Analytics approaches to improve strategic, operational, and clinical decision-making in healthcare
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Healthcare and medicine both contain many complex and critical biological, clinical, and operational processes that cope with uncertainty, and require timely and effective decisions. Analytical methods such as mathematical modeling and computational optimization, offer a useful framework to study the complex problems that are observed in healthcare systems and medical processes. This thesis presents three important and complex medical decision-making problems Çağlar Çağlayan studied during his doctoral studies, describes the analytical methods he utilized and developed, and discusses the methodological and numerical findings and contributions of his work. The works presented in this thesis make contributions to three research topics on clinical decision-making under uncertainty: (i) the development of an optimal multi-modality screening program for women at high-risk for breast cancer, (ii) the determination of optimal physician staffing levels in emergency department under time-varying arrivals, and (iii) the study of the clinical course of follicular and diffuse large B cell lymphomas with the goal of improving treatment outcomes. In Chapter 1, we study a multi-modality breast cancer screening problem for high-risk population and identify optimal and cost-effective population screening strategies based on the imaging technologies that are in widespread use. Women with certain risk factors such as BRCA 1/2 gene mutations and family history of breast or ovarian cancer are at significantly higher risk for breast cancer. For these high-risk women, the existing guidelines recommend intensified screening starting at an early age, where the use of ultrasound (US) and magnetic resonance imaging (MRI) might address some of the limitations of mammography, the standard screening modality for average-risk women. Yet, the cost and false positive rates of MRI, and the operator dependency of US raise concerns. Currently, there is no consensus on the optimal use of these technologies in conjunction with, or instead of, mammography in high-risk women. To study this problem, we develop a Markov model to capture the disease incidence and progression in high-risk women, and formulate a mixed integer linear program to identify the optimal structured strategies that are practical for implementation. We further study the structure of the optimal strategies, and establish the conditions under which a strategy with more frequent but less sensitive screens yields higher health benefits than a strategy with more sensitive but less frequent screens. Our results show that (1) for young women, annual screening with ultrasound, is affordable with moderate budgets, and optimal over a wide range of budget levels despite its high operator dependency, (2) for middle-aged women, annual mammography screening is robustly optimal and cost-effective, and (3) the use of MRI, alone or combined with mammogram, leads to outcomes that are not cost-effective. In Chapter 2, we study a physician staffing and an associated patient routing problem in emergency rooms (ERs) coping with time-varying demand. ERs are complex healthcare delivery systems, characterized by time-varying unscheduled arrivals, medium-to-long service times, high patient volumes, multiple patient classes, and multiple treatment stages. In such a complex system, optimizing the staffing levels of physicians, the most critical resources in ERs, is a major challenge. In this work, we study a staffing problem for ER physicians, and propose a new staffing algorithm that determines the optimum staffing levels stabilizing differentiated tail probability of delay (TPoD) type service targets. Taking a queuing theory approach, we develop a practical and intuitive multi-class multi-stage queuing network describing the ER care delivery as sequences of treatments and order bundles (i.e., groups of diagnostic medical processes). Employing this model, we capture time-varying patient flow in the ER and estimate its load on treatment stations, served by physicians. Treatment queues operate in efficiency-driven regime but experience negligible abandonment as abandonments nearly always occur at earlier stages of the ER care. This observation motivates our proposed new staffing algorithm, which translates the offered load into staffing decisions for efficiency driven queues with perfectly patient customers and TPoD type targets. We analytically show the asymptotic effectiveness of our staffing algorithm for M/M/s queues that operate in efficiency-driven mode. Then, we demonstrate its robustness via realistic and data-driven simulation experiments in various time-varying ER settings, considering non-homogeneous Poisson arrivals, multiple patient classes, multi-stage service, and centralized (pooled) (physicians) under several practical routing rules. Our results show that (1) our proposed staffing approach is effective and robust for optimizing the ER physician staffing levels in various ER settings, and (2) as the service complexity of an ER increases, the use of dynamic rules, using the current system state for routing decisions, and hybrid policies, combining pre-determined static routing rules with dynamic ones, become necessary to stabilize TPoD targets. In Chapter 3, we study the clinical course of two types of lymph node cancers, follicular lymphoma (FL) and diffuse large B cell lymphoma (DLBCL). These cancers have different characteristics, where DLBCL is aggressive and FL is recurrent, and have multiple clinical intermediate- or end-points such as the sequence of treatments or cause-specific death. Accordingly, we develop two different continuous-time, multi-state survival analysis models to investigate the clinical course of these diseases following initial treatment with the goal of improving treatment outcomes. We utilize Cox proportional hazards models to specify the impact of prognostic factors on overall survival and cause-specific deaths, and the Aalen-Johansen estimator to project the course of DLBCL over time. In particular, employing the multi-state FL model, we investigate the clinical course of FL under first, second and third line therapies for high-risk patients to assess the effectiveness of various treatment sequences. Our analysis shows that single R-CHOP therapy in any line of treatment improves overall survival for high-risk patients, achieving the most favorable outcome when provided as first-line therapy, but its multiple use for first- and second-line might lead to adverse outcomes. Using the DLBCL model, we examine the role of clinical and socio-demographic factors on DLBCL-associated mortality in the elderly population and identify a cutoff point to stop monitoring DLBCL patients receiving the standard R- CHOP therapy. Utilizing a large population-based dataset, our analysis (1) identifies age, sex, and Charlson comorbidity index as risk factors for DLBCL-specific and other causes of death, and (2) confirms a 5-year cure point for older patients receiving R-CHOP therapy, suggesting to transition survivorship surveillance plans from a focus on lymphoma recurrence-related deaths to non-cancer risks at five years after treatment. In Chapter 4, we summarize our studies, list our contributions, and conclude the thesis.