Patient progress modelling and results in Wilm's Tumour

The report describes the development of a mathematical model of the progress of patients with Wilm's Tumour using the methodology developed by Jackson & Aspden [1, 2]. The model incorporates two prognostic factors which are shown to influence patient progress. These are the stage of the tumour and the age of the patient at presentation. The model proved adequate to represent an initial set of patient data, and comparison runs were performed with data from a later time period. These runs highlighted changes in patient progress between the two groups and illustrated the usefulness of the model in this type of analysis. The analysis also underlined the poor prognosis of patients over 5 years old who relapsed.     

Financial planning for new products: Part I—Basis for model formulation

In a previous paper the author presented a staged approach methodology for the evaluation and selection of R & D projects. The present paper is intended to serve as its complement.The aim is the formulation of a matching overall long range budget planning policy which will attempt to answer the questions of “how many projects to prove” and “how much to fund” on the basis of satisfying the company growth objective.To achieve the above purpose, a staged budget planning model has been developed which recognizes and utilizes the specific attributes of the various R & D stages. Tje project stage survival rate and project stage cost ratio concepts are discussed. A steady flow of projects through the various R & D stage is maintained. The aim of the program is to produce periodically a planned number of new products fro commercial investment.This methodology may apply to R & D program with a sufficient number of moderately sized projects that justify the use of survival rate and cost ratio values. It should be constructed as a tentative effort for possible use within the staged limitations.     

The new treatment mode research of hepatitis B based on ant colony algorithm

Hepatitis B (HB) is a deadly disease that has a severe impact on infected individuals. In China, not only are the incidence and infection rates of HB very high, but also many HB patients suffer from mental illness associated with anxiety and fear because of HB-associated symptoms. This exacerbates the patients’ condition, potentially increasing the risk of mortality. In this paper, we propose a new treatment mode to improve the therapeutic efficiency and patients’ satisfaction with their healthcare. In a single process of this new treatment, several patients with similar disease symptoms are treated by one doctor at the same time. This new treatment mode can not only relieve the anxiety and fear of HB patients, and improve patients’ cognition rate of HB, but also reduce the HB infection rate, slow down the progression of disease symptoms, and shorten the course. If patients with similar disease symptoms are to be grouped together, there is a need to determine the optimal patient batch combination, which can be solved in the new mode, called patient combined problem (PCP). We also constructed a mathematical model of PCP, and present the ant colony (AC) algorithm and Enhanced AC with a P-3-exchange operator for PCP in the new treatment mode in this paper. We also performed an experiment that showed that our proposed algorithms are very fast and effective for solving this problem.

     

基于患者两阶段医疗服务过程的病床资源优化

随着医疗需求的日益增长，供需不平衡的矛盾日益显著，病床资源短缺已经成为制约医疗服务发展的重要因素之一。针对病床资源供需失衡的问题，本文构建患者两阶段医疗服务过程的病床资源优化模型。考虑患者的医疗服务是一个两阶段串联排队过程，第一阶段是强制治疗阶段，第二阶段是康复阶段。在患者排队系统中，服务台总数固定的前提下，本文利用增补变量方法给出了该排队系统的概率等式，通过求解偏微分方程得出系统的状态概率，并推导出医院拒绝患者的概率、平均康复时间等相关指标。考虑部分患者因病床资源不足而无法入院和康复阶段患者提前出院两种风险因素，本文基于排队指标构建多病种间的病床分配模型，再利用动态规划的求解思路得到病床分配的最优解。最后，本文采用2017年卫生统计数据和模拟数据相结合进行数值分析。研究结果表明与传统单阶段模型相比，两阶段模型对不同病种间病床数差别影响显著，并且患者入院率对病床分配影响较大。进一步，基于数值结果给出了医疗管理建议和研究展望。     

舆论领袖传播影响力的阶段式建模分析

在网络社会,无论是网络推手炒作谣言,还是官方微博积极应对,都可视作舆论领袖在舆情演化过程中发挥传播影响力。本文将舆情演化过程分为两个阶段,在两个阶段分别应用不同的仿真模型对不同作用舆论领袖的传播影响力进行分析。第一个阶段是舆情危机爆发阶段,即舆情危机"从无到有",分析网络推手在该阶段的扩散影响力,以SIR经典传染病模型为基础,构建包含有网络推手作用的扩散影响力模型;第二个阶段是舆情危机平息阶段,即舆情危机"从有到无",分析官方微博在该阶段的证伪影响力,以Lotka-Volterra竞争关系模型为基础,研究官方微博如何发挥证伪影响力与网络推手进行博弈。结合具体舆情实例对阶段式模型进行验证分析,并提出如何根据舆论领袖不同传播作用应对舆情危机相关政策建议,以期帮助决策者打击网络谣言、平息舆情危机。     

