Benjamin Armbruster

Formulating adaptive radiation therapy (ART) treatment planning into a closed-loop control framework*

While ART has been studied for years, the specific quantitative implementation details have not. In order for this new scheme of radiation therapy (RT) to reach its potential, an effective ART treatment planning strategy capable of taking into account the dose delivery history and the patients on-treatment geometric model must be in place. This paper performs a theoretical study of dynamic closed-loop control algorithms for ART and compares their utility with data from phantom and clinical cases. We developed two classes of algorithms: those Adapting to Changing Geometry and those Adapting to Geometry and Delivered Dose. The former class takes into account organ deformations found just before treatment. The latter class optimizes the dose distribution accumulated over the entire course of treatment by adapting at each fraction, not only to the information just before treatment about organ deformations but also to the dose delivery history. We showcase two algorithms in the class of those Adapting to Geometry and Delivered Dose. A comparison of the approaches indicates that certain closed-loop ART algorithms may significantly improve the current practice. We anticipate that improvements in imaging, dose verification and reporting will further increase the importance of adaptive algorithms.

Dynamic Spectrum Management With the Competitive Market Model

Ye [¿Competitive Communication Spectrum Economy and Equilibrium,¿ 2008, working paper] and Lin [¿Budget Allocation in a Competitive Communication Spectrum Economy,¿ EURASIP J. Adv. Signal Process., Article ID: 963717, vol. 2009, p. 12, Sep. 2009] have shown that dynamic spectrum management (DSM) using the market competitive equilibrium (CE), which sets a price for transmission power on each channel, leads to better system performance in terms of the total data transmission rate (by reducing cross talk), than using the Nash equilibrium (NE). But how to achieve such a CE is an open problem. We show that the CE is the solution of a linear complementarity problem (LCP) and can be computed efficiently. We propose a decentralized tatonnement process for adjusting the prices to achieve a CE. We show that under reasonable conditions, any tatonnement process converges to the CE. The conditions are that users of a channel experience the same noise levels and that the crosstalk effects between users are low-rank and weak.

The cost-effectiveness of expanded HIV screening in the United States

Objective:The current Centers of Disease Control and Prevention (CDC) guidelines from 2006 recommend a one-time test for low-risk individuals and annual testing for those at high risk. These guidelines may not be aggressive enough, even for those at low risk of infection, due to the earlier initiation of HAART and a movement towards a test-and-treat environment. We evaluated the optimal testing frequencies for various risk groups in comparison to the CDC recommendations. Methods:We build a deterministic mathematical model optimizing the tradeoff between the societal cost of testing and the benefits over a patients lifetime of earlier diagnosis. Results:Under a test-and-treat scenario with immediate initiation of HAART, the optimal testing frequency is every 2.4 years for low-risk (0.01% annual incidence) individuals; every 9 months for moderate risk (0.1% incidence) individuals; and every 3 months for high-risk (1.0% incidence) individuals. The incremental cost-effectiveness of the optimal policy is

Models and formulations for multivariate dominance-constrained stochastic programs

36 342/quality-adjusted life-years (QALY) for low-risk individuals and

Contact tracing to control infectious disease: when enough is enough

45 074/QALY for high-risk individuals compared with 20-year and annual testing, respectively. Conclusion:The current CDC guidelines for HIV testing are too conservative, and more frequent testing is cost-effective for all risk groups.

Decision Making Under Uncertainty When Preference Information Is Incomplete

The use of a stochastic dominance constraint to specify risk preferences in a stochastic program has been recently proposed in the literature. Such a constraint requires the random outcome resulting from one’s decision to stochastically dominate a given random comparator. These ideas have been extended to problems with multiple random outcomes, using the notion of positive linear stochastic dominance. This article proposes a constraint using a different version of multivariate stochastic dominance. This version is natural due to its connection to expected utility maximization theory and relatively tractable. In particular, it is shown that such a constraint can be formulated with linear constraints for the second-order dominance relation and with mixed-integer constraints for the first-order relation. This is in contrast with a constraint on second-order positive linear dominance, for which no efficient algorithms are known. The proposed formulations are tested in the context of two applications: budget allocation in a setting with multiple objectives and finding radiation treatment plans in the presence of organ motion.

