Multiple Patient Types Research Articles

Optimization of active surveillance strategies for heterogeneous patients with prostate cancer

Prostate cancer (PCa) is common in American men with long latent periods, during which the disease is asymptomatic. Active surveillance is a monitoring strategy commonly used for patients diagnosed with low‐risk PCa who may harbor latent high‐risk PCa. The optimal monitoring strategy attempts to minimize the disutility of testing while ensuring that the patient is detected at the earliest time when the disease progresses. Unfortunately, guidelines for the active surveillance of PCa are often one‐size‐fits‐all strategies that ignore the heterogeneity among multiple patient types. In contrast, personalized strategies based on partially observable Markov decision process (POMDP) models are challenging to implement in practice given the large number of possible strategies that can be used. This article presents a two‐stage stochastic programming approach that selects a set of strategies for predefined cardinality based on patients' disease risks. The first‐stage decision variables include binary variables for the selection of periods at which to test patients in each strategy and the assignment of multiple patient types to strategies. The objective is to maximize a weighted reward function that considers the need for cancer detection, missed detection, and cost of monitoring patients. We discuss the structure and complexity of the model and reformulate a logic‐based Bender's decomposition formulation that can solve realistic instances to optimality. We present a case study for the active surveillance of PCa and show that our model results in strategies that vary in intensity according to patient disease risk. Finally, we show that our model can generate a small number of strategies that can significantly improve the existing “one‐size‐fits‐all” guideline strategies used in practice.

Allocating Scarce Resources using a Weighted Lottery

Summary We determine the probability that a scarce resource, such as medicine, is awarded sequentially based on a weighted lottery. When every patient has an equal probability p of receiving medicine if it is available, then counterintuitively, depending on where the patient is in line relative to how many doses are available, the patient may have a higher probability of receiving medicine for lower p. We consider the tension between choosing p for an individual patient (such as the optimal value of p to receive medicine) and societal concerns (such as the allocation of medicine to be equitable across patients and to make sure that all the medicine is used). We extend the model to multiple types of patients who have different probabilities of receiving medicine when it is available.

Dynamic Allocation of Medical Resources During the Outbreak of Epidemics

During the outbreak of epidemics such as coronavirus disease (COVID-19), the local hospitals often withstand a sharp increase of patient influx, which renders the healthcare system on the verge of collapse. To alleviate the situation, the effective allocation of scarce medical resources during the pandemic plays a vital role. The essence of the healthcare system in time of emergency is to stay functional, and to be able to diagnose and hospitalize as many patients as possible. Fangcang shelter hospital, as a novel way to temporarily increase the capacity of the local healthcare system, is proven to be effective against the COVID-19 pandemic. To improve the performance of the healthcare system with Fangcang, many practical factors need to be taken into account, such as the patient deterioration during waiting to be admitted, the referral mechanism according to the severity of the patients, and the selective admission regulations. To address the high volatility and time-varying feature of the COVID-19, a multistage and multi-type medical service network model is established, and a dynamic allocation strategy of the medical resources at each stage is proposed based on a stochastic optimization problem, which is then solved via the fluid queueing approximation. Combined with the real data collected from Wuhan, it is revealed that the proposed algorithm could help with the allocation of medical resources during the outbreak of epidemics. Even with limited medical resources available, the method could still maintain a guaranteed service level while keeping the healthcare system operational. Furthermore, the simulation analysis validates that our method can effectively allocate medical resources at each stage, so as to stabilize the system performance and fulfill the medical demand for multiple types of patients. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To fend off the outbreak of epidemics, the lessons have to be learned from the past. The successful control of the spread of COVID-19 in Wuhan (China) is a classical example of applying modern medical practices and management tools. In the present article, the treating procedure of COVID-19 in Wuhan is modeled as a multistage decision problem, which includes the screening with nucleic acid testing, the further testing, the treatment of patients with mild/severe symptoms, or even critical patients. The introduction of Fangcang shelter hospital is crucial for winning the battle against COVID-19. The current study attempts to determine the timing of introducing the Fangcang shelter hospital during the outbreak of a major epidemic, and helps allocate the medical resources needed to contain the spread of the virus. It is discovered that the actual number of beds in the Fangcang shelter hospital is far more than what is necessary, and it would be better to have built the Fangcang some time in advance. In the meantime, the number of designated hospitals for COVID-19 is in line with the results obtained via the optimal staffing strategy proposed here, but it is also noticeable that these hospitals should be released of duty sooner to fight against not only COVID-19 but also other diseases in reality.

