Annual Report 2008.pdf - SAMSI

Naval Postgraduate School, Department of Operations Research
mcarlyle@nps.edu
Trilevel Optimization of Homeland Defense Problems
The U.S. Department of Homeland Security (DHS) is investing billions of dollars to protect us
from terrorist attacks and their expected damage (i.e., risk). We present prescriptive optimization
models to guide DHS investments in a set of defensive options that as an overall defense strategy
reduces our initial vulnerability to attack, while also equipping us to mitigate damage from an
attack after one happens. Our “Defender-Attacker-Defender risk-minimization model” assumes
that terrorist attackers will observe, and react to, any strategic defensive investment on the scale
required to protect our entire country: (a) the defender invests strategically in interdiction and/or
mitigation
options (for example, by inoculating health-care workers, or stockpiling a mix of emergency
vaccines) (b) the attacker observes those investments and attacks as effectively as possible, and
(c) the defender then optimally deploys the mitigation options that his investments have enabled.
We show with simple numerical examples some of the important insights offered by such
analysis. Our primary goal is prioritizing defensive strategies. Secondarily, we want to elicit
optimal attacker behavior, so we can focus intelligence collection on telltales of the most-likely
and most-lethal attacks.
Yu Cheng
University of Pittsburgh, Department of Statistics and Psychiatry
yucheng95@gmail.com
Association analyses of bivariate competing risks data
While nonparametric analyses of bivariate failure times under independent censoring have been
widely studied, nonparametric analyses of bivariate competing risks data have not been critically
examined. Such analyses are important in familial association studies, where multiple interacting
failure types may violate the independent censoring assumption. We develop nonparametric
estimators for the bivariate cumulative cause-specific hazards function and the bivariate
cumulative incidence function, which are natural analogs of their univariate counterparts and
make no assumptions about the dependence of the risks. The estimators are shown to be
uniformly consistent and to converge weakly to Gaussian processes. They provide the basis for
novel time-dependent
association measures, with the associated inferences yielding tests of cause-specific
independence in clusters. The methodology performs well in simulations with realistic sample
sizes. Its practical utility is illustrated in an analysis of dementia in the Cache County Study,
where the nonparametric methods indicate that mother-child disease associations are strongly
time-varying.
Todd Durham
Inspire Pharmaceuticals
tdurham@inspirepharm.com