A Data-Driven Simulation of HIV Spread Among Young Men Who Have Sex With Men: Role of Age and Race Mixing and STIs.

Contact tracing (also known as partner notification) is a primary means of controlling infectious diseases such as tuberculosis (TB), human immunodeficiency virus (HIV), and sexually transmitted diseases (STDs). However, little work has been done to determine the optimal level of investment in contact tracing. In this paper, we present a methodology for evaluating the appropriate level of investment in contact tracing. We develop and apply a simulation model of contact tracing and the spread of an infectious disease among a network of individuals in order to evaluate the cost and effectiveness of different levels of contact tracing. We show that contact tracing is likely to have diminishing returns to scale in investment: incremental investments in contact tracing yield diminishing reductions in disease prevalence. In conjunction with a cost-effectiveness threshold, we then determine the optimal amount that should be invested in contact tracing. We first assume that the only incremental disease control is contact tracing. We then extend the analysis to consider the optimal allocation of a budget between contact tracing and screening for exogenous infection, and between contact tracing and screening for endogenous infection. We discuss how a simulation model of this type, appropriately tailored, could be used as a policy tool for determining the appropriate level of investment in contact tracing for a specific disease in a specific population. We present an example application to contact tracing for chlamydia control.

Finding equitable convex partitions of points in a polygon efficiently

We consider the problem of optimal decision making under uncertainty but assume that the decision makers utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over other lotteries and being risk averse, S-shaped, or prudent. These criteria extend the ones used in the first-and second-order stochastic dominance framework. We then give tractable formulations for such decision-making problems. We formulate them as robust utility maximization problems, as optimization problems with stochastic dominance constraints, and as robust certainty equivalent maximization problems. We use a portfolio allocation problem to illustrate our results. This paper was accepted by Dimitris Bertsimas, optimization.

A packet filter placement problem with application to defense against spoofed denial of service attacks

Objective:Young men who have sex with men (YMSM) in the United States have a high HIV incidence with substantial racial disparities that are poorly understood. We use a data-driven simulation model to understand the impact of network-level mechanisms and sexually transmitted infections on the spread of HIV among YMSM. Methods:We designed and parameterized a stochastic agent-based network simulation model using results of a longitudinal cohort study of YMSM in Chicago. Within this model, YMSM formed and dissolved partnerships over time, and partnership types were stratified by length of partnership, sex, and age of the partner. In each partnership, HIV, gonorrhea, and chlamydia could be transmitted. Counterfactual scenarios were run to examine drivers of HIV. Results:Over a 15-year simulation, the HIV epidemic among YMSM continued to rise, with Latino/white YMSM facing a steeper increase in the HIV burden compared with black YMSM. YMSM in partnerships with older MSM, in particular black YMSM with older black MSM, were at highest risk for HIV, and 1 infection prevented with an older partner would prevent 0.8 additional infections among YMSM. Additionally, racial disparities in HIV were driven by differences in the HIV prevalence of YMSM partners. Finally, of all HIV infections among YMSM, 14.6% were attributable to NG and CT infections. Conclusion:Network-level mechanisms and sexually transmitted infections play a significant role in the spread of HIV and in racial disparities among YMSM. HIV prevention efforts should target YMSM across race, and interventions focusing on YMSM partnerships with older MSM might be highly effective.

Cost-effective control of chronic viral diseases: finding the optimal level of screening and contact tracing.

Previous work has developed algorithms for finding an equitable convex partition that partitions the plane into n convex pieces each containing an equal number of red and blue points. Motivated by a vehicle routing heuristic, we look at a related problem where each piece must contain one point and an equal fraction of the area of some convex polygon. We first show how algorithms for solving the older problem lead to approximate solutions for this new equitable convex partition problem. Then we demonstrate a new algorithm that finds an exact solution to our problem in O(N nlog N) time or operations, where n is the number of points, m the number of vertices or edges of the polygon, and N:=n+m the sum.