Using Simulation Optimization to Solve Patient Appointment Scheduling and Examination Room Assignment Problems for Patients Undergoing Ultrasound Examination.

This study investigates patient appointment scheduling and examination room assignment problems involving patients who undergo ultrasound examination with considerations of multiple examination rooms, multiple types of patients, multiple body parts to be examined, and special restrictions. Following are the recommended time intervals based on the findings of three scenarios in this study: In Scenario 1, the time interval recommended for patients’ arrival at the radiology department on the day of the examination is 18 min. In Scenario 2, it is best to assign patients to examination rooms based on weighted cumulative examination points. In Scenario 3, we recommend that three outpatients come to the radiology department every 18 min to undergo ultrasound examinations; the number of inpatients and emergency patients arriving for ultrasound examination is consistent with the original time interval distribution. Simulation optimization may provide solutions to the problems of appointment scheduling and examination room assignment problems to balance the workload of radiological technologists, maintain high equipment utilization rates, and reduce waiting times for patients undergoing ultrasound examination.

A discrete event simulation to evaluate impact of radiology process changes on emergency department computed tomography access.

Hospitals face the challenge of managing demand for limited computed tomography (CT) resources from multiple patient types while ensuring timely access. A discrete event simulation model was created to evaluate CT access time for emergency department (ED) patients at a large academic medical center with six unique CT machines that serve unscheduled emergency, semi-scheduled inpatient, and scheduled outpatient demand. Three operational interventions were tested: adding additional patient transporters, using an alternative creatinine lab, and adding a registered nurse dedicated to monitoring CT patients in the ED. All interventions improved access times. Adding one or two transporters improved ED access times by up to 9.8minutes (Mann-Whitney (MW) CI: [-11.0,-8.7]) and 10.3minutes (MW CI [-11.5, -9.2]). The alternative creatinine and RN interventions provided 3-minute (MW CI: [-4.0, -2.0]) and 8.5-minute (MW CI: [-9.7, -8.3]) improvements. Adding one transporter provided the greatest combination of reduced delay and ability to implement. The projected simulation improvements have been realized in practice.

Admission and Discharge Control in Intensive Care Units

Intensive Care Units (ICUs) are scarce resources that usually operate under high occupancy rates. When faced with limited bed availability, arriving patients are sometimes rejected or admitted by discharging an existing patient early which may result in increased readmission rates or patient/hospital related costs. Yet, there is not a well-defined admission and discharge policy to decrease such adverse consequences. We formulate a comprehensive ICU model with multiple patient types, multiple health stages, and a so-called readmission orbit whose population consists of patients who will seek readmission after an ICU discharge. The ICU model also differentiates first-time and recurring patients. We propose two easy-to-implement heuristic control policies, one based on a Markov Decision Processes model and the other based on a deterministic fluid model. We compare the performances of these policies with the ones of two state-of-the-art policies via discrete-event simulation. According to the numerical results, our proposed policies significantly outperform the state-of-the-art policies by carefully balancing rejection and early-discharge decisions. Moreover, they complement each other since the fluid-based policy performs well in large ICUs that operate in an overloaded regime, while the one-bed policy performs well in small ICUs or ICUs operating in critically or under-loaded regimes.

