Linearized Wasserstein dimensionality reduction with approximation guarantees

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability measures rather than points in $\mathbb{R}^n$, and that finding low-dimensional descriptions of such datasets requires manifold learning algorithms in the Wasserstein space. Most available algorithms are based on computing the pairwise Wasserstein distance matrix, which can be computationally challenging for large datasets in high dimensions. Our algorithm leverages approximation schemes such as Sinkhorn distances and linearized optimal transport to speed-up computations, and in particular, avoids computing a pairwise distance matrix. We provide guarantees on the embedding quality under such approximations, including when explicit descriptions of the probability measures are not available and one must deal with finite samples instead. Experiments demonstrate that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.Comment: 38 pages, 10 figures. Submitte

Manifold learning in Wasserstein space

This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of $\mathbb{R}^d$, metrized with the Wasserstein-2 distance $W$. We begin by introducing a natural construction of submanifolds $\Lambda$ of probability measures equipped with metric $W_\Lambda$, the geodesic restriction of $W$ to $\Lambda$. In contrast to other constructions, these submanifolds are not necessarily flat, but still allow for local linearizations in a similar fashion to Riemannian submanifolds of $\mathbb{R}^d$. We then show how the latent manifold structure of $(\Lambda,W_{\Lambda})$ can be learned from samples $\{\lambda_i\}_{i=1}^N$ of $\Lambda$ and pairwise extrinsic Wasserstein distances $W$ only. In particular, we show that the metric space $(\Lambda,W_{\Lambda})$ can be asymptotically recovered in the sense of Gromov--Wasserstein from a graph with nodes $\{\lambda_i\}_{i=1}^N$ and edge weights $W(\lambda_i,\lambda_j)$. In addition, we demonstrate how the tangent space at a sample $\lambda$ can be asymptotically recovered via spectral analysis of a suitable "covariance operator" using optimal transport maps from $\lambda$ to sufficiently close and diverse samples $\{\lambda_i\}_{i=1}^N$. The paper closes with some explicit constructions of submanifolds $\Lambda$ and numerical examples on the recovery of tangent spaces through spectral analysis

Pancratistatin induces apoptosis in clinical leukemia samples with minimal effect on non-cancerous peripheral blood mononuclear cells

<p>Abstract</p> <p>Background</p> <p>Pancratistatin, a natural compound extracted from <it>Hymenocallis littoralis</it>, can selectively induce apoptosis in several cancer cell lines. In this <it>ex vivo </it>study, we evaluated the effect of pancratistatin on peripheral blood mononuclear cells obtained from 15 leukemia patients prior to clinical intervention of newly diagnosed patients, as well as others of different ages in relapse and at various disease progression states.</p> <p>Results</p> <p>Mononuclear cells from healthy volunteers and leukemia patients were exposed to 1 μM pancratistatin for up to 48 h. Irrespective of leukemia type, pancratistatin induced apoptosis in the leukemic samples, with minimal effects on non-cancerous peripheral blood mononuclear control cells.</p> <p>Conclusion</p> <p>Our results show that pancratistatin is an effective and selective anti-cancer agent with potential for advancement to clinical trials.</p

Patient vital signs in relation to ICU admission in treatment of acute leukemia: a retrospective chart review

Objectives: The objective of the current study was to investigate the relationship between changes in vital signs and intensive care unit (ICU) admission. Windsor Regional Hospital treats 15–20 new patients a year with acute leukemia. These patients are at increased risk of neutropenic fevers and admission to the ICU following induction chemotherapy. Methods: Retrospective review examined the correlation between acute leukemia patient vitals and ICU admission. The analysis included 37 patients: 7 ICU versus 30 controls. Changes were compared to baseline over 24 hours prior to ICU admission or 5 days after the initiation of induction chemotherapy in the following vital signs: heart rate (HR), mean arterial pressure (MAP), temperature (T), respiratory rate (RR), and fraction of inspired oxygen (FiO2) required to maintain a stable oxygen saturation. Results: RR and FiO2 demonstrated significant change over baseline leading up to ICU admission within the ICU group. T, HR and MAP did not demonstrate significant changes over time in either group. RR, FiO2 and HR were significantly higher in the ICU group at time zero compared with the control group. RR was recorded least frequently in the 24 hours leading up to ICU admission. Discussion: Changes in RR and FiO2 predicted clinical deterioration requiring ICU admission in acute leukemia patients. This is consistent with the predominant reason for ICU admission which was respiratory failure. Conclusion: We present preliminary evidence to support enhanced monitoring of RR and FiO2 in acute leukemia patients following induction chemotherapy with early intervention if identified

Breast Cancer Care in California and Ontario: Primary Care Protections Greatest Among the Most Socioeconomically Vulnerable Women Living in the Most Underserved Places

Background: Better health care among Canada’s socioeconomically vulnerable versus America’s has not been fully explained. We examined the effects of poverty, health insurance and the supply of primary care physicians on breast cancer care. Methods: We analyzed breast cancer data in Ontario (n = 950) and California (n = 6300) between 1996 and 2000 and followed until 2014. We obtained socioeconomic data from censuses, oversampling the poor. We obtained data on the supply of physicians, primary care and specialists. The optimal care criterion was being diagnosed early with node negative disease and received breast conserving surgery followed by adjuvant radiation therapy. Results: Women in Ontario received more optimal care in communities well supplied by primary care physicians. They were particularly advantaged in the most disadvantaged places: high poverty neighborhoods (rate ratio = 1.65) and communities lacking specialist physicians (rate ratio = 1.33). Canadian advantages were explained by better health insurance coverage and greater primary care access. Conclusions: Policy makers ought to ensure that the newly insured are adequately insured. The Medicaid program should be expanded, as intended, across all 50 states. Strengthening America’s system of primary care will probably be the best way to ensure that the Affordable Care Act’s full benefits are realized

