Browsing by Author "Schaefer, Andrew J."
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Item A Gilmore-Gomory Construction of Integer Programming Value Functions(2021-04-28) Brown, Seth; Schaefer, Andrew J.In this thesis, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. We use a Gilmore-Gomory approach to find parametrized IP value functions over a restricted set of variables. We introduce the notion of maximal connected \color{black}subsets of level sets - volumes in which changes to the constraint right-hand side have no effect on the value function - and relate these structures to IP value functions and optimal solutions.Item Convergence of K-indicators Clustering with Alternating Projection Algorithms(2017-11-21) Yang, Yuchen; Zhang, Yin; Schaefer, Andrew J.; Hand, Paul EData clustering is a fundamental unsupervised machine learning problem, and the most widely used method of data clustering over the decades is k-means. Recently, a newly proposed algorithm called KindAP, based on the idea of subspace matching and a semi-convex relaxation scheme, outperforms k-means in many aspects, such as no random replication and insensitivity to initialization. Unlike k-means, empirical evidence suggests that KindAP can correctly identify well-separated globular clusters even when the number of clusters is large, but a rigorous theoretical analysis is necessary. This study improves the algorithm design and establishes the first-step theory for KindAP. KindAP is actually a two-layered alternating projection procedure applied to two non-convex sets. The inner loop solves an intermediate model via a semi-convex relaxation scheme that relaxes one more complicated non-convex set while keeping the other intact. We first derive a convergence result for this inner loop. Then under the “ideal data” assumption where n data points are exactly located at k positions, we prove that KindAP converges globally to the global minimum with the help of outer loop. Further work is ongoing to extend this analysis from the ideal data case to more general cases.Item Impact of Optimized Breastfeeding on the Costs of Necrotizing Enterocolitis in Extremely Low Birthweight Infants(Elsevier, 2016) Colaizy, Tarah T.; Bartick, Melissa C.; Jegier, Briana J.; Green, Brittany D.; Reinhold, Arnold G.; Schaefer, Andrew J.; Bogen, Debra L.; Schwarz, Eleanor Bimla; Stuebe, Alison M.Objective: To estimate risk of necrotizing enterocolitis (NEC) for extremely low birth weight (ELBW) infants as a function of preterm formula (PF) and maternal milk intake and calculate the impact of suboptimal feeding on the incidence and costs of NEC. Study design: We used aORs derived from the Glutamine Trial to perform Monte Carlo simulation of a cohort of ELBW infants under current suboptimal feeding practices, compared with a theoretical cohort in which 90% of infants received at least 98% human milk. Results: NEC incidence among infants receiving ≥98% human milk was 1.3%; 11.1% among infants fed only PF; and 8.2% among infants fed a mixed diet (P = .002). In adjusted models, compared with infants fed predominantly human milk, we found an increased risk of NEC associated with exclusive PF (aOR = 12.1, 95% CI 1.5, 94.2), or a mixed diet (aOR 8.7, 95% CI 1.2-65.2). In Monte Carlo simulation, current feeding of ELBW infants was associated with 928 excess NEC cases and 121 excess deaths annually, compared with a model in which 90% of infants received ≥98% human milk. These models estimated an annual cost of suboptimal feeding of ELBW infants of $27.1 million (CI $24 million, $30.4 million) in direct medical costs, $563 655 (CI $476 191, $599 069) in indirect nonmedical costs, and $1.5 billion (CI $1.3 billion, $1.6 billion) in cost attributable to premature death. Conclusions: Among ELBW infants, not being fed predominantly human milk is associated with an increased risk of NEC. Efforts to support milk production by mothers of ELBW infants may prevent infant deaths and reduce costs.Item Optimized decision support for selection of transoral robotic surgery or (chemo)radiation therapy based on posttreatment swallowing toxicity(Wiley, 2023) Hemmati, Mehdi; Barbon, Carly; Mohamed, Abdallah S.R.; van Dijk, Lisanne V.; Moreno, Amy C.; Gross, Neil D.; Goepfert, Ryan P.; Lai, Stephen Y.; Hutcheson, Katherine A.; Schaefer, Andrew J.; Fuller, Clifton D.Background A primary goal in transoral robotic surgery (TORS) for oropharyngeal squamous cell cancer (OPSCC) survivors is to optimize swallowing function. However, the uncertainty in the outcomes of TORS including postoperative residual positive margin (PM) and extranodal extension (ENE), may necessitate adjuvant therapy, which may cause significant swallowing toxicity to survivors. Methods A secondary analysis was performed on a prospective registry data with low- to intermediate-risk human papillomavirus–related OPSCC possibly resectable by TORS. Decision trees were developed to model the uncertainties in TORS compared with definitive radiation therapy (RT) and chemoradiation therapy (CRT). Swallowing toxicities were measured by Dynamic Imaging Grade of Swallowing Toxicity (DIGEST), MD Anderson Dysphagia Inventory (MDADI), and the MD Anderson Symptom Inventory–Head and Neck (MDASI-HN) instruments. The likelihoods of PM/ENE were varied to determine the thresholds within which each therapy remains optimal. Results Compared with RT, TORS resulted in inferior swallowing function for moderate likelihoods of PM/ENE (>60% in short term for all instruments, >75% in long term for DIGEST and MDASI) leaving RT as the optimal treatment. Compared with CRT, TORS remained the optimal therapy based on MDADI and MDASI but showed inferior swallowing outcomes based on DIGEST for moderate-to-high likelihoods of PM/ENE (>75% for short-term and >40% for long-term outcomes). Conclusion In the absence of reliable estimation of postoperative PM/ENE concurrent with significant postoperative PM, the overall toxicity level in OPSCC patients undergoing TORS with adjuvant therapy may become more severe compared with patients receiving nonsurgical treatments thus advocating definitive (C)RT protocols.