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People are often reluctant to sell a house, or shares of stock, below the price at which they originally bought it. While this is generally not consistent with rational utility maximization, it does reflect two strong empirical regularities that are central to the behavioral science of human decision-making: a tendency to evaluate outcomes relative to a reference point determined by context (in this case the original purchase price), and the phenomenon of loss aversion in which people are particularly prone to avoid outcomes below the reference point. Here we explore the implications of reference points and loss aversion in optimal stopping problems, where people evaluate a sequence of options in one pass, either accepting the option and stopping the search or giving up on the option forever. The best option seen so far sets a reference point that shifts as the search progresses, and a biased decision-maker's utility incurs an additional penalty when they accept a later option that is below this reference point. We formulate and study a behaviorally well-motivated version of the optimal stopping problem that incorporates these notions of reference dependence and loss aversion. We obtain tight bounds on the performance of a biased agent in this model relative to the best option obtainable in retrospect (a type of prophet inequality for biased agents), as well as tight bounds on the ratio between the performance of a biased agent and the performance of a rational one. We further establish basic monotonicity results, and show an exponential gap between the performance of a biased agent in a stopping problem with respect to a worst-case versus a random order. As part of this, we establish fundamental differences between optimal stopping problems for rational versus biased agents, and these differences inform our analysis., Comment: To appear in the 2021 ACM Conference on Economics and Computation (EC'21)

To analyze the impact of target delineation on local control (LC) after stereotactic body radiotherapy (SBRT) for spine metastasis.Patients with de novo metastasis of the spine treated with SBRT, excluding those with prostate or hematologic malignancies, were retrospectively reviewed. Deviations from consensus contouring guidelines included incomplete coverage of involved vertebral compartments, omission of adjacent compartments, or unnecessary circumferential coverage. Univariable and multivariable Cox proportional hazard analyses were performed using death as a competing risk.283 patients with 360 discrete lesions were included with a median follow up of 14.6 months (range 1.2-131.3). The prescription dose was 24-27 Gy in 2-3 fractions for the majority of lesions. Median survival after SBRT was 18.3 months (95 % confidence interval [CI]: 14.8-22.8). The 1 and 2-year local control (LC) rates were 81.1 % (95 % CI: 75.5-85.6 %) and 70.6 % (95 % CI: 63.2-76.8 %), respectively. In total, 60 deviations (16.7 %) from consensus contouring guidelines were identified. Deviation from guidelines was associated with inferior LC (1-year LC 63.0 % vs 85.5 %, p 0.001). Gastrointestinal primary, epidural extension, and paraspinal extension were all associated with inferior LC on univariable analyses. After adjusting for confounding factors, deviation from guidelines was the strongest predictor of inferior LC (HR 3.52, 95 % CI: 2.11-5.86, p 0.001). Among guideline-compliant treatments, progressions were mainly in field (61 %) and/or epidural (49 %), while marginal (42 %) and/or epidural progressions (58 %) were most common for those with deviations.Adherence to consensus contouring guidelines for spine SBRT is associated with superior LC and fewer marginal misses.

BACKGROUND CONTEXT With improvements in adjuvant radiotherapy and minimally invasive surgical techniques, separation surgery has become the default surgical intervention for spine metastases at many centers. However, it is unclear if there is clinical benefit from anterior column resection in addition to simple epidural debulking prior to stereotactic body radiotherapy (SBRT). PURPOSE To examine the effect of anterior column debulking versus epidural disease resection alone in the local control of metastases to the bony spine. STUDY DESIGN Retrospective cohort study. PATIENT SAMPLE Ninety-seven patients who underwent open surgery followed by SBRT for spinal metastases at a single comprehensive cancer center. OUTCOME MEASURES Local tumor recurrence following surgery and SBRT. METHODS Data were collected regarding radiation dose, cancer histology, extent of anterior column resection, and recurrence. Tumor involvement was categorized using the International Spine Radiosurgery Consortium guidelines. Univariable analyses were conducted to determine predictors of local recurrence and time to local recurrence. RESULTS Among the 97 included patients, mean age was 60.5±11.4 years and 51% of patients were male. The most common primary tumor types were lung (20.6%), breast (17.5%), kidney (13.4%) and prostate (12.4%). Recurrence was seen in 17 patients (17.5%) and local control rates were: 85.5% (1-year), 81.1% (2-year), and 54.9% (5-year). Overall predictors of local recurrence were tumor pathology (p