Incorporating patient preferences in the design and operation of cancer screening facility networks

High participation by target populations is one of the key success factors of publicly funded and population-based cancer screening programs. Patient preferences are a major factor distinguishing preventive screening from treatment, specifically regarding participation and choice of facility. Here, we explore the effect of facility attributes on patients’ choices for cancer screening and propose a quantitative modeling framework to study the impact of various system- and facility-level interventions by incorporating the choice behaviors of heterogeneous patient populations. EPPM integrates an empirical study on patient preferences and a simulation-based optimization model that incorporates the preferences of multiple patient types into an M/G/s queuing network of facilities, each working with appointment. Based on our framework's application via an extensive case study on the Quebec Breast Cancer Screening Program in Montreal, we provide insights into improving participation in cancer screening networks. Specifically, we identify trade-offs that women make when choosing facilities with different attribute configurations and show the heterogeneity in patient preferences. We also find that facility-level interventions, such as providing free parking and improving staff manners, are more effective and less expensive than system-level interventions.

Two-Tiered Ambulance Dispatch and Redeployment considering Patient Severity Classification Errors.

A two-tiered ambulance system, consisting of advanced and basic life support for emergency and nonemergency patient care, respectively, can provide a cost-efficient emergency medical service. However, such a system requires accurate classification of patient severity to avoid complications. Thus, this study considers a two-tiered ambulance dispatch and redeployment problem in which the average patient severity classification errors are known. This study builds on previous research into the ambulance dispatch and redeployment problem by additionally considering multiple types of patients and ambulances, and patient classification errors. We formulate this dynamic decision-making problem as a semi-Markov decision process and propose a mini-batch monotone-approximate dynamic programming (ADP) algorithm to solve the problem within a reasonable computation time. Computational experiments using realistic system dynamics based on historical data from Seoul reveal that the proposed approach and algorithm reduce the risk level index (RLI) for all patients by an average of 11.2% compared to the greedy policy. In this numerical study, we identify the influence of certain system parameters such as the percentage of advanced-life support units among all ambulances and patient classification errors. A key finding is that an increase in undertriage rates has a greater negative effect on patient RLI than an increase in overtriage rates. The proposed algorithm delivers an efficient two-tiered ambulance management strategy. Furthermore, our findings could provide useful guidelines for practitioners, enabling them to classify patient severity in order to minimize undertriage rates.

An adaptive priority policy for radiotherapy scheduling

In radiotherapy, treatment needs to be delivered in time. Long waiting times can result in patient anxiety and growth of tumors. They are often caused by inefficient use of radiotherapy equipment, the linear accelerators (LINACs). However, making an efficient schedule is very challenging, especially when we have multiple types of patients, having different service requirements and waiting time constraints. Moreover, in radiotherapy a patient needs to go through a LINAC multiple times over multiple days, to complete the treatment. In this paper we model the radiotherapy treatment process as a queueing system with multiple queues, and we propose a new class of scheduling policies that are simple, flexible and fair to patients. Numerical experiments show that our new policy outperforms the commonly used policies. We also extend the policy to an adaptive one to deal with unknown and fluctuating arrival rates. Our adaptive policy turns out to be quite efficient in absorbing the effects caused by these changes. Due to the complexity of our problem, we select the parameters of the policies through simulation-based optimization heuristics. Our work may also have important implications for managers in other service systems such as call centers.

Public Hospital Inpatient Room Allocation and Patient Scheduling Considering Equity