Blocking in Healthcare Operations: A New Heuristic and an Application

We consider the problem of optimal capacity allocation in a hospital setting, where patients pass through a set of units, for example intensive care and acute care (AC), or AC and post‐acute care. If the second stage is full, a patient whose service at the first stage is complete is blocked and cannot leave the first stage. We develop a new heuristic for tandem systems to efficiently evaluate the effects of such blocking on system performance and we demonstrate that this heuristic performs well when compared with exact solutions and other approaches presented in the literature. In addition, we show how our tandem heuristic can be used as a building block to model more complex multi‐stage hospital systems with arbitrary patient routing, and we derive insights and actionable capacity strategies for a real hospital system where such blocking occurs between units.     

A Mathematical Model of Protease-Antiprotease Homeostasis Failure in Chronic Obstructive Pulmonary Disease (COPD)

Chronic obstructive pulmonary disease (COPD), the fourth leading cause of death worldwide, has a puzzling etiology. Although it is a smoking-associated disease, only a minority of smokers develop it. Moreover, the disease continues to progress in COPD patients, even after smoking ceases. This article proposes a mathematical model of COPD that offers one possible explanation for both observations. Building on a conceptual model of COPD causation as resulting from protease-antiprotease imbalance in the lung, leading to ongoing proteolysis (digestion) of lung tissue by excess proteases, we formulate a system of seven ordinary differential equations (ODEs) with 18 parameters to describe the network of interacting homeostatic processes regulating the levels of key proteases (macrophage elastase (MMP-12) and neutrophil elastase (NE)) and antiproteases (alpha-1-antitrypsin and tissue inhibitor of metalloproteinase-1). We show that this system can be simplified to a single quadratic equation with only two parameters to predict the equilibrium behavior of the entire network. The model predicts two possible equilibrium behaviors: a unique stable "normal" (healthy) equilibrium or a "COPD" equilibrium with elevated levels of MMP-12 and NE (and of lung macrophages and neutrophils) and reduced levels of antiproteases. The COPD equilibrium is induced in the model only if cigarette smoking increases the average production of MMP-12 per alveolar macrophage above a certain threshold. Following smoking cessation, the predicted COPD equilibrium levels of MMP-12 and other disease markers decline, but do not return to their original (presmoking) levels. These and other predictions of the model are consistent with limited available human data.     

Providing health care to human beings trapped in the poverty culture

The culture of poverty impacts everything patients in this socioeconomic group think and do. If what poor patients say does not sit well with the way we think, that doesn't mean they are wrong. Physicians have to adjust their mental model and think in different cultural terms. The author recently completed his thirtieth year of a career dedicated to providing health care to people living in poverty. He shares seven concepts important in building a mental model that will enable physicians to successfully provide health care to this patient population: (1) Poverty is the number one health problem; (2) we see same diseases as everyone else; (3) patients are trapped in the poverty culture; (4) patients' behavior is often manipulative; (5) compliance is a unique challenge; (6) patients have limited resources; and (7) the ultimate contributors to poverty are unwanted adolescent pregnancy and substance abuse. These concepts can help physicians to be more effective in providing health care to patients living in poverty. They can help them understand what is happening, so that their experience might be fulfilling rather than demoralizing.     

An Analytical Framework for Designing Community‐Based Care for Chronic Diseases

In this study, we propose a methodological framework to provide a road map to clinicians and system planners in developing chronic disease management strategies, and designing community‐based care. We extend the analytical epidemiologic model by utilizing a patient flow approach, in order to model the multiple care‐provider visit patterns of patients with a specific chronic illness. The patterns of care received by a group of patients are represented in compact form by means of a Markov model that is based on a disease‐specific state space. Our framework also reflects the case‐mix biases as well as the care‐provider level clustering of the patients. By using this approach, we identify the patterns of care, determine the care provider and patient characteristics associated with optimal management of care, and estimate the potential influence of various interventions. The framework is applied to the data of 4000+ stroke patients discharged from the acute care hospitals of Quebec to their homes. Our findings provide a basis for designing community‐based care initiatives for stroke survivors in the province.     

