Phase-type survival trees and mixed distribution survival trees for clustering patients' hospital length of stay

Clinical investigators, health professionals and managers are often interested in developing criteria for clustering patients into clinically meaningful groups according to their expected length of stay. In this paper, we propose two novel types of survival trees; phase-type survival trees and mixed distribution survival trees, which extend previous work on exponential survival trees. The trees are used to cluster the patients with respect to length of stay where partitioning is based on covariates such as gender, age at the time of admission and primary diagnosis code. Likelihood ratio tests are used to determine optimal partitions. The approach is illustrated using nationwide data available from the English Hospital Episode Statistics (HES) database on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period.peer-reviewe

A Phase-Type Distribution for the Sum of Two Concatenated Markov Processes Application to the Analysis Survival in Bladder Cancer

[EN] Stochastic processes are useful and important for modeling the evolution of processes that take different states over time, a situation frequently found in fields such as medical research and engineering. In a previous paper and within this framework, we developed the sum of two independent phase-type (PH)-distributed variables, each of them being associated with a Markovian process of one absorbing state. In that analysis, we computed the distribution function, and its associated survival function, of the sum of both variables, also PH-distributed. In this work, in one more step, we have developed a first approximation of that distribution function in order to avoid the calculation of an inverse matrix for the possibility of a bad conditioning of the matrix, involved in the expression of the distribution function in the previous paper. Next, in a second step, we improve this result, giving a second, more accurate approximation. Two numerical applications, one with simulated data and the other one with bladder cancer data, are used to illustrate the two proposed approaches to the distribution function. We compare and argue the accuracy and precision of each one of them by means of their error bound and the application to real data of bladder cancer.This paper has been supported by the Generalitat Valenciana grant AICO/2020/114.García Mora, MB.; Santamaria Navarro, C.; Rubio Navarro, G. (2020). A Phase-Type Distribution for the Sum of Two Concatenated Markov Processes Application to the Analysis Survival in Bladder Cancer. Mathematics. 8(12):1-15. https://doi.org/10.3390/math8122099S115812Rodríguez, J., Lillo, R. E., & Ramírez-Cobo, P. (2015). Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process. Reliability Engineering & System Safety, 134, 126-133. doi:10.1016/j.ress.2014.10.020García‐Mora, B., Santamaría, C., & Rubio, G. (2020). Markovian modeling for dependent interrecurrence times in bladder cancer. Mathematical Methods in the Applied Sciences, 43(14), 8302-8310. doi:10.1002/mma.6593Montoro-Cazorla, D., & Pérez-Ocón, R. (2014). Matrix stochastic analysis of the maintainability of a machine under shocks. Reliability Engineering & System Safety, 121, 11-17. doi:10.1016/j.ress.2013.07.002Fackrell, M. (2008). Modelling healthcare systems with phase-type distributions. Health Care Management Science, 12(1), 11-26. doi:10.1007/s10729-008-9070-yGarg, L., McClean, S., Meenan, B. J., & Millard, P. (2011). Phase-Type Survival Trees and Mixed Distribution Survival Trees for Clustering Patients’ Hospital Length of Stay. Informatica, 22(1), 57-72. doi:10.15388/informatica.2011.314Marshall, A. H., & McClean, S. I. (2003). Conditional phase-type distributions for modelling patient length of stay in hospital. International Transactions in Operational Research, 10(6), 565-576. doi:10.1111/1475-3995.00428Marshall, A. H., & McClean, S. I. (2004). Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital. Health Care Management Science, 7(4), 285-289. doi:10.1007/s10729-004-7537-zFackrell, M. (2012). A semi-infinite programming approach to identifying matrix-exponential distributions. International Journal of Systems Science, 43(9), 1623-1631. doi:10.1080/00207721.2010.549582García-Mora, B., Santamaría, C., Rubio, G., & Pontones, J. L. (2013). Computing survival functions of the sum of two independent Markov processes: an application to bladder carcinoma treatment. International Journal of Computer Mathematics, 91(2), 209-220. doi:10.1080/00207160.2013.765560Kenney, C., & Laub, A. J. (1989). Condition Estimates for Matrix Functions. SIAM Journal on Matrix Analysis and Applications, 10(2), 191-209. doi:10.1137/0610014Jackson, C. H. (2011). Multi-State Models for Panel Data: ThemsmPackage forR. Journal of Statistical Software, 38(8). doi:10.18637/jss.v038.i08Mullin, L., & Raynolds, J. (2014). Scalable, Portable, Verifiable Kronecker Products on Multi-scale Computers. Studies in Computational Intelligence, 111-129. doi:10.1007/978-3-319-04280-0_1

