Mortality modeling and regression with matrix distributions

In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can lead to reasonably accurate and relatively parsimonious models for mortality curves across the entire lifespan. A particular feature of the proposed model framework is that it allows for a more direct interpretation of the implied underlying aging process than some previous approaches. Subsequently, towards applications of the approach for multi-population mortality modeling, we introduce regression via the concept of proportional intensities, which are more flexible than proportional hazard models, and we show that the two classes are asymptotically equivalent. We illustrate how the model parameters can be estimated from data by providing an adapted EM algorithm for which the likelihood increases at each iteration. The practical feasibility and competitiveness of the proposed approach are illustrated for several sets of mortality data

An Analytics Approach To Reducing Hospital Readmission

One of the significant sources of waste in the Unites States health care systems is preventable hospital readmission. About 2.3 million Medicare fee-for-service beneficiaries are re-hospitalized within 30 days after discharge which incurs an annual cost of $17 billion. However, it is reported by the Medicare Payment Advisory Commission that about 75% of such readmissions can and should be avoided because they are the results of factors such as poor planning for follow up care transitions, inadequate communication of discharge instructions, and failure to reconcile and coordinate medications. Hence, reducing unnecessary rehospitalization through care transition and systems engineering principles has attracted policymakers and health organizations as a way to simultaneously improve quality of care and reduce costs. In this dissertation we investigated predictive and prescriptive analytics approaches for discharge planning and hospital readmission problem. Motivated by the gaps in research, we first develop a new readmission metric based on administrative data that can identify potentially avoidable readmissions from all other types of readmission. The approach is promising and uses a comprehensive risk adjustment, Diagnostic Cost Group Hierarchical Condition Category, to assess the clinical relevance between a readmission and its initial hospitalizations. Next, we tackle the difficulties around selecting an appropriate readmission time interval by proposing a generic Continuous Time Markov Chain (CTMC) approach conceptualizing the movements of patients after discharge. We found that cutoff point defining readmission time interval must not depend on the instantaneous risk of readmission but rather it has to be based on quality of inpatient or outpatient care received. We further assert that the government endorsed 30 day time window which has been used for profiling hospitals and public reporting is not appropriate for chronic conditions such as chronic obstructive pulmonary disease. Thus, we propose a special case of the CTMC method and obtain the optimal cut point that best stratifies among inpatient and outpatient care episodes. Third, we proposed a novel tree based prediction method, phase time survival forest (PTSF), for patient risk of readmission that combines good aspects of traditional classification methods and timing based models. The method is simple to implement and can be able to (1) model the effect of partially known information (censored observations) into the risk of readmission, and (2) directly incorporate patient\u27s history of readmission and risk factors changes over time. The latter property is highly favorable especially when repeated measurements of patient factors or recurrent readmissions are likely. The basic idea is quite generic and it works by modifying the traditional replicate based bootstrap samples to account for correlations among repeated records of a subject. We demonstrated the superiority of our model over current solutions with respect to various accuracy and misclassification criteria. Further, to confirm that the high discrimination ability of our proposal is irrespective to overfitting, we performed internal and external validation with 2011-12 Veterans Health Administration data from inpatients hospitalized for heart failure, acute myocardial infarction, pneumonia, or chronic obstructive pulmonary disease in the Mid West facilities. Results indicated improved discrimination power compared to the literature (c statistics greater than 80%) and good calibration. Overall, the current research outlined a successful multifaceted analytics framework that enables medical decision makers to systematically characterize, predict, and reduce avoidable readmissions and contribute to patient care quality improvements

Integrating visualisation into the systems modelling toolkit: Applications to clinical and health process systems