The supply of physicians and care for breast cancer in Ontario and California, 1998 to 2006

INTRODUCTION: We examined the differential effects of the supply of physicians on care for breast cancer in Ontario and California. We then used criteria for optimum care for breast cancer to estimate the regional needs for the supply of physicians. METHODS: Ontario and California registries provided 951 and 984 instances of breast cancer diagnosed between 1998 and 2000 and followed until 2006. These cohorts were joined with the supply of county-level primary care physicians (PCPs) and specialists in cancer care and compared on care for breast cancer. RESULTS: Significant protective PCP thresholds (7.75 to = 8.25 PCPs per 10 000 inhabitants) were observed for breast cancer diagnosis (odds ratio [OR] 1.62), receipt of adjuvant radiotherapy (OR 1.64) and 5-year survival (OR 1.87) in Ontario, but not in California. The number of physicians seemed adequate to optimize care for breast cancer across diverse places in California and in most Ontario locations. However, there was an estimated need for 550 more PCPs and 200 more obstetrician-gynecologists in Ontario\u27s rural and small urban areas. We estimated gross physician surpluses for Ontario\u27s 2 largest cities. CONCLUSION: Policies are needed to functionally redistribute primary care and specialist physicians. Merely increasing the supply of physicians is unlikely to positively affect the health of Ontarians

Health insurance mediation of the Mexican American non-Hispanic white disparity on early breast cancer diagnosis

We examined health insurance mediation of the Mexican American (MA) non-Hispanic white (NHW) disparity on early breast cancer diagnosis. Based on social capital and barrio advantage theories, we hypothesized a 3-way ethnicity by poverty by health insurance interaction, that is, that 2-way poverty by health insurance interaction effects would differ between ethnic groups. We secondarily analyzed registry data for 303 MA and 3,611 NHW women diagnosed with breast cancer between 1996 and 2000 who were originally followed until 2011. Predictors of early, node negative (NN) disease at diagnosis were analyzed. Socioeconomic data were obtained from the 2000 census to categorize neighborhood poverty: high (30% or more of the census tract households were poor), middle (5% to 29% poor) and low (less than 5% poor). Barrios were neighborhoods where 50% or more of the residents were MA. Primary health insurers were Medicaid, Medicare, private or none. MA women were 13% less likely to be diagnosed early with NN disease (RR = 0.87), but this MA-NHW disparity was completely mediated by the main and interacting effects of health insurance. Advantages of health insurance were largest in low poverty neighborhoods among NHW women (RR = 1.20) while among MA women they were, paradoxically, largest in high poverty, MA barrios (RR = 1.45). Advantages of being privately insured were observed for all. Medicare seemed additionally instrumental for NHW women and Medicaid for MA women. These findings are consistent with the theory that more facilitative social and economic capital is available to MA women in barrios and to NHW women in more affluent neighborhoods. It is there that each respective group of women is probably best able to absorb the indirect and direct, but uncovered, costs of breast cancer screening and diagnosis

Gender differences on the interacting effects of marital status and health insurance on long-term colon cancer survival in California, 1995-2014

Objectives. Long-term colon cancer survival is not well explained by main effects. We explored the interaction of age, gender, marital status, health insurance and poverty on 10-year colon cancer survival. Methods. California registry data were analyzed for 5,776 people diagnosed from 1995 to 2000; followed until 2014. Census data classified neighborhood poverty. We tested interactions with regressions and described them with standardized rates and rate ratios (RR). Results. The 5-way interaction was significant, suggesting larger 4-way disadvantages among non-Medicare-eligible people. A significant 4-way interaction was a 3-way interaction in non-high poverty neighborhoods only. Private insurance was protective for unmarried men (RR = 1.60) but not women, while it was protective for married women (RR = 1.22) but not men. This pattern seemed explained by lower-incomes of certain groups of unmarried women and married men and more prevalent underinsuring of unmarried men. Conclusions. Structural inequities related to the institutions of marriage and health care seem to affect women and men quite differently. Policy makers ought to be cognizant of such structural imbalances as future reforms of American health care are considered

Disparities among Minority Women with Breast Cancer Living in Impoverished Areas of California

Background: Interaction effects of poverty and health care insurance coverage on overall survival rates of breast cancer among women of color and non-Hispanic white women were explored. Methods: We analyzed California registry data for 2,024 women of color (black, Hispanic, Asian, Pacific Islander, American Indian, or other ethnicity) and 4,276 non-Hispanic white women (Anglo-European ancestries and no Hispanic-Latin ethnic backgrounds) diagnosed with breast cancer between the years 1996 and 2000 who were then followed until 2011. The 2000 US census categorized rates of neighborhood poverty. Health care insurance coverage was either private, Medicare, Medicaid, or none. Cox regression was used to model rates of survival. Results: A 3-way interaction between ethnicity, health care insurance coverage, and poverty was observed. Women of color inadequately insured and living in poor or near-poor neighborhoods in California were the most disadvantaged. Women of color adequately insured and who lived in such neighborhoods in California were also disadvantaged. The incomes of such women of color were typically lower than the incomes of non-Hispanic white women. Conclusions: Women of color with or without insurance coverage are disadvantaged in poor and near-poor neighborhoods of California. Such women may be less able to bare the indirect, direct, or uncovered costs of health care for breast cancer treatment