基于差异产品的政府最优R&D补贴策略研究

本文建立考虑产品差异的三阶段双寡头博弈模型:第一阶段政府选择R&D(Research and Development)补贴率,第二阶段企业确定自己的R&D水平,第三阶段企业确定产品价格进行伯川德竞争。根据双寡头在第二和第三阶段是否合作,给出了R&D竞争、R&D卡特尔、共同实验、技术共享联盟和研究共同体等五种R&D策略,得到了相应的政府最优R&D补贴率。研究表明,当技术溢出程度较低且产品水平差异不大时,政府给予采用R&D竞争策略企业的补贴率不高于采用R&D卡特尔策略的企业;当技术溢出程度较高且产品水平差异较大时,结果则相反。在政府进行最优补贴后,从促进技术进步、扩大企业规模以及社会福利最大化的角度来看,五种R&D策略中,共同实验最差,技术共享联盟和研究共同体则最优。     

应对并购风险的可转债与阶段性支付模型与案例研究

本文运用模型研究了可转债和阶段性支付在抑制双边道德风险以及减小不确定性风险中所发挥的作用,并通过SZ能源集团并购案例详细考察了我国国有上市公司在并购过程中所存在的各种风险。结果表明,内嵌转股期权的可转债支付合约可以有效抑制并购中的双边道德风险,在阶段性支付的辅助下,则更能有效地防范市场相关风险。最后,为了更好的说明可转债和阶段性支付对于并购风险的防范作用,我们进一步通过案例分析了可转债和阶段支付的应用情况,发现阶段性支付思想已经体现在并购的现金支付方式中,但是可转债支付在国内并购中的应用尚不多见。     

A Simulation Model for Occupational Tuberculosis Transmission

A simulation model of tuberculosis (TB) transmission among hospital employees is described. A hypothetical cohort of 1000 workers was divided into low-, medium-, and high-risk groups. The number of TB patients admitted daily was treated as a Poisson random variable. A patient imparted a daily infection risk that was identical for all workers within a risk group but that varied between risk groups. In some scenarios, infected employees were assigned a daily risk of developing TB disease. If disease developed, the individual remained on the job for 3 calendar weeks and imparted a substantial infection risk to 25 close contacts. Simulations were run over 5-year intervals. Cumulative infection incidence increased over time and with more TB patients admitted. Given a scenario in which there were 600, 300, and 100 susceptibles in the low-, medium-, and high risk groups, respectively, 50 TB patients admitted annually and accounting for disease among infected employees, at 5 years there were approximately 100 primary infections (due to infection by patients), 40 secondary infections (due to infection by diseased coworkers), five primary disease cases, and two secondary disease cases. The input parameter values and simulation outcomes were reasonably consistent with the sparse information reported in the literature.     

Quantitative Assessment of the Health Risk for Livestock When Animal Viruses Are Applied in Human Oncolytic Therapy: A Case Study for Seneca Valley Virus

Some viruses cause tumor regression and can be used to treat cancer patients; these viruses are called oncolytic viruses. To assess whether oncolytic viruses from animal origin excreted by patients pose a health risk for livestock, a quantitative risk assessment (QRA) was performed to estimate the risk for the Dutch pig industry after environmental release of Seneca Valley virus (SVV). The QRA assumed SVV excretion in stool by one cancer patient on Day 1 in the Netherlands, discharge of SVV with treated wastewater into the river Meuse, downstream intake of river water for drinking water production, and consumption of this drinking water by pigs. Dose–response curves for SVV infection and clinical disease in pigs were constructed from experimental data. In the worst scenario (four log₁₀ virus reduction by drinking water treatment and a farm with 10,000 pigs), the infection risk is less than 1% with 95% certainty. The risk of clinical disease is almost seven orders of magnitude lower. Risks may increase proportionally with the numbers of treated patients and days of virus excretion. These data indicate that application of wild‐type oncolytic animal viruses may infect susceptible livestock. A QRA regarding the use of oncolytic animal virus is, therefore, highly recommended. For this, data on excretion by patients, and dose–response parameters for infection and clinical disease in livestock, should be studied.     

