University of Michigan

**Abstract**:
In drug development it is often necessary to screen through large numbers of
compounds prior to locating one that deserves further attention,
and somewhat similar concerns arise in preclinical and efficacy studies.
This situation also arises in acceptance-rejection sampling where sample products must be tested before an entire batch is deemed acceptable.
Since there may be virtually limitless compounds, products or candidates
available for testing, one would like the average screening trial to be quick,
inexpensive, and accurate.

We describe results from an algorithm for optimizing a decision-theoretic approach to the design of screening trials. The algorithm can optimize a variety of decision and experimental costs and constraints. The designs produced can range from a single stage through to fully sequential, depending on the sampling cost structures.

We believe that decision-theoretic approaches, using flexible cost and constraint structures, allow one to address important aspects of sampling designs. There are a wide range of situations, each with its unique characteristics, and the more flexibility the programs permit in modeling such situations, the better the design will be. In this work, stopping or decision costs are generalized and need not correspond to merely rates of false positives and false negatives; e.g., distance from cutoff can be incorporated. Sampling costs are far more flexible than those of previous researchers, and hence the screening designs are not artificially restricted to fit asymptotic analysis or an overly simplified program. Important operational constraints, such as maximum number of samples per stage, or maximum total number of samples, are also incorporated.

By adjusting costs as control variables, this approach can also be used to meet design goals previously studied, producing more efficient designs, i.e., designs that have smaller expected sample sizes.

In addition to constructing optimal designs, the paper also evaluates some of their operating characteristics. Evaluations can be frequentist, such as pointwise expected sample sizes, or Bayesian, such as robustness with respect to prior misspecification. These exact evaluations are carried out through the use of path induction.

**Keywords**:
response adaptive sampling procedure, sequential,
acceptance sampling,
staged procedure, stopping rule,
drug testing, design of experiments, Bayesian, decision theory

**Complete paper**.
This paper appears in
*Journal of Statistical Planning and Inference* 132 (2005),
pp. 149-162.

- Seminar Presentation:
- Optimal Screening Designs with Flexible Cost Structures.
- Adaptive Allocation:
- Here is an explanation of response-adaptive sampling, including a description of bandit problems, and here are our relevant publications.
- Dynamic Programming (also known as Backward Induction):
- Here is an overview of our work on
dynamic programming.

Preliminary versions of portions of this material appeared in
Q.F Stout and J. Hardwick, "Minimizing the cost of screening trials",
*Computing Science and Statistics* 31 (1999), pp. 440-444,
and in J. Hardwick and Q.F. Stout, "Optimal Screening Designs with Flexible
Cost Structures", *Simulation 2001*,
S.M. Ermakov,
Yu.N. Kashtanov, and V.B. Melas, eds.,
NII Chemistry St. Petersburg, 2001, pp. 253-260.

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