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This paper introduces the formal study of process flexibility to the novel domain of sports analytics. In baseball, positional flexibility is the analogous concept to process flexibility from manufacturing. We study the flexibility of players (plants) on a baseball team who produce innings-played at different positions (products). We develop models and metrics to evaluate expected and worst-case performance under injury risk (capacity uncertainty) with continuous player-position capabilities. Using Major League Baseball data, we quantify the impact of flexibility on team and individual performance and explore the player chains that arise when injuries occur. We discover that top teams can attribute at least one to two wins per season to flexibility alone, generally as a result of long subchains in the infield or outfield. The least robust teams to worst-case injury, those whose performance is driven by one or two star players, are over four times as fragile as the most robust teams. We evaluate several aspects of individual flexibility, such as how much value individual players bring to their team in terms of average and worst-case performance. Finally, we demonstrate the generalizability of our framework for player evaluation by quantifying the value of potential free agent additions and uncovering the true 'MVP' of a team. History: Accepted by Vishal Gaur, operations management. Supplemental Material: Data are available at https://doi.org/10.1287/mnsc.2017.3004. Keywords: baseball * analytics * positional flexibility * process flexibility * capacity uncertainty. optimization, 1. Introduction In this paper, we examine a long-standing, open question in baseball analytics: what is the value of positional flexibility? To illustrate the concept of positional flexibility, which refers [...]

In classical inverse linear optimization, one assumes that a given solution is a candidate to be optimal. Real data are imperfect and noisy, so there is no guarantee that this assumption is satisfied. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is nonconvex, we derive a closed-form solution and present the geometric intuition. Our goodness-of-fit metric, [rho], the coefficient of complementarity, has similar properties to [R.sup.2] from regression and is quasi-convex in the input data, leading to an intuitive geometric interpretation. While [rho] is computable in polynomial time, we derive a lower bound that possesses the same properties, is tight for several important model variations, and is even easier to compute. We demonstrate the application of our framework for model estimation and evaluation in production planning and cancer therapy. History: Accepted by Yinyu Ye, optimization. Funding: This research was supported in part by the Natural Sciences and Engineering Research Council of Canada. Keywords: inverse optimization * goodness of fit * linear programming * model estimation, 1. Introduction In inverse optimization, one seeks to impute the cost function or other parameters of an optimization problem to render a given solution optimal. This paper is motivated by [...]

Out-of-hospital cardiac arrest is a significant public health issue, and treatment, namely, cardiopulmonary resuscitation and defibrillation, is very time sensitive. Public access defibrillation programs, which deploy automated external defibrillators (AEDs) [...]

In this paper, we use k-means clustering to define distinct player types for each of the three positions on a National Hockey League (NHL) team and then use regression to [...]

Background: The optimal locations and cost-effectiveness of placing automated external defibrillators (AEDs) for out-of-hospital cardiac arrest (OHCAs) in urban residential neighbourhoods are unclear.Methods: We used prospectively collected data from 2016 to 2018 from the British Columbia OHCA Registry to examine the utilization and cost-effectiveness of hypothetical AED deployment in municipalities with a population of over 100 000. We geo-plotted OHCA events using seven hypothetical deployment models where AEDs were placed at the exteriors of public schools and community centers and fetched by bystanders. We calculated the "radius of effectiveness" around each AED within which it could be retrieved and applied to an individual prior to EMS arrival, comparing automobile and pedestrian-based retrieval modes. For each deployment model, we estimated the number of OHCAs within the "radius of effectiveness".Results: We included 4017 OHCAs from ten urban municipalities. The estimated radius of effectiveness around each AED was 625 m for automobile and 240 m for pedestrian retrieval. With AEDs placed outside each school and community center, 2567 (64%) and 605 (15%) of OHCAs fell within the radii of effectiveness for automobile and pedestrian retrieval, respectively. For each AED, there was an average of 1.20-2.66 and 0.25-0.61 in-range OHCAs per year for automobile retrieval and pedestrian retrieval, respectively, depending on the deployment model. All of our proposed surpassed the cost-effectiveness threshold of 0.125 OHCA/AED/year provided > 5.3-11.6% in-range AEDs were brought-to-scene.Conclusions: The systematic deployment of AEDs at schools and community centers in urban neighbourhoods may result in increased application and be a cost-effective public health intervention. [ABSTRACT FROM AUTHOR]