Many areas of modern society, including healthcare, can be thought of as process systems. Such systems can be understood in terms of a sequence of inputs, work activities and outputs which become difficult to understand and control as a result of complexity arising from interactions between components within these system. Such complexity can hamper the ability to make decisions relating to these process systems. Operations Research/Management Science (OR/MS) has responded to this challenge with the development of systems models, which create a representation of the system under investigation that can be used to help make decisions about the process system. OR/MS literature has developed a wide variety of techniques for systems modelling, including computational, statistical and mathematical approaches to assisting decision-making. This suite of methods can be referred to as the OR/MS toolkit for systems modelling. OR/MS practice often involves the use of visualisation to aid undertanding, interpret results from systems modelling, or otherwise assist OR/MS practitioners in working with systems. This widespread use of visualisation has occurred due to its ability to flexibly and intuitively represent large amounts of information. However, there has been little discussion within OR/MS literature on the use of visualisation as a tool for systems modelling. Likewise, there is a lack of explicit knowledge on how visualisation should be applied in an OR/MS context, and a lack of reported, general knowledge on how to integrate visualisation with conventional OR/MS tools. Given that visualisation provides an intuitive means for understanding complex information, this presents an opportunity for OR/MS experts to better model process systems and provide support for decision-makers by making use of visualisation as a tool for systems modelling. This thesis seeks to advance the use of visualisation in systems modelling by addressing these gaps. We provide a systematic review on the use of visualisation within OR/MS literature, and from this synthesise a series of general visualisation principles to guide beneficial visualisation properties, and a series of general visualisation practices which suggest means of following these principles. We then use the results of this synthesis to develop an original Visual Systems Modelling Framework which provides a method for integrating visualisation into the systems modelling toolkit. This framework draws from established OR/MS theory and practice by explicitly setting out a conceptual model describing the system, the intended purpose of modelling the system, and plans for any conventional OR/MS tools which will be used to model the system. It links these aspects of conventional OR/MS methodology to the visualisation principles identified by the systematic literature review. The thesis provides illustrative case studies of this framework in action by applying it in the development of four models for clinical or health process systems. First, we describe several novel contributions to literature on the conventional OR/MS toolkit that were made in the development of these models. These include a novel dissimilarity measure that can be used to compare and group sequences of ordinal data where sequence length can vary, and systematic validation of a method of clustering survival data using Coxian Phase-Type distributions. These contributions are then used in the case studies which follow the Visual Systems Modelling Framework. The first case study is in the context of the care of Traumatic Spinal Cord Injury (TSCI). The care of TSCI involves several healthcare processes working together in unison to treat a patient who may have many different co-existing injuries resulting from the same event which lead to the spinal cord injury. This heterogeneity among patients results in organisational uncertainty regarding the specific care pathways taken by patients, making it almost impossible to make decisions which will improve care processes for this patient group. Before improvements to this system can be made, a greater understanding of the TSCI healthcare process is required. The Visual Systems Modelling Framework is applied in this system to generate new insights and promote discussion about TSCI healthcare processes. The second case study is in the context of investigating the role of neurorehabilitative physiotherapy in the recovery of stroke survivors. There are open questions within clinical literature on stroke rehabilitation regarding what physiotherapy regimens lead to better patient outcomes. In this application, the Visual Systems Modelling Framework is used to allow clinical researchers the ability to identify patterns in and explore the relationships between physiotherapy regimens and patient health, thereby developing an understanding which can improve the care provided in stroke rehabilitation. The third case study is in the same neurorehabilitative system as the second case study. In this application, the Visual Systems Modelling Framework is used to develop a model which predicts patient outcomes based on their received physiotherapy regimen. This assists clinical researchers seeking to identify what physiotherapy regimens are likely to improve patient outcomes. The final case study is in the context of planning an major clinical trial in stroke rehabilitation which uses an adaptive trial design. Adaptive clinical trials use prespecified rules to adjust the behaviour of the trial based on data as it is accrued by the trial. These rules can be used to address ethical concerns regarding giving patients experimental treatments which appear to be ineffective, enforce balancing of important prognostic factors across treatment arms, or any number of other desired features. However, such designs can lead to complex and counter-intuitive behaviour in the trial, requiring both careful planning and understanding of these behaviours. In this application, the Visual Systems Modelling Framework is used to model this clinical trial to assist planning and communicate the behaviours arising from the adaptive trial design. Through these four case studies, this thesis provides illustrations of how the Visual Systems Modelling Framework can be used across multiple systems, each with their own requirements and modelling purpose. This thesis demonstrates how visualisation can be integrated in the OR/MS systems modelling toolkit, and contributes to OR/MS literature by providing a method for applying visualisation as a systems modelling tool

