert Oehmke     Quentin F. Stout
University of Michigan


Abstract: We consider the ways in which adaptive allocation is altered when some of the observations become unavailable. Such ``missing outcomes'' are a strong form of censoring. The problems analyzed involve adaptive sampling from two Bernoulli populations. Fully sequential, 3-stage and 2-stage ("few-stage") and fixed designs are examined. For each type of design, we developed an algorithm to determine the optimal design.

Prior approaches were ad hoc and did not fully optimize under the censoring assumptions. Perhaps one reason for this is that censoring turns the populations into 3-outcome populations, which greatly increases the complexity of the problem. A parallel program was developed to optimize the fully sequential design, while serial programs could be used to optimize the other designs. The parallel program used is a simple modification of the program developed for the 3-arm bandit model.

To compare our optimal design to other alternatives, we we also convert designs for uncensored problems into natural designs for the censored problem. Specific objective functions that were evaluated were the 2-arm bandit, which tries to maximize successes, and the product of means, which tries to minimize the mean squared error of the estimate of the success probabilities of the two populations.

Keywords: adaptive sampling, censored observations, design of experiments, bandit problem, controlled clinical trial, path induction, staged allocation, dynamic programming, stochastic optimization, decision theory, computational statistics

Complete paper. This paper appears in Computing Science and Statistics 30 (1998), pp. 219-223.


Related Work
Adaptive Allocation:
Here is an explanation of adaptive sampling including a description of bandit problems, and here are our relevant papers
Dynamic Programming (also known as Backward Induction):
Here is an overview of our work.
Parallel Computing:
A modest explanation of parallel computing.
A tutorial on parallel computing.
An overview of our work, and relevant papers.

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