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Background: Patient characteristics, clinical care, resource use and outcomes associated with admission to hospital for coronavirus disease 2019 (COVID-19) in Canada are not well described.Methods: We described all adults with COVID-19 or influenza discharged from inpatient medical services and medical-surgical intensive care units (ICUs) between Nov. 1, 2019, and June 30, 2020, at 7 hospitals in Toronto and Mississauga, Ontario. We compared patient outcomes using multivariable regression models, controlling for patient sociodemographic factors and comorbidity level. We validated the accuracy of 7 externally developed risk scores to predict mortality among patients with COVID-19.Results: There were 1027 hospital admissions with COVID-19 (median age 65 yr, 59.1% male) and 783 with influenza (median age 68 yr, 50.8% male). Patients younger than 50 years accounted for 21.2% of all admissions for COVID-19 and 24.0% of ICU admissions. Compared with influenza, patients with COVID-19 had significantly greater in-hospital mortality (unadjusted 19.9% v. 6.1%, adjusted relative risk [RR] 3.46, 95% confidence interval [CI] 2.56-4.68), ICU use (unadjusted 26.4% v. 18.0%, adjusted RR 1.50, 95% CI 1.25-1.80) and hospital length of stay (unadjusted median 8.7 d v. 4.8 d, adjusted rate ratio 1.45, 95% CI 1.25-1.69). Thirty-day readmission was not significantly different (unadjusted 9.3% v. 9.6%, adjusted RR 0.98, 95% CI 0.70-1.39). Three points-based risk scores for predicting in-hospital mortality showed good discrimination (area under the receiver operating characteristic curve [AUC] ranging from 0.72 to 0.81) and calibration.Interpretation: During the first wave of the pandemic, admission to hospital for COVID-19 was associated with significantly greater mortality, ICU use and hospital length of stay than influenza. Simple risk scores can predict in-hospital mortality in patients with COVID-19 with good accuracy. [ABSTRACT FROM AUTHOR]

Purpose: To develop a knowledge‐based automated planning pipeline that generates treatment plans without feature engineering, using deep neural network architectures for predicting three‐dimensional (3D) dose. Methods: Our knowledge‐based automated planning (KBAP) pipeline consisted of a knowledge‐based planning (KBP) method that predicts dose for a contoured computed tomography (CT) image followed by two optimization models that learn objective function weights and generate fluence‐based plans, respectively. We developed a novel generative adversarial network (GAN)‐based KBP approach, a 3D GAN model, which predicts dose for the full 3D CT image at once and accounts for correlations between adjacent CT slices. Baseline comparisons were made against two state‐of‐the‐art deep learning–based KBP methods from the literature. We also developed an additional benchmark, a two‐dimensional (2D) GAN model which predicts dose to each axial slice independently. For all models, we investigated the impact of multiplicatively scaling the predictions before optimization, such that the predicted dose distributions achieved all target clinical criteria. Each KBP model was trained on 130 previously delivered oropharyngeal treatment plans. Performance was tested on 87 out‐of‐sample previously delivered treatment plans. All KBAP plans were evaluated using clinical planning criteria and compared to their corresponding clinical plans. KBP prediction quality was assessed using dose‐volume histogram (DVH) differences from the corresponding clinical plans. Results: The best performing KBAP plans were generated using predictions from the 3D GAN model that were multiplicatively scaled. These plans satisfied 77% of all clinical criteria, compared to the clinical plans, which satisfied 67% of all criteria. In general, multiplicatively scaling predictions prior to optimization increased the fraction of clinical criteria satisfaction by 11% relative to the plans generated with nonscaled predictions. Additionally, these KBAP plans satisfied the same criteria as the clinical plans 84% and 8% more frequently as compared to the two benchmark methods, respectively. Conclusions: We developed the first knowledge‐based automated planning framework using a 3D generative adversarial network for prediction. Our results, based on 217 oropharyngeal cancer treatment plans, demonstrated superior performance in satisfying clinical criteria and generated more realistic plans as compared to the previous state‐of‐the‐art approaches. [ABSTRACT FROM AUTHOR]

