Epidemic Management via Imperfect Testing: A Multi-criterial Perspective

Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.

Use of dose-area product to assess plan quality in robotic radiosurgery

PURPOSE

In robotic stereotactic radiosurgery (SRS), optimal selection of collimators from a set of fixed cones must be determined manually by trial and error. A unique and uniformly scaled metric to characterize plan quality could help identify Pareto-efficient treatment plans.

METHODS

The concept of dose-area product (DAP) was used to define a measure (DAPratio) of the targeting efficiency of a set of beams by relating the integral DAP of the beams to the mean dose achieved in the target volume. In a retrospective study of five clinical cases of brain metastases with representative target volumes (range: 0.5-5.68 ml) and 121 treatment plans with all possible collimator choices, the DAPratio was determined along with other plan metrics (conformity index CI, gradient index R50%, treatment time, total number of monitor units TotalMU, radiotoxicity index f12, and energy efficiency index η50%), and the respective Spearman's rank correlation coefficients were calculated. The ability of DAPratio to determine Pareto efficiency for collimator selection at DAPratio < 1 and DAPratio < 0.9 was tested using scatter plots.

RESULTS

The DAPratio for all plans was on average 0.95 ± 0.13 (range: 0.61-1.31). Only the variance of the DAPratio was strongly dependent on the number of collimators. For each target, there was a strong or very strong correlation of DAPratio with all other metrics of plan quality. Only for R50% and η50% was there a moderate correlation with DAPratio for the plans of all targets combined, as R50% and η50% strongly depended on target size. Optimal treatment plans with CI, R50%, f12, and η50% close to 1 were clearly associated with DAPratio < 1, and plans with DAPratio < 0.9 were even superior, but at the cost of longer treatment times and higher total monitor units.

CONCLUSIONS

The newly defined DAPratio has been demonstrated to be a metric that characterizes the target efficiency of a set of beams in robotic SRS in one single and uniformly scaled number. A DAPratio < 1 indicates Pareto efficiency. The trade-off between plan quality on the one hand and short treatment time or low total monitor units on the other hand is also represented by DAPratio.

A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem

In many real-world optimization problems, more than one objective plays a role and input parameters are subject to uncertainty. In this paper, motivated by applications in disaster relief and public facility location, we model and solve a bi-objective stochastic facility location problem. The considered objectives are cost and covered demand, where the demand at the different population centers is uncertain but its probability distribution is known. The latter information is used to produce a set of scenarios. In order to solve the underlying optimization problem, we apply a Benders' type decomposition approach which is known as the L-shaped method for stochastic programming and we embed it into a recently developed branch-and-bound framework for bi-objective integer optimization. We analyze and compare different cut generation schemes and we show how they affect lower bound set computations, so as to identify the best performing approach. Finally, we compare the branch-and-Benders-cut approach to a straight-forward branch-and-bound implementation based on the deterministic equivalent formulation.

Chemometrics-assisted optimization of liquid chromatography-quadrupole-time-of-flight mass spectrometry analysis for targeted metabolomics

Mass spectrometry-based metabolomics is characterized by a vast number of variables leading to a great degree of complexity. In this work, we aimed to simplify this process with a stepped chemometric optimization of the both funnel technology (funnel exit DC, FDC; funnel RF LP, FLC; funnel RF HP, FRP) and ion source parameters (Octopolo, Oct; and Fragmentor, Frag) of a quadrupole-time of flight (qTOF) for a human urinary metabolites. The workflow comprised a Box-Behnken experimental design with 47 experiments followed by the identification and quantification of a set of metabolites using high-resolution full-scan MS mode and feature extraction with an inclusion list. Metabolite peak areas were grouped according to abundance (high and low) and modeled by Random Forest regression (variance explained >85%). The full three-level factorial design consisting in 243 experiments was predicted and top 10 solutions for desirability function and those comprising the Pareto front were extracted and investigated. To guarantee the quality of results, we compared the Pareto front solutions with those achieved by standard instrumental parameters suggested by the manufacturer. A set of five solutions were identified that increased the mean peak area by 56-59% and 17%, for high- and low-abundance metabolites, respectively. The optimal parameters were determined to be: FLP, 100 V; FDC, 40 and 30 V; Frag, 275 and 400 V; and Oct, 600 and 800 V. The methodology applied throughout this work represents a flexible strategy to optimize instrumental parameters and exploit the performance of a qTOF MS detector.