## Future Research

### Easy Extensions

- Cost structures, ethical factors, and multiple objective functions
(these have already been incorporated in some of
our work on other problems). Generalized cost criteria include
money, time, resources, or ethical factors such as failures or
expected successes lost. Costs may be optimization criteria or
evaluation criteria.
- Optional (and optimal) stopping.
- Randomization

### Harder Extensions

- More populations. The time/space complexity is polynomial in the
sample size, but exponential in the number of populations.
- Covariates.
- Correlated populations. We are currently engaged in joint work
with Connie Page involving an
estimation
problem where different
types of observations yield different information about the same
parameter. As more medical diagnostics become available, such
situations will become increasingly important.
- Non-binary responses. It is extremely hard to optimize designs in
such situations, and so one needs to emphasize locating "good" designs.
- Delayed responses. Note that hyperopic designs may be useful here,
because they provide a natural way to incorporate partial information.
- Vastly larger sample sizes. We may use extrapolation or interpolation
approaches to achieve near-optimal designs.

A related project is to explore using a variety of graphical techniques for
examining procedure behavior. For example, commonly expressed
complaints about the OS procedure include:

- it is too hard to compute
- it is too hard to understand

We have already shown that the first of these is no longer true, and we hope
that visualization approaches might help overcome the second.

References
Outline
Points of
Interest