Costing hospital resources for stroke patients using phase-type models

Optimising resources in healthcare facilities is essential for departments to cope with the growing population’s requirements. An aspect of such performance modelling involves investigating length of stay, which is a key performance indicator. Stroke disease costs the United Kingdom economy seven billion pounds a year and stroke patients are known to occupy long periods of time in acute and long term beds in hospital as well as requiring support from social services. This may be viewed as an inefficient use of resources. Thrombolysis is a therapy which uses a clot-dispersing drug which is known to decrease the institutionalisation of eligible stroke patients if administered 3 h after incident but it is costly to administer to patients. In this paper we model the cost of treating stroke patients within a healthcare facility using a mixture of Coxian phase type model with multiple absorbing states. We also discuss the potential benefits of increasing the usage of thrombolysis and if these benefits balance the expense of administering the drug.peer-reviewe

Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit

The problem of hospital patients’ delayed discharge or ‘bed blocking’ has long been a challenge for healthcare managers and policymakers. It negatively affects the hospital performance metrics and has other severe consequences for the healthcare system, such as affecting patients’ health. In our previous work, we proposed the phase-type survival tree (PHTST)-based analysis to cluster patients into clinically meaningful patient groups and an extension of this approach to examine the relationship between the length of stay in hospitals and the destination on discharge. This paper describes how PHTST-based clustering can be used for modelling delayed discharge and its effects in a stroke care unit, especially the extra beds required, additional cost, and bed blocking. The PHTST length of stay distribution of each group of patients (each PHTST node) is modelled separately as a finite state continuous-time Markov chain using Coxian-phase-type distributions. Delayed discharge patients waiting for discharge are modelled as the Markov chain, called the ‘blocking state’ in a special state. We can use the model to recognise the association between demographic factors and discharge delays and their effects and identify groups of patients who require attention to resolve the most common delays and prevent them from happening again. The approach is illustrated using five years of retrospective data of patients admitted to the Belfast City Hospital with a stroke diagnosis

Costing mixed coxian phase-type systems in a given time interval

Previously we have introduced a modelling framework to classify individuals in Mixed Coxian Phase-type Systems. We here add costs and obtain results for moments of total costs in (0, t], for an individual, and a cohort arriving at time zero. Based on data from the Belfast City Hospital Stroke Unit we use the overall modelling framework to obtain results for total cost in a given time interval to facilitate planners who have limited time horizons for budget planning.peer-reviewe

Quantifying cognitive and mortality outcomes in older patients following acute illness using epidemiological and machine learning approaches

Introduction: Cognitive and functional decompensation during acute illness in older people are poorly understood. It remains unclear how delirium, an acute confusional state reflective of cognitive decompensation, is contextualised by baseline premorbid cognition and relates to long-term adverse outcomes. High-dimensional machine learning offers a novel, feasible and enticing approach for stratifying acute illness in older people, improving treatment consistency while optimising future research design. Methods: Longitudinal associations were analysed from the Delirium and Population Health Informatics Cohort (DELPHIC) study, a prospective cohort ≥70 years resident in Camden, with cognitive and functional ascertainment at baseline and 2-year follow-up, and daily assessments during incident hospitalisation. Second, using routine clinical data from UCLH, I constructed an extreme gradient-boosted trees predicting 600-day mortality for unselected acute admissions of oldest-old patients with mechanistic inferences. Third, hierarchical agglomerative clustering was performed to demonstrate structure within DELPHIC participants, with predictive implications for survival and length of stay. Results: i. Delirium is associated with increased rates of cognitive decline and mortality risk, in a dose-dependent manner, with an interaction between baseline cognition and delirium exposure. Those with highest delirium exposure but also best premorbid cognition have the “most to lose”. ii. High-dimensional multimodal machine learning models can predict mortality in oldest-old populations with 0.874 accuracy. The anterior cingulate and angular gyri, and extracranial soft tissue, are the highest contributory intracranial and extracranial features respectively. iii. Clinically useful acute illness subtypes in older people can be described using longitudinal clinical, functional, and biochemical features. Conclusions: Interactions between baseline cognition and delirium exposure during acute illness in older patients result in divergent long-term adverse outcomes. Supervised machine learning can robustly predict mortality in in oldest-old patients, producing a valuable prognostication tool using routinely collected data, ready for clinical deployment. Preliminary findings suggest possible discernible subtypes within acute illness in older people

