## DIMACS TR: 2004-20

##
Subject Allocation and Study Curtailment for Fixed Event Comparative Poisson Trials

### Author: Donald R. Hoover

**
ABSTRACT
**
Comparative Poisson trials of prophylactic interventions, such as vaccines,
can be lengthy and costly. We evaluate two easily implemented approaches to
reduce numbers of disease cases and person years of follow up (N_{u+t}) for
comparative Poisson trials with fixed numbers of cases (T); i) altering k the
portion of N_{u+t} allocated to treatment, and ii) curtailed stopping before
T cases if numbers of cases in the treatment or control group indicate that
H_o has already been rejected or will not be rejected at T cases. Normal and
arcsine approximations as well as discrete exact tests are evaluated. For
studies not stopped early, allocating about 1/(1+\sqrt(r_a)) of person years
to treatment roughly minimizes T needed for given size and power (where r_a
is the alternative hypothesized relative disease incidence in treated subjects
used to power the study). This reduces T moderately V_s equal allocation
(k=0.5); by 2-3 cases in our examples with exact tests. However, the common
practice of allocating k=0.5 of the person years to treatment may be the
overall best strategy to minimize N_{u+t} for studies that are not stopped
early. For studies analyzed by exact test and planned with a one sided \alpha
ranging from 0.005 to 0.025, \beta from 0.1 to 0.2 and r_a from 0.2 to 0.5,
curtailed stopping reduces both number of disease cases and N_{u+t} by 6%
to 40% depending on true treatment benefit. With curtailed stopping,
allocating k=0.5 person years to treatment approximately minimizes numbers
of cases and person years under most conditions, although k as large as 0.6
often performs comparably well. If a specific localized k is selected to
minimize disease cases for a study analyzed by exact test, the study may be
underpowered should the final allocation deviate even slightly from that k
when it is conducted.
Key Words: Comparative Poisson, Curtailed Stopping, Power, Sample Size, Subject Allocation

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-20.ps.gz

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