This article studies the optimal allocation of inpatient rooms for multiple types of patients in public hospitals and the patient scheduling problem with planned acceptance ratios (ARs). For public hospitals, it is important to allocate limited resources to multiple types of patients and manage patient access for maximizing hospital revenue and upholding service equity. The problem is formulated as two-stage models. Considering uncertainties in patients’ arrival and length of stay, we first propose a nonlinear stochastic programming (NSP) model for inpatient room allocation with the objective of maximizing revenue under the constraints of maintaining equity. To solve this problem, we transform the complex NSP model into a deterministic mixed-integer linear programming model, which is solved by CPLEX, by reformulating the chance constraints as knapsack constraints based on a linearization technique and a simulation model. Given the allocated capacity and planned AR, we further propose a two-stage stochastic mixed-integer program combined with a goal program model to optimize patient scheduling. To solve the model, a Benders decomposition based on the sample average approximation approach is proposed. The real data-based experimental results demonstrate the applicability and effectiveness of our models and approaches. The impacts of some parameters on the objective and decisions are also explored. A simulation procedure is developed to compare the performances of different patient scheduling methods, from which the results show that our proposed approach outperforms a benchmark policy. Note to Practitioners —Inpatient rooms are critical resources for hospitals. Against the background of aging populations and environmental problems, the twofold predicament—involving escalating healthcare demands and insufficient room-based resources—has led to the necessity for hospitals to operate more effectively and efficiently. Capacity management and patient scheduling are thus the two most important operations for hospital management. Because of the self-financing feature of hospitals and the quasi-public nature of medical services, it is important for public hospitals to judiciously allocate limited room capacities to multiple types of patients for balancing revenue and equity and schedule the arrival demands dynamically according to the planned capacity and acceptance ratio. In this article, we propose mathematical models and solution approaches for these two-stage problems, and their applicability and effectiveness are demonstrated by experiments based on real data. The managerial insights suggest that hospitals should improve the service equity gradually according to their financial situation because of the increasing marginal cost and should apply the scientific approaches and techniques, rather than by their experiences, to aid their management for better performance. By using approaches proposed in this article, hospital managers can be equipped with a decision support tool for effective capacity allocation and patient scheduling decisions. The parameters of our models could be tuned based on the preferences of different hospitals. Furthermore, these approaches can be applied to other settings with similar problems, such as government budget allocation considering both utility and equity, and service system management with waiting time requirement.

A Capacity Allocation Planning Model for Integrated Care and Access Management.

The prevailing first-come-first-served approach to outpatient appointment scheduling ignores differing urgency levels, leading to unnecessarily long waits for urgent patients. In data from a partner healthcare organization, we found in some departments that urgent patients were inadvertently waiting longer for an appointment than non-urgent patients. This paper develops a capacity allocation optimization methodology that reserves appointment slots based on urgency in a complicated, integrated care environment where multiple specialties serve multiple types of patients. This optimization reallocates network capacity to limit access delays (indirect waiting times) for initial and downstream appointments differentiated by urgency. We formulate this problem as a queueing network optimization and approximate it via deterministic linear optimization to simultaneously smooth workloads and guarantee access delay targets. In a case study of our industry partner we demonstrate the ability to (1) reduce urgent patient mean access delay by 27% with only a 7% increase in mean access delay for non-urgent patients, and (2) increase throughput by 31% with the same service levels and overtime.

A decision support system for real-time scheduling of multiple patient classes in outpatient services.

We propose a methodology to provide real-time assistance for outpatient scheduling involving multiple patient types. Schedulers are shown how each prospective placement in the appointment book would impact a day's operational performance for patients and providers. Rooted in prior literature and analytical findings, the information provided to schedulers about vacant slots is based on the probabilities that the calling patient, the already-existing appointments, and the session-end time will be unduly delayed. The information is updated in real-time before and after every new booking; calculations are driven by each patient type's historical consultation times and no-show data, and implemented via a simulation tool based on the underlying analytical methodology. Our findings lead to practical guidelines for dynamically constructing templates that provide allowances for different consultation durations, service time variability, no-show rates, and provider-driven performance targets for patient waiting and provider overtime. Extensions to healthcare batch scheduling applications such as radiology, surgery, or chemotherapy-where patient mixes may be known in advance-are suggested as future research opportunities since avoiding session overtime and procedures' completion time delays involve similar considerations.