This paper builds on a recently developed Markov Decision Process-based (MDP) handicap system for tennis, which aims to make amateur matches more competitive. The system gives points to the weaker player based on skill difference, which is measured by the point-win probability. However, estimating point-win probabilities at the amateur level is challenging since point-level data is generally only available at the professional level. On the other hand, tennis rating systems are widely used and provide an estimate of the difference in ability between players, but a rigorous determination of handicap using rating systems is lacking. Therefore, our goal is to develop a mapping between the Universal Tennis Rating (UTR) system and the MDP-based handicaps, so that two amateur players can determine an appropriate handicap for their match based only on their UTRs. We first develop and validate an approach to extract server-independent point-win probabilities from match scores. Then, we show how to map server-independent point-win probabilities to server-specific point-win probabilities. Finally, we use the estimated probabilities to produce handicaps via the MDP model, which are regressed against UTR differences between pairs of players. We conclude with thoughts on how a handicap system could be implemented in practice. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging (MRI) is a powerful diagnostic tool that has become the imaging modality of choice for soft-tissue visualization in radiation therapy. Emerging technologies aim to integrate MRI with a medical linear accelerator to form novel cancer therapy systems (MR-linac), but the design of these systems to date relies on heuristic procedures. This paper develops an exact, optimization-based approach for magnet design that 1) incorporates the most accurate physics calculations to date, 2) determines precisely the relative spatial location, size, and current magnitude of the magnetic coils, 3) guarantees field homogeneity inside the imaging volume, 4) produces configurations that satisfy, for the first time, small-footprint feasibility constraints required for MR-linacs. Our approach leverages modern mixed-integer programming (MIP), enabling significant flexibility in magnet design generation, e.g., controlling the number of coils and enforcing symmetry between magnet poles. Our numerical results demonstrate the superiority of our method versus current mainstream methods. [ABSTRACT FROM AUTHOR]

Introduction: Drone-delivered automated external defibrillators (AEDs) may reduce delays to defibrillation for out-of-hospital cardiac arrests (OHCAs). We sought to determine how integration of drones and selection of drone bases between emergency service stations (i.e., paramedic, fire, police) would affect 9-1-1 call-to-arrival intervals.Methods: We identified all treated OHCAs in southern Vancouver Island, British Columbia, Canada from Jan. 2014 to Dec. 2020. We developed mathematical models to select 1-5 optimal drone base locations from each of: paramedic stations, fire stations, police stations, or an unrestricted grid-based set of points to minimize drone travel time to OHCAs. We evaluated models on the estimated first response interval assuming that drones were integrated with existing OHCA response. We compared median response intervals with historical response, as well as across drone base locations.Results: A total of 1610 OHCAs were included in the study with a historical median response interval of 6.4 minutes (IQR 5.0-8.6). All drone-integrated response systems significantly reduced the median response interval to 4.2-5.4 minutes (all P < 0.001), with grid-based stations using 5 drones resulting in the lowest response interval (4.2 minutes). Median response times between drone base location types differed by 6-16 seconds, all comparisons of which were statistically significant (all P < 0.02).Conclusion: Integrating drone-delivered AEDs into OHCA response may reduce first response intervals, even with a small quantity of drones. Implementing drone response with only one emergency service resulted in similar response metrics regardless of the emergency service hosting the drone base and was competitive with unrestricted drone base locations. [ABSTRACT FROM AUTHOR]

