Information Technology Reference
In-Depth Information
The courts of many other states have followed
Plemmel
. “The better
practice may be for the expert to testify to a range of prior probabilities,
such as 10, 50 and 90 percent, and allow the trier of fact to determine
which to use.”
26
Applications to Experiments and Clinical Trials
Outside the courtroom, where the rules of evidence are less rigorous, we
have much greater latitude in the adoption of
a prior
distributions for the
unknown parameter(s). Two approaches are common:
1. Adopting some synthetic distribution—a normal or a Beta.
2. Using subjective probabilities.
The synthetic approach, though common among the more computa-
tional, is difficult to justify. The theoretical basis for an observation having
a normal distribution is well known—the observation will be the sum of a
large number of factors, each of which makes only a minute contribution
to the total. But could such a description be applicable to a population
parameter?
Here is an example of this approach taken from a report by D. A.
Berry
27
: “A study reported by Freireich et al.
28
was designed to evaluate
the effectiveness of a chemotherapeutic agent 6-mercaptopurine (6-MP)
for the treatment of acute leukemia. Patients were randomized to therapy
in pairs. Let
p
be the population proportion of pairs in which the 6-MP
patient stays in remission longer than the placebo patient. (To distinguish
probability
p
from a probability distribution concerning
p
, I will call it a
population proportion or a propensity.) The null hypothesis
H
0
is
p
= 1/2:
no effect of 6-MP. Let
H
1
stand for the alternative hypothesis that
p
> 1/2. There were 21 pairs of patients in the study, and 18 of them
favored 6-MP.”
“Suppose that the prior probability of the null hypothesis is 70 percent
and that the remaining probability of 30 percent is on the interval (0,1)
uniformly....So under the alternative hypothesis
H
1
,
p
has a uniform(0,1)
distribution. This is a mixture prior in the sense that it is 70 percent dis-
crete and 30 percent continuous.”
26
County of El Dorado v. Misura, 33 Cal. App. 4th 73 (1995) citing Plemel, supra, at
p. 1219; Peterson (1982 at p. 691, fn. 74), Paternity of M.J.B., 144 Wis.2d 638, 643; State
v. Jackson, 320 N.C.452, 455 (1987), and Kammer v. Young, 73 Md. App. 565, 571 (1988).
See also State v. Spann, 130 N.J. 484 at p. 499 (1993).
27
The full report titled “Using a Bayesian Approach in Medical Device Development” may
be obtained from Donald A. Berry at the Institute of Statistics & Decision Sciences and
Comprehensive Cancer Center, Duke University, Durham, NC 27708.
28
Blood
1963; 21:699-716.