A systematic review of the prediction of hospital length of stay:Towards a unified framework

Hospital length of stay of patients is a crucial factor for the effective planning and management of hospital resources. There is considerable interest in predicting the LoS of patients in order to improve patient care, control hospital costs and increase service efficiency. This paper presents an extensive review of the literature, examining the approaches employed for the prediction of LoS in terms of their merits and shortcomings. In order to address some of these problems, a unified framework is proposed to better generalise the approaches that are being used to predict length of stay. This includes the investigation of the types of routinely collected data used in the problem as well as recommendations to ensure robust and meaningful knowledge modelling. This unified common framework enables the direct comparison of results between length of stay prediction approaches and will ensure that such approaches can be used across several hospital environments. A literature search was conducted in PubMed, Google Scholar and Web of Science from 1970 until 2019 to identify LoS surveys which review the literature. 32 Surveys were identified, from these 32 surveys, 220 papers were manually identified to be relevant to LoS prediction. After removing duplicates, and exploring the reference list of studies included for review, 93 studies remained. Despite the continuing efforts to predict and reduce the LoS of patients, current research in this domain remains ad-hoc; as such, the model tuning and data preprocessing steps are too specific and result in a large proportion of the current prediction mechanisms being restricted to the hospital that they were employed in. Adopting a unified framework for the prediction of LoS could yield a more reliable estimate of the LoS as a unified framework enables the direct comparison of length of stay methods. Additional research is also required to explore novel methods such as fuzzy systems which could build upon the success of current models as well as further exploration of black-box approaches and model interpretability

Statistical analysis and data mining of Medicare patients with diabetes.

The purpose of this dissertation is to find ways to decrease Medicare costs and to study health outcomes of diabetes patients as well as to investigate the influence of Medicare, part D since its introduction in 2006 using the CMS CCW (Chronic Condition Data Warehouse) Data and the MEPS (Medical Expenditure Panel Survey) data. In this dissertation, we introduce pattern recognition analysis into the study of medical characteristics and demographic characteristics of the inpatients who have a higher readmission risk. We also broaden the cost-effectiveness analysis by including medical resources usage when investigating the effects of Medicare, part D. In addition, we apply several statistical linear models such as the generalized linear model and data mining techniques such as the neural network model to study the costs and outcomes of both inpatients and outpatients with diabetes in Medicare. Moreover, some descriptive statistics such as kernel density estimation and survival analysis are also employed. One important conclusion from these analyses is that only diseases and procedures, rather than age are key factors to inpatients\u27 mortality rate. Another important discovery is that at the influence of Medicare part 0, insulin is the most efficient oral anti-diabetes drug treatment and that the drug usage in 2006 is not as stable as that in 2005. We also find that the patients who are discharged to home or hospice are more likely to re-enter the hospital after discharge within 30 days. Two - way interaction effect analysis demonstrates that diabetes complications interact with each other, which makes healthcare costs and health outcomes different between a case with one complication and a case with two complications. Accordingly, we propose some useful suggestions. For instance, as for how to decrease Medicare payments for outpatients with diabetes, we suggest that the patients should often monitor their blood glucose level. We also recommend that inpatients with diabetes should pay more attention to their kidney disease, and use prevention to avoid such diseases to decrease the costs

Acute myocardial infarction patient data to assess healthcare utilization and treatments.