Background: Although several Utstein variables are known to independently improve survival, how they moderate the effect of emergency medical service (EMS) response times on survival is unknown.Objectives: To quantify how public location, witnessed status, bystander CPR, and bystander AED shock individually and jointly moderate the effect of EMS response time delays on OHCA survival.Methods: This retrospective cohort study was a secondary analysis of the Resuscitation Outcomes Consortium Epistry-Cardiac Arrest database (December 2005 to June 2015). We included all adult, non-traumatic, non-EMS witnessed, and EMS-treated OHCAs from eleven sites across the US and Canada. We trained a logistic regression model with standard Utstein control variables and interaction terms between EMS response time and the four aforementioned OHCA characteristics.Results: 102,216 patients were included. Three of the four characteristics - witnessed OHCAs (OR = 0.962), bystander CPR (OR = 0.968) and public location (OR = 0.980) - increased the negative effect of a one-minute delay on the odds of survival. In contrast, a bystander AED shock decreased the negative effect of a one-minute response time delay on the odds of survival (OR = 1.064). The magnitude of the effect of a one-minute delay in EMS response time on the odds of survival ranged from 1.3% to 9.8% (average: 5.3%), depending on the underlying OHCA characteristics.Conclusions: Delays in EMS response time had the largest reduction in survival odds for OHCAs that did not receive a bystander AED shock but were witnessed, occurred in public, and/or received bystander CPR. A bystander AED shock appears to be protective against a delay in EMS response time. [ABSTRACT FROM AUTHOR]

Aim: Quantifying the ratio describing the difference between "true route" and "straight-line" distances from out-of-hospital cardiac arrests (OHCAs) to the closest accessible automated external defibrillator (AED) can help correct likely overestimations in AED coverage. Furthermore, we aimed to examine to what extent the closest AED based on true route distance differed from the closest AED using "straight-line".Methods: OHCAs (1994-2016) and AEDs (2016) in Copenhagen, Denmark and in Toronto, Canada (2007-2015 and 2015, respectively) were identified. Three distances were calculated between OHCA and target AED: 1) the straight-line distance ("straight-line") to the closest AED, 2) the corresponding true route distance to the same AED ("true route"), and 3) the closest AED based only on true route distance ("shortest true route"). The ratio between "true route" and "straight-line" distance was calculated and differences in AED coverage (an OHCA ≤ 100 m of an accessible AED) were examined.Results: The "straight-line" AED coverage of 100 m was 24.2% (n = 2008/8295) in Copenhagen and 6.9% (n = 964/13916) in Toronto. The corresponding "true route" distance reduced coverage to 9.5% (n = 786) and 3.8% (n = 529), respectively. The median ratio between "true route" and "straight-line" distance was 1.6 in Copenhagen and 1.4 in Toronto. In 26.1% (n = 2167) and 22.9% (n = 3181) of all Copenhagen and Toronto OHCAs respectively, the closest AED in "shortest true route" was different than the closest AED initially found by "straight-line".Conclusions: Straight-line distance is not an accurate measure of distance and overestimates the actual AED coverage compared to a more realistic true route distance by a factor 1.4-1.6. [ABSTRACT FROM AUTHOR]

Background: Mathematical optimization can be used to place automated external defibrillators (AEDs) in locations that maximize coverage of out-of-hospital cardiac arrests (OHCAs). We sought to determine whether optimization can improve alignment between AED locations and OHCA counts across levels of socioeconomic deprivation.Methods: All suspected OHCAs and registered AEDs in Scotland between Jan. 2011 and Sept. 2017 were included and mapped to a corresponding socioeconomic deprivation level using the Scottish Index of Multiple Deprivation (SIMD). We used mathematical optimization to determine optimal locations for placing 10%, 25%, 50%, and 100% additional AEDs, as well as locations for relocating existing AEDs. For each AED placement policy, we examined the impact on AED distribution and OHCA "coverage" (suspected OHCA occurring within 100 m of AED) with respect to SIMD quintiles.Results: We identified 49,432 suspected OHCAs and 1532 AEDs. The distribution of existing AED locations across SIMD quintiles significantly differed from the distribution of suspected OHCAs (P < 0.001). Optimization-guided AED placement increased coverage of suspected OHCAs compared to existing AED locations (all P < 0.001). Optimization resulted in more AED placements and increased OHCA coverage in areas of greater socioeconomic deprivation, such that resulting distributions across SIMD quintiles matched the shape of the OHCA count distribution. Optimally relocating existing AEDs achieved similar OHCA coverage levels to that of doubling the number of total AEDs.Conclusions: Mathematical optimization results in AED locations and suspected OHCA coverage that more closely resembles the suspected OHCA distribution and results in more equitable coverage across levels of socioeconomic deprivation. [ABSTRACT FROM AUTHOR]