A Capacity Allocation Planning Model for Integrated Care and Access Management

The prevailing first-come-first-served approach to outpatient appointment scheduling ignores differing urgency levels, leading to unnecessarily long waits for urgent patients. In data from a partner healthcare organization, we found in some departments that urgent patients were inadvertently waiting longer for an appointment than non-urgent patients. This paper develops a capacity allocation optimization methodology that reserves appointment slots based on urgency in a complicated, integrated care environment where multiple specialties serve multiple types of patients. This optimization reallocates network capacity to limit access delays (indirect waiting times) for initial and downstream appointments differentiated by urgency. We formulate this problem as a queueing network optimization and approximate it via deterministic linear optimization to simultaneously smooth workloads and guarantee access delay targets. In a case study of our industry partner we demonstrate the ability to (1) reduce urgent patient mean access delay by 27% with only a 7% increase in mean access delay for non-urgent patients, and (2) increase throughput by 31% with the same service levels and over.

Stochastic integer programming for multi-disciplinary outpatient clinic planning

Scheduling appointments in a multi-disciplinary clinic is complex, since coordination between disciplines is required. The design of a blueprint schedule for a multi-disciplinary clinic with open access requirements requires an integrated optimization approach, in which all appointment schedules are jointly optimized. As this currently is an open question in the literature, our research is the first to address this problem. This research is motivated by a Dutch hospital, which uses a multi-disciplinary cancer clinic to communicate the diagnosis and to explain the treatment plan to their patients. Furthermore, also regular patients are seen by the clinicians. All involved clinicians therefore require a blueprint schedule, in which multiple patient types can be scheduled. We design these blueprint schedules by optimizing the patient waiting time, clinician idle time, and clinician overtime. As scheduling decisions at multiple time intervals are involved, and patient routing is stochastic, we model this system as a stochastic integer program. The stochastic integer program is adapted for and solved with a sample average approximation approach. Numerical experiments evaluate the performance of the sample average approximation approach. We test the suitability of the approach for the hospital’s problem at hand, compare our results with the current hospital schedules, and present the associated savings. Using this approach, robust blueprint schedules can be found for a multi-disciplinary clinic of the Dutch hospital.

Outpatient appointment scheduling with unpunctual patients

This study examines the design of appointment scheduling policies with considerations of not only the conventional factors, for example, the random consultation time and multiple patient types, but also of a new factor, particularly, patient unpunctuality, that is, one patient may arrive earlier or later than the appointment time. Patient unpunctuality negatively affects the appointment scheduling system, for example, such behaviour, reduces provider productivity and clinical efficiency, increases health care costs, and limits the ability of a clinic to serve its patients population by reducing the clinic’s effective capacity. In this study, while considering patient unpunctuality, we first introduce an analytical model and show the optimality of a fixed-interval policy for a simplified two-patient model. Motivated by the result, we propose an easy-to-implement heuristic policy with a simple structure using a simulation framework to improve the performance of the appointment scheduling system. The simulation result shows that our policy is overwhelmingly preponderant in current practice. We also measure the effect of patient unpunctuality and other factors. Actual data are used to add realism to the input parameters, and practical guidelines are developed for appointment scheduling.

The Impact of Delays on Service Times in the Intensive Care Unit

Mainstream queueing models are frequently employed in modeling healthcare delivery in a number of settings, and they further are used in making operational decisions for the same. The vast majority of these queueing models ignore the effects of delay experienced by a patient awaiting care. However, long delays may have adverse effects on patient outcomes and can potentially lead to a longer length of stay (LOS) when the patient ultimately does receive care. This work sets out to understand these delay issues from an operational perspective. Using data of more than 57,000 emergency department (ED) visits, we use an instrumental variable approach to empirically measure the impact of delays in intensive care unit (ICU) admission, i.e., ED boarding, on the patient’s ICU LOS for multiple patient types. Capturing these empirically observed effects in a queueing model is challenging because the effect introduces potentially long-range correlations in service and interarrival times. We propose a queueing model that incorporates these measured delay effects and characterizes approximations to the expected work in the system when the service time of a job is adversely impacted by the delay experienced by that job. Our approximation demonstrates an effect of system load on work that grows much faster than the traditional 1/(1 − ρ) relationship seen in most queueing systems. As such, it is imperative that the relationship of delays and LOS be better understood by hospital managers so that they can make capacity decisions that prevent even seemingly moderate delays from causing dire operational consequences. This paper was accepted by Yossi Aviv, operations management.