The goal of this study is to use a data mining framework to assess the three main treatments for acute myocardial infarction: thrombolytic therapy, percutaneous coronary intervention (percutaneous angioplasty), and coronary artery bypass surgery. The need for a data mining framework in this study arises because of the use of real world data rather than highly clean and homogenous data found in most clinical trials and epidemiological studies. The assessment is based on determining a profile of patients undergoing an episode of acute myocardial infarction, determine resource utilization by treatment, and creating a model that predicts each treatment resource utilization and cost. Text Mining is used to find a subset of input attributes that characterize subjects who undergo the different treatments for acute myocardial infarction as well as distinct resource utilization profiles. Classical statistical methods are used to evaluate the results of text clustering. The features selected by supervised learning are used to build predictive models for resource utilization and are compared with those features selected by traditional statistical methods for a predictive model with the same outcome. Sequence analysis is used to determine the sequence of treatment of acute myocardial infarction. The resulting sequence is used to construct a probability tree that defines the basis for cost effectiveness analysis that compares acute myocardial infarction treatments. To determine effectiveness, survival analysis methodology is implemented to assess the occurrence of death during the hospitalization, the likelihood of a repeated episode of acute myocardial infarction, and the length of time between reoccurrence of an episode of acute myocardial infarction or the occurrence of death. The complexity of this study was mainly based on the data source used: administrative data from insurance claims. Such data source was not originally designed for the study of health outcomes or health resource utilization. However, by transforming record tables from many-to-many relations to one-to-one relations, they became useful in tracking the evolution of disease and disease outcomes. Also, by transforming tables from a wide-format to a long-format, the records became analyzable by many data mining algorithms. Moreover, this study contributed to field of applied mathematics and public health by implementing a sequence analysis on consecutive procedures to determine the sequence of events that describe the evolution of a hospitalization for acute myocardial infarction. This same data transformation and algorithm can be used in the study of rare diseases whose evolution is not well understood

AliClu - Temporal sequence alignment for clustering longitudinal clinical data

The authors acknowledge funding the Portuguese Foundation for Science and Technology (Fundação para a Ciência e a Tecnologia - FCT) under contracts INESC-ID (UID/CEC/50021/2019) and IT (UID/EEA/50008/2019), projects PREDICT (PTDC/CCI-CIF/29877/2017), PERSEIDS (PTDC/EMS-SIS/0642/2014) and NEUROCLINOMICS2 (PTDC/EEI-SII/1937/2014). The funders had no role in the design of the study, collection, analysis and interpretation of data, or writing the manuscript.BACKGROUND: Patient stratification is a critical task in clinical decision making since it can allow physicians to choose treatments in a personalized way. Given the increasing availability of electronic medical records (EMRs) with longitudinal data, one crucial problem is how to efficiently cluster the patients based on the temporal information from medical appointments. In this work, we propose applying the Temporal Needleman-Wunsch (TNW) algorithm to align discrete sequences with the transition time information between symbols. These symbols may correspond to a patient's current therapy, their overall health status, or any other discrete state. The transition time information represents the duration of each of those states. The obtained TNW pairwise scores are then used to perform hierarchical clustering. To find the best number of clusters and assess their stability, a resampling technique is applied. RESULTS: We propose the AliClu, a novel tool for clustering temporal clinical data based on the TNW algorithm coupled with clustering validity assessments through bootstrapping. The AliClu was applied for the analysis of the rheumatoid arthritis EMRs obtained from the Portuguese database of rheumatologic patient visits (Reuma.pt). In particular, the AliClu was used for the analysis of therapy switches, which were coded as letters corresponding to biologic drugs and included their durations before each change occurred. The obtained optimized clusters allow one to stratify the patients based on their temporal therapy profiles and to support the identification of common features for those groups. CONCLUSIONS: The AliClu is a promising computational strategy to analyse longitudinal patient data by providing validated clusters and by unravelling the patterns that exist in clinical outcomes. Patient stratification is performed in an automatic or semi-automatic way, allowing one to tune the alignment, clustering, and validation parameters. The AliClu is freely available at https://github.com/sysbiomed/AliClu.publishersversionpublishe