Aims: To determine if mathematical optimization of in-hospital defibrillator placements can reduce in-hospital cardiac arrest-to-defibrillator distance compared to existing defibrillators in a single hospital.Methods: We identified treated IHCAs and defibrillator placements in St. Michael's Hospital in Toronto, Canada from Jan. 2013 to Jun. 2017 and mapped them to a 3-D computer model of the hospital. An optimization model identified an equal number of optimal defibrillator locations that minimized the average distance between IHCAs and the closest defibrillator using a 10-fold cross-validation approach. The optimized and existing defibrillator locations were compared in terms of average distance to the out-of-sample IHCAs. We repeated the analysis excluding intensive care units (ICUs), operating theatres (OTs), and the emergency department (ED). We also re-solved the model using fewer defibrillators to determine when the average distance matched the performance of existing defibrillators.Results: We identified 433 treated IHCAs and 53 defibrillators. Of these, 167 IHCAs and 31 defibrillators were outside of ICUs, OTs, and the ED. Optimal defibrillator placements reduced the average IHCA-to-defibrillator distance from 16.1 m to 2.7 m (relative decrease of 83.0%; P = 0.002) compared to existing defibrillator placements. For non-ICU/OT/ED IHCAs, the average distance was reduced from 24.4 m to 11.9 m (relative decrease of 51.3%; P = 0.002. 8-9 optimized defibrillator locations were sufficient to match the average IHCA-to-defibrillator distance of existing defibrillator placements.Conclusions: Optimization-guided placement of in-hospital defibrillators can reduce the distance from an IHCA to the closest defibrillator. Equivalently, optimization can match existing defibrillator performance using far fewer defibrillators. [ABSTRACT FROM AUTHOR]

Background: Immediate access to an automated external defibrillator (AED) increases the chance of survival for out-of-hospital cardiac arrest (OHCA). Current deployment usually considers spatial AED access, assuming AEDs are available 24 h a day.Objectives: The goal of this study was to develop an optimization model for AED deployment, accounting for spatial and temporal accessibility, to evaluate if OHCA coverage would improve compared with deployment based on spatial accessibility alone.Methods: This study was a retrospective population-based cohort trial using data from the Toronto Regional RescuNET Epistry cardiac arrest database. We identified all nontraumatic public location OHCAs in Toronto, Ontario, Canada (January 2006 through August 2014) and obtained a list of registered AEDs (March 2015) from Toronto Paramedic Services. Coverage loss due to limited temporal access was quantified by comparing the number of OHCAs that occurred within 100 meters of a registered AED (assumed coverage 24 h per day, 7 days per week) with the number that occurred both within 100 meters of a registered AED and when the AED was available (actual coverage). A spatiotemporal optimization model was then developed that determined AED locations to maximize OHCA actual coverage and overcome the reported coverage loss. The coverage gain between the spatiotemporal model and a spatial-only model was computed by using 10-fold cross-validation.Results: A total of 2,440 nontraumatic public OHCAs and 737 registered AED locations were identified. A total of 451 OHCAs were covered by registered AEDs under assumed coverage 24 h per day, 7 days per week, and 354 OHCAs under actual coverage, representing a coverage loss of 21.5% (p < 0.001). Using the spatiotemporal model to optimize AED deployment, a 25.3% relative increase in actual coverage was achieved compared with the spatial-only approach (p < 0.001).Conclusions: One in 5 OHCAs occurred near an inaccessible AED at the time of the OHCA. Potential AED use was significantly improved with a spatiotemporal optimization model guiding deployment. [ABSTRACT FROM AUTHOR]