A stochastic programming model for outpatient appointment scheduling considering unpunctuality

Many papers on outpatient appointment scheduling assume that patients arrive on time. However, unpunctuality is a stochastic factor that is inevitable in practice, which leads to patients arriving out of order. A schedule may not be reasonable if a clinic neglects the influence of patient unpunctuality. This paper addresses the outpatient scheduling problem considering unpunctuality (OS-U) by developing a stochastic programming model. We compare the performance of the OS-U system with the strict-punctuality (OS-P) system. We illustrate that the model has an exact and unified formula for cases of patients arriving in the appointment order and arriving out of order. The OS-U problem is solved by using Benders decomposition combined with the sample average approximation (BD-SAA) technique to determine the global optimal set of appointment intervals with the goal of minimizing the weighted sum of all patient waiting times, doctor idle times, and overtime. Numerical experiments indicate that the appointment rule changes when considering unpunctuality, although the set of optimal appointment intervals still takes the shape of dome (interval width increases at first, then remains nearly constant and eventually decreases for the last patients). The OS-P system schedules the first two patients together at the start of a session, whereas the OS-U system schedules them with different appointment times and requires a longer slot between the first two patients if patients tend to arrive early rather than late. The variance of unpunctuality has little impact. The no-show probability has a greater influence on system performances in an OS-U system than those in an OS-P system.     

Appointment Overbooking in Health Care Clinics to Improve Patient Service and Clinic Performance

The problem of no‐shows (patients who do not arrive for scheduled appointments) is particularly significant for health care clinics, with reported no‐show rates varying widely from 3% to 80%. No‐shows reduce revenues and provider productivity, increase costs, and limit patient access by reducing effective clinic capacity. In this article, we construct a flexible appointment scheduling model to mitigate the detrimental effects of patient no‐shows, and develop a fast and effective solution procedure that constructs near‐optimal overbooked appointment schedules that balance the benefits of serving additional patients with the potential costs of patient waiting and clinic overtime. Computational results demonstrate the efficacy of our model and solution procedure, and connect our work to prior research in health care appointment scheduling.     

Emergency Department Staff Planning to Improve Patient Care and Reduce Costs

In the face of high staffing costs, uncertain patient arrivals, and patients unsatisfied with long wait times, staffing of medical emergency departments (EDs) is a vexing problem. Using empirical data collected from three active EDs, we develop an analytic model to provide an effective staffing plan for EDs. Patient demand is aggregated into discrete time buckets and used to model the stochastic distribution of patient demand within these buckets, which considerably improves model tractability. This model is capable of scheduling providers with different skill profiles who work either individually or in teams, and with patients of varying acuity levels. We show how our model helps to balance staffing costs and patient service levels, and how it facilitates examination of important ED staffing policies.     

Bounds in Competing Risks Models and the War on Cancer

In 1971, President Nixon declared war on cancer. Thirty years later, many declared this war a failure: the age‐adjusted mortality rate from cancer in 2000 was essentially the same as in the early 1970s. Meanwhile the age‐adjusted mortality rate from cardiovascular disease fell dramatically. Since the causes that underlie cancer and cardiovascular disease are likely dependent, the decline in mortality rates from cardiovascular disease may partially explain the lack of progress in cancer mortality. Because competing risks models (used to model mortality from multiple causes) are fundamentally unidentified, it is difficult to estimate cancer trends. We derive bounds for aspects of the underlying distributions without assuming that the underlying risks are independent. We then estimate changes in cancer and cardiovascular mortality since 1970. The bounds for the change in duration until death for either cause are fairly tight and suggest much larger improvements in cancer than previously estimated.     

Designing Personalized Treatment: An Application to Anticoagulation Therapy

In this study, we develop an analytical framework for personalizing the anticoagulation therapy of patients who are taking warfarin. Consistent with medical practice, our treatment design consists of two stages: (i) the initiation stage, modeled using a partially‐observable Markov decision process, during which the physician learns through systematic belief updates about the unobservable patient sensitivity to warfarin, and (ii) the maintenance stage, modeled using a Markov decision process, during which the physician relies on his formed belief about patient sensitivity to determine the stable, patient‐specific, warfarin dose to prescribe. We develop an expression for belief updates in the POMDP, establish the optimality of the myopic policy for the MDP, and derive conditions for the existence and uniqueness of a myopically optimal dose. We validate our models using a real‐life patient data set gathered at the Hematology Clinic of the Jewish General Hospital in Montreal. The proposed analytical framework and case study enable us to develop useful clinical insights, for example, concerning the length of the initiation period and the importance of correctly assessing patient sensitivity.