Improving Emergency Department Patient Flow Through Near Real-Time Analytics

ABSTRACT IMPROVING EMERGENCY DEPARTMENT PATIENT FLOW THROUGH NEAR REAL-TIME ANALYTICS This dissertation research investigates opportunities for developing effective decision support models that exploit near real-time (NRT) information to enhance the operational intelligence within hospital Emergency Departments (ED). Approaching from a systems engineering perspective, the study proposes a novel decision support framework for streamlining ED patient flow that employs machine learning, statistical and operations research methods to facilitate its operationalization. ED crowding has become the subject of significant public and academic attention, and it is known to cause a number of adverse outcomes to the patients, ED staff as well as hospital revenues. Despite many efforts to investigate the causes, consequences and interventions for ED overcrowding in the past two decades, scientific knowledge remains limited in regards to strategies and pragmatic approaches that actually improve patient flow in EDs. Motivated by the gaps in research, we develop a near real-time triage decision support system to reduce ED boarding and improve ED patient flow. The proposed system is a novel variant of a newsvendor modeling framework that integrates patient admission probability prediction within a proactive ward-bed reservation system to improve the effectiveness of bed coordination efforts and reduce boarding times for ED patients along with the resulting costs. Specifically, we propose a cost-sensitive bed reservation policy that recommends optimal bed reservation times for patients right during triage. The policy relies on classifiers that estimate the probability that the ED patient will be admitted using the patient information collected and readily available at triage or right after. The policy is cost-sensitive in that it accounts for costs associated with patient admission prediction misclassification as well as costs associated with incorrectly selecting the reservation time. To achieve the objective of this work, we also addressed two secondary objectives: first, development of models to predict the admission likelihood and target admission wards of ED patients; second, development of models to estimate length-of-stay (LOS) of ED patients. For the first secondary objective, we develop an algorithm that incorporates feature selection into a state-of-the-art and powerful probabilistic Bayesian classification method: multi-class relevance vector machine. For the second objective, we investigated the performance of hazard rate models (in particual, the non-parametric Cox proportional hazard model, parametric hazard rate models, as well as artificial neural networks for modeling the hazard rate) to estimate ED LOS by using the information that is available at triage or right after as the covariates in the models. The proposed models are tested using extensive historical data from several U.S. Department of Veterans Affairs Medical Centers (VAMCs) in the Mid-West. The Case Study using historical data from a VAMC demonstrates that applying the proposed framework leads to significant savings associated with reduced boarding times, in particular, for smaller wards with high levels of utilization. For theory, our primary contribution is the development of a cost sensitive ward-bed reservation model that effectively accounts for various costs and uncertainties. This work also contributes to the development of an integrated feature selection method for classification by developing and validating the mathematical derivation for feature selection during mRVM learning. Another contribution stems from investigating how much the ED LOS estimation can be improved by incorporating the information regarding ED orderable item lists. Overall, this work is a successful application of mixed methods of operation research, machine learning and statistics to the important domain of health care system efficiency improvement

Ensemble Risk Model of Emergency Admissions (ERMER)

Introduction About half of hospital readmissions can be avoided with preventive interventions. Developing decision support tools for identification of patients’ emergency readmission risk is an important area of research. Because, it remains unclear how to design features and develop predictive models that can adjust continuously to a fast-changing healthcare system and population characteristics. The objective of this study was to develop a generic ensemble Bayesian risk model of emergency readmission. Methods We produced a decision support tool that predicts risk of emergency readmission using England's Hospital Episode Statistics inpatient database. Firstly, we used a framework to develop an optimal set of features. Then, a combination of Bayes Point Machine (BPM) models for different cohorts was considered to create an optimised ensemble model, which is stronger than the individual generative and non-linear classifications. The developed Ensemble Risk Model of Emergency Admissions (ERMER) was trained and tested using three time-frames: 1999-2004, 2000-05 and 2004-09, each of which includes about 20% of patients in England during the trigger year. Results Comparisons are made for different time-frames, sub-populations, risk cut-offs, risk bands and top risk segments. The precision was 71.6% to 73.9%, the specificity was 88.3% to 91.7% and the sensitivity was 42.1% to 49.2% across different time-frames. Moreover, the Area Under the Curve was 75.9% to 77.1%. Conclusions The decision support tool performed considerably better than the previous modelling approaches, and it was robust and stable with high precision. Moreover, the framework and the Bayesian model allow the model to continuously adjust it to new significant features, different population characteristics and changes in the system

NEW STATISTICAL METHODS TO BETTER LEVERAGE EMERGING HEALTH CARE UTILIZATION DATA

Improving the healthcare system is an important task that is always both socially and individually beneficial, and statistics is one of the useful tools that have been applied in pursuit of this goal. However, limitations on current methods and the introduction of new forms of data have created many new challenges and research opportunities. It is therefore crucial to explore and extend statistical methods to better understand and leverage healthcare utilization data, particularly recent and emerging data in new forms. In this dissertation, we develop and apply various innovative statistical methods to address five specific healthcare issues. First, we successfully develop a novel approach to model the length of hospital stay using mixture distributions through an EM algorithm. Second, we extend a two-state continuous time Markov chain to estimate patient readmission risk at a large academic hospital in the U.S. Third, we study changes in accessibility in emergency departments from 2016 to 2018 among 21 hospitals in Maryland Region III. Fourth, we investigate the impact of the global budget payment model on emergency department accessibility. Lastly, we use a multi-state Markov model to explore cascading events during emergency room crowding, also in Region III of Maryland