Objective Stereotactic body radiotherapy (SBRT) for spine metastases is associated with post-treatment vertebral compression fracture (VCF). The purpose of this study is to identify clinical and radiation planning characteristics that predict post-SBRT VCF through a novel normal tissue complication probability (NTCP) analysis. Methods Patients with de novo spine metastases treated with SBRT between 2009 and 2018 at a single institution were included. Those who had surgical stabilization or radiation to the same site prior to SBRT were excluded. VCF was defined as new development or progression of existing vertebral body height loss not attributable to tumor growth. Probit NTCP models were constructed and fitted using a maximum likelihood approach. A multivariate proportional hazard model was used to estimate time to VCF using the Fine and Gray method. Results Three hundred and two vertebral segments from 193 patients were treated with a median dose of 24 Gy in 3 fractions (range 15–30 Gy in 1–5 fractions). With a median follow up of 13.9 months, local control was 89.3% at 1 year. A total of 26 SBRT-induced VCFs were observed, with 1 and 2-year cumulative incidences of 4.6% and 6.7%. NTCP modeling demonstrated a steep response of VCF risk to the dose to 80% and 50% volume of the planning target volume (PTV D80% and D50%), but not maximum dose or dose to 1 cc or 10% of PTV. D80% of 25 Gy and D50% of 28 Gy in 3 fractions corresponded to 10% VCF risk. On multivariate analysis, lower body mass index (HR 0.90 per unit increase, p = 0.04), total spinal instability neoplastic score (SINS, HR 2.44 unstable vs stable, p = 0.04), and PTV D80% (HR 1.11 for every Gy increase, p = 0.003) were associated with increased VCF risk. Conclusions SBRT provides excellent tumor control for spinal metastases and is associated with low rate of VCF in our cohort. NTCP modeling suggests that the larger volume of spine receiving lower doses are more closely associated with post-SBRT VCF than high dose regions. Under current target delineation methods, common SBRT regimens such as 24 Gy in 2 fractions or 27 Gy in 3 fractions may be inherently associated with VCF risk of 10% or greater. Consensus contouring guidelines should be reevaluated to minimize the volume of irradiated spine in light of these new data.

Purpose In patients with spinal instability, cord compression, or neurologic deficits, the standard of care is surgery followed by radiation therapy (RT). Recurrence rates after conventional RT remain high. The purpose of this study is to prospectively examine the efficacy of postoperative stereotactic body RT (SBRT) in patients who have undergone surgical intervention for spine metastases. We hypothesize that postoperative SBRT to the spine would be associated with higher local control than historical rates after conventional RT. Methods and Materials Thirty-five adult patients with a Karnofsky Performance Status score ≥40 and spine metastases from solid tumors with no prior overlapping RT and target volumes ≤3 consecutive vertebral levels were enrolled. Thirty-three patients were treated. Two patients underwent treatment to 2 target volumes for a total of 35 target volumes. All patients received SBRT 30 Gy in 5 fractions. Patients were followed with neurological examinations and computed tomography and/or magnetic resonance imaging every 3 months. Neurologic function was assessed at the same time points using the American Spinal Injury Association (ASIA) impairment score. Pain was rated according to the 10-point visual analogue scale and MD Anderson Cancer Center brief pain index. Toxicity was recorded according to National Cancer Institute Common Toxicity Criteria for Adverse Events Version 4. The primary objective was the rate of radiographic local recurrence at 12 months after completion of SBRT. Results Patient characteristics were as follows: 34.3% had radioresistant primaries; 71.4% were ASIA E and the remainder ASIA D; and the median baseline Karnofsky Performance Status score was 70 (range, 50-100). Radiographic and symptomatic local control at 1 year were 90% (95% confidence interval, 76%-98%). The median time to recurrence in these 3 patients was 3.5 months (range, 3.4-5.8 months), all had radiosensitive tumors, and all recurrences were epidural. No patients experienced wound dehiscence, hardware failure, or spinal cord myelopathy. The median time to return to systemic therapy was 0.5 months (range, 0-9.4 months). Conclusions This prospective study of postoperative spine SBRT demonstrates excellent local control with low toxicity. These data suggest superior rates of local control compared with conventional RT; however, a formal comparative study is warranted.

Brain metastasis velocity (BMV) is a prognostic metric that describes the recurrence rate of new brain metastases after initial treatment with radiosurgery (SRS). We have previously risk stratified patients into high, intermediate, and low-risk BMV groups, which correlates with overall survival (OS). We sought to externally validate BMV in a multi-institutional setting.Patients from nine academic centers were treated with upfront SRS; the validation cohort consisted of data from eight institutions not previously used to define BMV. Patients were classified by BMV into low (4 BMV), intermediate (4-13 BMV), and high-risk groups (13 BMV). Time-to-event outcomes were estimated using the Kaplan-Meier method. Cox proportional hazards methods were used to estimate the effect of BMV and salvage modality on OS.Of 2829 patients, 2092 patients were included in the validation dataset. Of these, 921 (44.0%) experienced distant brain failure (DBF). Median OS from initial SRS was 11.2 mo. Median OS for BMV 4, BMV 4-13, and BMV 13 were 12.5 mo, 7.0 mo, and 4.6 mo (p 0.0001). After multivariate regression modeling, melanoma histology (β: 10.10, SE: 1.89, p 0.0001) and number of initial brain metastases (β: 1.52, SE: 0.34, p 0.0001) remained predictive of BMV (adjusted RThis multi-institutional dataset validates BMV as a predictor of OS following initial SRS. BMV is being utilized in upcoming multi-institutional randomized controlled trials as a stratification variable for salvage whole brain radiation versus salvage SRS after DBF.