Managing Patient Admissions in a Neurology Ward

We study patient admission policies in a neurology ward where there are multiple types of patients with different medical characteristics. Patients receive specialized care inside the neurology ward and delays in admission to the ward will have negative impact on their health status. The level of this impact varies among patient types and depends on the severity of patients. Patients are also different in terms of arrival rate and length of stay at the ward. The patients normally wait in the emergency department until a ward bed is assigned to them. We formulate this problem as an infinite-horizon average cost dynamic program and propose an efficient approximation scheme to solve large-scale problem instances. The computational results from applying our model to a neurology ward show that dynamic policies generated by our approach can reduce the overall deterioration in patients’ health status compared to several alternative policies. The online appendix is available at https://doi.org/10.1287/opre.2016.1574 .

Applying the best of oncology drug development paradigms to the non-malignant space

With 80-90% of drugs entering the clinic not meeting regulatory approval (a high cost of failure), there is a major need for innovation in the clinical development space. Features of the new era of practice-changing innovation in oncology have included novel clinical trial designs incorporating multiple new molecular entities and/or multiple patient types, patient selection strategies (which allow detection of early signs of efficacy), and use of surrogate endpoints to achieve speedy regulatory approval. Disease areas beyond oncology could benefit from the application of specific aspects of these approaches. Here, we describe several such potential adaptations of the approaches, with scenarios and prerequisites, which could help reduce the costs of, and accelerate, clinical drug development with confidence.

A network flow approach for tactical resource planning in outpatient clinics.

This paper introduces a deterministic model to plan the physician requirements for outpatient clinics to achieve service targets for the appointment lead-times of patients. The Ministry of Health of Singapore has established targets for the median, 95th percentile, and 100th percentile of appointment lead-times for patients, since long appointment postponements are regarded as being unacceptable for health care services. The study is to match the capacity of the healthcare providers to the patient demand for a re-entry system, subject to restrictions on the appointment lead-times for patients. We propose a mixed-integer programming model for planning capacity with the minimization of the maximum required capacity as its objective. In the model we assume a finite planning horizon, deterministic arrivals, multiple types of patients, identical physicians, and dependent demand between types of patients. We solve this model with a Branch and Cut algorithm. We test the model with numerical experiments using real data from the chosen specialty at the outpatient clinic of the studied hospital. The results show the value of the proposed model via a systematic push-pull mechanism in scheduling patients' requests to minimize the objective. The clinic should use one of the appointment lead-time targets to determine the patients' appointment dates. Finally, from the sensitivity analyses we demonstrate that the objective is negatively correlated with first-visit patients' appointment lead-time targets, the discharge rates, and the re-visit patients' mean appointment lead-time; we find a positive correlation between the first-visit patients' mean appointment lead-time and the appointment lead-time targets.

Appointment scheduling of outpatient surgical services in a multistage operating room department

This article addresses the appointment scheduling of outpatient surgeries in a multistage operating room (OR) department with stochastic service times serving multiple patient types. We discuss many challenges, such as the limited availability of multiple resources (e.g., staff, operating rooms, surgeons, and recovery beds), and the compatibility of patient and surgeon types. In addition, availability of surgeons is restricted by time window constraints. Three simulation-based optimization methods have been proposed to minimize the patients’ wait time, patients’ completion time, and number of surgery cancellations. The first method is simulation-based tabu search (STS). It combines discrete-event simulation and tabu search to schedule surgery cases. The second and third methods are integer programming enhanced tabu search (IPETS) and binary programming enhanced tabu search (BPETS). IPETS and BPETS improve on STS by incorporating integer programming and binary programming models, respectively. This article includes a case study of an OR department in a major Canadian hospital. We further expand the actual data obtained in the case study to cover a wide range of parameters in sets of test problems, and provide analysis on the efficiency and effectiveness of the proposed methods in comparison with several scheduling rules. Finally, comments on the applications of the proposed methods are provided.